Computational Modeling of Multilevel Organisational Learning and Its Control Using Self-modeling Network Models 9783031287343, 9783031287350

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Studies in Systems, Decision and Control 468

Gülay Canbaloğlu  Jan Treur  Anna Wiewiora Editors

Computational Modeling of Multilevel Organisational Learning and Its Control Using Self-modeling Network Models

Studies in Systems, Decision and Control Volume 468

Series Editor Janusz Kacprzyk, Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

The series “Studies in Systems, Decision and Control” (SSDC) covers both new developments and advances, as well as the state of the art, in the various areas of broadly perceived systems, decision making and control–quickly, up to date and with a high quality. The intent is to cover the theory, applications, and perspectives on the state of the art and future developments relevant to systems, decision making, control, complex processes and related areas, as embedded in the fields of engineering, computer science, physics, economics, social and life sciences, as well as the paradigms and methodologies behind them. The series contains monographs, textbooks, lecture notes and edited volumes in systems, decision making and control spanning the areas of Cyber-Physical Systems, Autonomous Systems, Sensor Networks, Control Systems, Energy Systems, Automotive Systems, Biological Systems, Vehicular Networking and Connected Vehicles, Aerospace Systems, Automation, Manufacturing, Smart Grids, Nonlinear Systems, Power Systems, Robotics, Social Systems, Economic Systems and other. Of particular value to both the contributors and the readership are the short publication timeframe and the worldwide distribution and exposure which enable both a wide and rapid dissemination of research output. Indexed by SCOPUS, DBLP, WTI Frankfurt eG, zbMATH, SCImago. All books published in the series are submitted for consideration in Web of Science.

Gülay Canbalo˘glu · Jan Treur · Anna Wiewiora Editors

Computational Modeling of Multilevel Organisational Learning and Its Control Using Self-modeling Network Models

Editors Gülay Canbalo˘glu Social AI Group, Department of Computer Science Vrije Universiteit Amsterdam Amsterdam, The Netherlands

Jan Treur Social AI Group, Department of Computer Science Vrije Universiteit Amsterdam Amsterdam, The Netherlands

Anna Wiewiora Faculty of Business and Law Queensland University of Technology Brisbane, QLD, Australia

ISSN 2198-4182 ISSN 2198-4190 (electronic) Studies in Systems, Decision and Control ISBN 978-3-031-28734-3 ISBN 978-3-031-28735-0 (eBook) https://doi.org/10.1007/978-3-031-28735-0 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Preface

Learning within an organisation is a complex phenomenon that occurs across different levels, crosses multiple pathways and uses a variety of mechanisms. This can include individual learning, learning through interactions between individuals, learning within and from teams, feed forward organisational learning from individuals to teams or from teams to the organisation, and feedback organisational learning from the organisation to teams or from teams to individuals. There is no single unique way of learning, as usually similar learning results can be achieved through different pathways or learning flows. Learning outcomes may show major differences depending on which learning mechanisms and learning pathways are deployed to stimulate learning flows. Organisational learning also depends on various contextual factors, such as the characteristics of the individuals in the organisation, type of organisational culture and leadership that (may) exert some forms of control over the learning flows. These multilevel organisational learning processes function as a complex adaptive and dynamic system, partly functioning with some form of control. Although there is much literature on organisational learning, computational formalisation and simulation has not been well addressed, which may not be a surprise, given the complexity of the learning processes as sketched above. Computational simulations are useful to determine the best possible learning flows by uncovering avenues via which learning between the levels can be most effective. By simulating learning flows, it can also be explored how learning flows are affected by changing learning mechanisms and adjusting organisational and environmental context factors. Computational modeling can be used to model various learning scenarios and test the influence of various factors on the learning outcomes, which were previously uncovered by using traditional exploratory research methods, such as case studies or interviews. This can make it a very useful practical tool to predict the most effective learning pathways and ultimately achieve the desired organisational outcomes. By using computational simulations, organisations can explore and test the effectiveness of new options for learning mechanisms and flows, without the need to first invest and implement costly and untested changes.

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Despite these clear benefits, in management studies, computational modeling has had a very slow uptake. This may be attributed to the complexity of multilevel organisational learning dynamics as well as the unique methodological approach of computational modeling, which is outside the common methods used in management research. Multilevel organisational learning indeed is a complex phenomenon, affected by a range of mechanisms including culture, leadership, social networks, structure, just to name a few. It also depends on the contextual factors, such as the internal and external environment of the organisation, which adds to the complexity of the setting within which multilevel learning occurs. The many organisational variables pose a serious challenge to using computational modeling. Management scholars tend to fear that the computational model can provide only a partial representation of reality, ignoring certain salient characteristics. Computational modeling is still considered outside of the management realm and is considered to require much time and investment to learn the relevant tools and methods, hence many management scholars may be reluctant to use it. In this book, we explain the utility and application of computational modeling to study multilevel organisational learning dynamics. This book can be used by management scholars as an introduction to computational modeling in studying complex management systems, as well as by data scientists and software engineers to demonstrate how computational modeling can be applied in examining real world scenarios. The presented approach captured in this book was mainly developed within 2021 and 2022. A start was made during the summer of 2021 when Gülay Canbalo˘glu from Koç University Istanbul visited Jan Treur’s Lab at Vrije Universiteit Amsterdam for a three-months internship based on an Erasmus grant. Soon after arrival she strongly preferred to work on the much more challenging topic of computational modeling of organisational learning instead of the less challenging one on mental models originally proposed. The basis for Part III and Part IV of this book was developed during that internship. From September 2021 on, a multidisciplinary collaboration with Anna Wiewiora from the School of Management, Queensland University of Technology, Brisbane was established and based on this collaboration the work has further developed to cover more realistic case studies involving for example organisational culture and leadership. This can be found in Part V and Part VI. Moreover, in Part VII the approach has been deepened by addressing further mathematical analysis of the computational approach. To address the challenges sketched, there was at least one fortunate circumstance. In recent years a new computational modeling approach was developed within AI and Network Science based on self-modeling (causal) networks (also referred to by network reification) and described in detail in the 2020 Springer Nature book ‘Network-Oriented Modeling for Adaptive Networks’ by Jan Treur. Moreover, in the 2022 Springer Nature book Mental Models and their Dynamics, Adaptation and Control edited by Jan Treur and Laila van Ments it was shown in detail how this modeling approach can be used to obtain a three-level architecture to model dynamics, adaptation, and control in the context of complex (mental model) learning processes. See Part II for more details on these approaches. The current book shows how the self-modeling network modeling approach has turned out very

Preface

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helpful to address computational modeling of organisational learning flows and their control. We hope that this book can also serve as an exemplar on how to bridge distinct research areas and use multidisciplinary research to develop novel research contributions. The material covered in the book has been presented in a variety of conferences in 2021 and 2022: CoMeSySo’21, BICA*AI’21, COMPLEXNETWORKS’21, ICICT’22, ICCCI’22, InCITe’22, AHFE’22, BICA*AI’22, USERN’22, COMPLEXNETWORKS’22 and in the journals Cognitive Systems Research and Journal of Information and Telecommunication. Moreover, it has been presented via Keynote Speeches in the conferences MLIS’21, ArtIntel’22, JCRAI’22, and SSPHE’22. The editors want to thank all others who have contributed to chapters in this book: Peter Roelofsma, Sam Kuilboer, Wesley Sieraad, Laila Van Ments, Debby Bouma, Natalie Samhan, Wioleta Kucharska, Lars Rass. Amsterdam, The Netherlands Amsterdam, The Netherlands Brisbane, Australia January 2023

Gülay Canbalo˘glu Jan Treur Anna Wiewiora

Contents

Part I 1

Introduction: Multilevel Organisational Learning and its Computational Analysis and Simulation

On Computational Analysis and Simulation for Multilevel Organisational Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gülay Canbalo˘glu, Jan Treur, and Anna Wiewiora

Part II

Background Knowledge

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Multilevel Organisational Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Anna Wiewiora

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Modeling Dynamics, Adaptivity and Control by Self-modeling Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jan Treur

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Modeling Mental Models: Their Use, Adaptation and Control . . . . . Gülay Canbalo˘glu and Jan Treur

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Part III Overall Computational Network Models of Organisational Learning 5

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From Conceptual to Computational Mechanisms for Multilevel Organisational Learning . . . . . . . . . . . . . . . . . . . . . . . . . . Gülay Canbalo˘glu, Jan Treur, and Anna Wiewiora

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Using Self-modeling Networks to Model Organisational Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gülay Canbalo˘glu, Jan Treur, and Peter H. M. P. Roelofsma

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A Controlled Adaptive Self-modeling Network Model of Multilevel Organisational Learning for Individuals, Teams or Projects, and Organisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 Gülay Canbalo˘glu, Jan Treur, and Peter H. M. P. Roelofsma

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Organisational Learning and Usage of Mental Models for a Team of Match Officials: A Second-Order Adaptive Network Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 Sam Kuilboer, Wesley Sieraad, Gülay Canbalo˘glu, Laila van Ments, and Jan Treur

Part IV Approaches to Aggregation in the Formation of Shared Mental Models in Organisational Learning 9

Heuristic Context-Sensitive Control of Mental Model Aggregation for Multilevel Organisational Learning . . . . . . . . . . . . . . 185 Gülay Canbalo˘glu and Jan Treur

10 Adaptive Mental Model Aggregation in Organisational Learning Using Boolean Propositions of Context Factors . . . . . . . . . . 217 Gülay Canbalo˘glu and Jan Treur Part V

Computational Analysis of the Role of Leadership in Real-World Scenarios for Multilevel Organisational Learning

11 Computational Analysis of the Role of Leadership Style for Its Context-Sensitive Control over Multilevel Organisational Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253 Gülay Canbalo˘glu, Jan Treur, and Anna Wiewiora 12 Computational Analysis of a Real-World Scenario of Organisational Learning for a Project Management Organisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289 Gülay Canbalo˘glu, Jan Treur, and Anna Wiewiora 13 Computational Analysis of the Influence of Leadership and Communication on Learning Within an Organisation . . . . . . . . 327 Debby Bouma, Gülay Canbalo˘glu, Jan Treur, and Anna Wiewiora Part VI

Computational Analysis of the Role of Organisational Culture for Multilevel Organisational Learning

14 Computational Simulation of the Effects of Different Culture Types and Leader Qualities on Mistake Handling and Organisational Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363 Natalie Samhan, Jan Treur, Wioleta Kucharska, and Anna Wiewiora 15 Computational Analysis of Transformational Organisational Change with Focus on Organisational Culture and Organisational Learning: An Adaptive Dynamical Systems Modeling Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 409 Lars Rass, Jan Treur, Wioleta Kucharska, and Anna Wiewiora

Contents

Part VII

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Mathematical Analysis for Network Models and Organisation Learning

16 Modeling and Analysis of Adaptive Dynamical Systems via Their Canonical Self-modeling Network Representation . . . . . . . 455 Jan Treur 17 Equilibrium Analysis for Multilevel Organisational Learning Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473 Gülay Canbalo˘glu and Jan Treur Part VIII Finalising 18 Discussion: Perspectives on Computational Modeling of Multilevel Organisational Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . 505 Gülay Canbalo˘glu, Jan Treur, and Anna Wiewiora Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513

Part I

Introduction: Multilevel Organisational Learning and its Computational Analysis and Simulation

This part presents an introduction and overview for this volume.

Chapter 1

On Computational Analysis and Simulation for Multilevel Organisational Learning Gülay Canbalo˘glu, Jan Treur, and Anna Wiewiora

Abstract As organisational learning concerns highly dynamic, multilevel and nonlinear processes involving several contextual factors, it is far from trivial how computational analysis and simulation can be developed in a systematic and transparent manner for it. This chapter serves as a brief introduction of the many challenges to be addressed for such an endavour. Moreover, it provides a global overview of how organisational learning challenges were addressed based on a multilevel adaptive dynamical systems modeled as self-modeling networks. Finally, an overview is given of how all this was brought together in the different parts and chapters of this volume. Keywords Organisational learning · Computational analysis · Simulation · Adaptive dynamical systems · Self-modeling networks

1.1 Introduction Organisations provide a rich context in which learning takes place. Organisations come in many forms and shapes. Almost every step of technological and scientific inventions, medical improvements, sociological progress, policy changes take

G. Canbalo˘glu · J. Treur (B) Social AI Group, Department of Computer Science, Vrije Universiteit Amsterdam, Amsterdam, Netherlands e-mail: [email protected] G. Canbalo˘glu e-mail: [email protected] A. Wiewiora School of Management, QUT Business School, Queensland University of Technology, Brisbane, Australia e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 G. Canbalo˘glu et al. (eds.), Computational Modeling of Multilevel Organisational Learning and Its Control Using Self-modeling Network Models, Studies in Systems, Decision and Control 468, https://doi.org/10.1007/978-3-031-28735-0_1

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place within organisations. Small family businesses, technology companies, hospitals, start-ups, research centers, scientific communities, parliaments and even governments are different types of organisations where the learning processes take place. Families, for instance, are the first ‘small-scale’ organisations that we fall into just after birth. These small organisations can form our main character and even our learning style. The behavioral and relational dynamics of our families play an essential role in our learning processes. Then, schools can also be considered as organisations where natural learning takes place and where the seeds of expected future development are planted. That’s why, to analyze and improve the quality and sustainability of organisational learning in schools deserve great importance and attention. Thus, we, humans, as social beings, are almost always a part of an organisation involved in learning and this is how we exist. Learning within organiaations occurs on different levels. The socio-cognitive perspective on learning (Kim 1993) argues that learning initiates within individuals who adjust their mental models when they are exposed to new experiences or process new information. Individuals, by sharing their mental models with others via discussions or join problem solving, transfer that learning to other individuals and groups. Once that learning is institutionalised or becomes embedded in organisational routines, it becomes collective. Organizational learning is more than just a collection of individual learnings, and can remain within the organisation, stored in systems, manuals, and policies, even after individuals leave. Organisational learning is a dynamic, multilevel and non-linear process involving individuals and independent of individuals. It is dynamic because it involves people, it is multilevel because it can also occur on a team or organisational level, and it is non-linear because it has multiple feedback mechanisms which allows individuals to learn from the organisation and the organisation to learn from individuals; see also Fig. 1.1. Organisational learning can be influenced by organisational culture, structure, organisational politics, and leaders who are powerful individuals and who can promote, but also restrict the learning process. However, learning takes place regardless of the degree of ideality of the required environment. Learning is an essential part of individual and organizational survival and has been intensively studied in management and organisational studies, for example, in Argyris and Schön (1978), Bogenrieder (2002), Crossan Lane and White (1999), Kim (1993), McShane and Glinow (2010), Stelmaszczyk (2016), Wiewiora et al. (2019). This book (Canbalo˘glu et al. 2023d ) explores and examines organisational learning processes and various contextual aspects influencing that learning, such as organisational culture, leadership, and other contextual elements. Transfers between individual and organisational learning are key points of understanding and directing the learning process of organisations as put forward in Kim (1993), which is one of the most influential papers on organisational learning with around 5000 citations (5062 in Google Scholar dd. April 26, 2023). The following quote from Kim (1993) briefly sketches this perspective: Organizational learning is dependent on individuals improving their mental models; making those mental models explicit is crucial to developing new shared mental models. This process allows organizational learning to be independent of any specific individual. Why put so much

1 On Computational Analysis and Simulation for Multilevel … Fig. 1.1 Multilevel organisational learning: multiple levels and nested cycles (with depth 3)

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ORGANISATION

TEAMS or PROJECTS

Feedback learning

Feed forward learning

Learning within and between teams or projects

Learning within and between individuals

INDIVIDUALS

emphasis on mental models? Because the mental models in individuals’ heads are where a vast majority of an organization’s knowledge (both know-how and know-why) lies. (Kim 1993), p. 44

Multilevel organisational learning involves multiple levels within the organisation and is both dependent on individuals and independent of individuals. It is a non-linear type of learning with multiple nested cycles. It involves learning via feed forward and feedback pathways through the level of individuals, intermediate levels of teams or groups or projects, and the level of the entire organisation: Through feed-forward processes, new ideas and actions flow from the individual to the group to the organization levels. At the same time, what has already been learned feeds back from the organization to group and individual levels, affecting how people act and think (Crossan et al. 1999), p. 532.

There is growing consensus in the literature that the theory of organisational learning should consider individual, team and organisational levels (e.g. Crossan et al. 1999; Wiewiora et al. 2019).

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1.2 Types of Learning and Challenges for Computational Modeling Organisational learning literature, although extensive and well established, has some deficiencies when it comes to computational models for it. There seems to be no detailed computational formalization of a clearly defined organisational learning process from beginning to end. In this book (Canbalo˘glu et al. 2023d), a self-modeling network modeling perspective is used to model the different processes and phases of organisational learning. As also proposed by Kim (1993), the notion of mental model is extensively used here, see also (Bhalwankar and Treur 2021; Craik 1943; DeChurch, Mesmer-Magnus 2010; De Kleer and Brown 1983; Doyle and Ford 1998; Gentner and Stevens 1983; Johnson-Laird 1983; Langan-Fox, Code, Langfield-Smith 2000; Mathieu, Hefner, Goodwin, Salas, Cannon-Bowers 2000; Nini, 2019; Shih and Alessi 1993; Treur and Van Ments 2022; Van Ments and Treur 2021). The following main types of learning are considered: • Individual learning – By creating a mental model of how a task will be done, e.g., by using imagination – By performing the tasks – By reflecting on the task in hand while performing it – By instructional interaction from documents • Learning within dyads or groups – One member instructs another member – By observational learning from someone else performing the tasks – By working together • Feed forward organisational learning – Formation of new shared mental models – Combination of existing mental models – Different forms of aggregation of the mental models from different sources • Feedback organisational learning – Learning from shared mental models – Learning from existing organisational memory – Using routines to perform a task • Learning from mistakes – Noticing mistakes and speaking up instead of ignoring or hiding them – Addressing mistakes by developing remedies and preventions – Making others aware of one’s mistakes for collective learning from mistakes

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There is a range of contextual factors influencing organisational learning processes: • Context-sensitivity: impact from context factors – Differences in knowledgeability (reflects the amount of learning available) – Differences in trustworthiness (reflects willingness of an individual to share their learnings with other without a fear or risk) • The role of leadership – – – –

Initiatives for and guidance of specific learning processes by a manager Encouragement and stimulation Assessment and approval Feedback

• The role of organisational culture – – – –

Different types of culture and their impact on learning Combination with leadership style Mistake handling culture Changing organisational culture

To obtain computational models of these processes, one needs to consider the following: • • • • • • • •

Different learning mechanisms at different levels The complexity of interactions between the levels The interaction between providing versus acquiring learning Aggregation and revision of knowledge Addressing context-sensitivity The effects of leadership style The effects of culture type Organisational change processes

Above all of this, the aim was to achieve acceptable transparency of the types of models. This was achieved by using the self-modeling network modeling approach which is based on declarative specifications and is very general as any smooth adaptive dynamical system has a canonical self-modeling network representation (Hendrikse, Treur, Koole 2023). For example, based on this modeling approach, the following has been achieved and used as input for this volume: (Canbalo˘glu and Treur 2021; Canbalo˘glu, Treur, Roelofsma 2021; Canbalo˘glu and Treur 2022a; Canbalo˘glu and Treur 2022b; Canbalo˘glu, Treur, Roelofsma 2023c; Canbalo˘glu, Treur, Wiewiora 2023a; Canbalo˘glu, Treur, Wiewiora 2023b).

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1.3 Overview of This Volume Based on the above, this volume (Canbalo˘glu et al. 2023d) is composed of the following parts: Introduction, Background knowledge, Overall computational models of multilevel organisational learning, Aggregation in the formation of shared mental models in organisational learning, Computational analysis of the role of leadership in real-world scenarios for multilevel organisational learning, Computational analysis of the role of organisational culture for multilevel organisational learning, Mathematical analysis for network models and organisation learning, Finalising.

1.3.1 Part II Background Knowledge This part gives an overview of elements that were brought together in this book. In this part, Chapter 2 provides an overview of literature from Management Science with emphasis on multilevel learning models and learning mechanisms. In Chapter 3 an introduction of the modeling approach based on self-modeling network models is provided which is used throughout the book. Different types of self-model states used for different features with pointers to the other chapters are explained. Chapter 4 provides an introduction of a three-level cognitive architecture with levels for dynamics, adaptation and control and how this can be modeled by a self-modeling network. This is illustrated by an example model for context-sensitive control of focussing on a mental model.

1.3.2 Part III Overall Computational Models of Multilevel Organisational Learning This part provides an introduction and illustration of the first basic models. Chapter 5 addresses formalisation and computational modeling of multilevel organisational learning, which is one of the major challenges for the area of organisational learning. It is discussed how various conceptual mechanisms in multilevel organisational learning as identified in the literature, can be formalised by computational mechanisms which provide mathematical formalisations that enable computer simulation. The formalisations have been expressed using a self-modeling network modeling approach. In Chapter 6 it is shown how within organisational learning literature, mental models are considered as a vehicle for both individual learning and organisational learning. By learning individual mental models (and making them explicit), a basis for formation of shared mental models for the level of the organisation is created, which after its formation can then be adopted by individuals. This provides mechanisms for organisational learning. These mechanisms have been used as a basis

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for an adaptive computational network model. The model is illustrated by a not too complex but realistic case study. Chapter 7 focuses on modeling multilevel organisational learning. In this, mental models are used as a vehicle for the interplay of individual, team and organisational learning processes. By learning individual mental models, a basis for formation of shared team mental models is created, and based on the different shared team mental models, a shared organisation mental model is obtained. This pathway is indicated by feed forward learning. In addition, feedback learning follows the opposite pathway: shared team mental models can be learned from a shared organisation mental model and individual mental models can be learned from shared team mental models. These pathways and their interactions provide complex dynamic and adaptive mechanisms that together constitute multilevel organisational learning. These mechanisms form a basis for an adaptive computational network model for multilevel organisational learning. The model is illustrated by a not too complex but realistic case study. Chapter 8 illustrates a multi-level adaptive network model for mental processes making use of shared mental models in the context of organisational learning in team-related performances for a referee team. The chapter describes the value of using shared mental models to illustrate the concept of organisational learning, and factors that influence team performances by using the analogy of a team of match officials during a game of football and show their behavior in a simulation of the shared mental model. The chapter discusses potential elaborations of the different studied concepts, as well as implications of the chapter in the domain of teamwork and team performance, and in terms of organisational learning.

1.3.3 Part IV Aggregation in the Formation of Shared Mental Models in Organisational Learning In this part the models are refined in oreder to address context-sensitive control of aggregation. In Chapter 9 the focus on a heuristic-based aggregation process, which may depend on a number of contextual factors. It is shown how a secondorder adaptive network model for organisation learning can be used to model this process of aggregation of individual mental models in a heuristic context-dependent manner. In Chapter 10 it is explored how Boolean functions of these context factors can be used to model a nonheuristic, logical form of aggregation. Again the control over such aggregation is modeled explicitly at a second-order self-model level. It is shown how in such a network model at the second-order self-model level, Boolean functions can be used to express logical combinations of context factors and by this can exert context-sensitive control over the mental model aggregation process. Thus, the process of aggregation of individual mental models to form shared mental models takes place in an adaptive context-dependent manner based on any Boolean combinations of context factors.

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1.3.4 Part V Computational Analysis of the Role of Leadership in Real-World Scenarios for Multilevel Organisational Learning This part addresses the role of leadership. Chapter 11 addresses formalisation and computational modeling of context-sensitive control over multilevel organisational learning and in particular the role of the leadership style in influencing feed forward learning flows. It addresses a realistic case study with focus on the role of managers for control of multilevel organisational learning. To this end a second-order adaptive self-modeling network model is introduced and an example simulation for the case study is discussed. In Chapter 12 it is shown how a real-world scenario for how an existing large project management organization actually achieved a shared mental model for project management can be modeled by a self-modeling network. Chapter 13 addresses the influence of leadership and communication on learning within an organisation by direct mutual interactions in dyads. This is done in combination with multilevel organisational learning as an alternative route, which includes feed forward and feedback learning. The results show that effective communication (triggered by the active team leader, and/or by natural, informal communication), leads to a faster learning process within an organisation com-pared to the longer route via feed forward and feedback formal organizational learning. However, this more direct form of bilateral learning in general may take more of the employee’s time, as a quadratic number of dyadic interactions in general is less efficient than a linear number of interactions needed for feed forward and feedback organisational learning.

1.3.5 Part VI Computational Analysis of the Role of Organisational Culture for Multilevel Organisational Learning This part addressing the role of organisational culture. Chap. 14 chapter investigates computationally the following research hypotheses: (1) Higher flexibility and discretion in organisational culture results in better mistake management and thus better organisational learning, (2) Effective organisational learning requires a transformational leader to have both high social and formal status and consistency, and (3) Company culture and leader’s behavior must align for the best learning effects. Computational simulations of the introduced adaptive network were analyzed in different contexts varying in organisation culture and leader characteristics. Statistical analysis results proved to be significant and sup-ported the research hypotheses. Ultimately, this chapter provides insight into how organisations that foster a mistaketolerant attitude in alignment with the leader, can result in significantly better organisational learning on a team and individual level. In Chap. 15 it is discussed how Transformative Organisational Change becomes more and more significant both

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practically and academically, especially in the context of organisational culture and learning. However computational modeling and a formalisation of organisational change and learning processes are still largely unexplored. This chapter aims to provide an adaptive network model of transformative organisational change and translate a selection of organisational learning and change processes into computationally modeled processes. It exploits the dynamic systems view of organisations modeled by self-modeling network models. The creation of the model and the implemented mechanisms of organisational processes are based on extrapolations of an extensive literature study and grounded in related work in this field, and then applied to a specified hospital-related case scenario in the context of safety culture. The model was evaluated by running several simulations and variations thereof. The results of these were investigated by qualitative analysis and comparison to expected emergent behaviour based on related available academic literature. Observations about various interplays and effects of the mechanism have been made, and they exposed that acceptance of mistakes as a part of learning culture facilitates transformational change and may foster sustainable change in the long run.

1.3.6 Part VII Mathematical Analysis for Network Models and Organisation Learning This part addresses some mathematical analysis behind the developed models. In Chapter 16 more conceptual background is discussed on computational modeling by dynamical systems. For adaptive network models results on the generality are presented: it is shown how every smooth adaptive dynamical system can be modeled in a canonical manner by a self-modeling network representation. Moreover, it is discussed how equilibrium analysis can be done for adaptive network models, taking into account their connectivity structure and properties of the aggregation used. In Chapter 17 it is shown how equilibrium analysis can be done for organisational learning models, illustrated in particular for specific properties of the aggregation of mental models to obtain shared team and organisation mental models by feed forward learning and how team and individual mental models can be learnt from shared organisation mental models by feedback learning.

1.3.7 Part VIII Finalising Chapter 18 discusses further perspectives on organisational learning and its dynamics, adaptation and control and the way to model these processes by self-modeling network models. With further prospects and research themes.

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Furlough, C.S., Gillan, D.J.: Mental models: structural differences and the role of experience. J. Cogn. Eng. Decis. Making 12(4), 269–287 (2018) Gentner, D., Stevens, A.L.: Mental Models. Erlbaum, Hillsdale NJ (1983) Hendrikse, S.C.F., Treur, J., Koole, S.L.: Modeling Emerging Interpersonal Synchrony and its Related Adaptive Short-Term Affiliation and Long-Term Bonding: A Second-Order MultiAdaptive Neural Agent Model. International Journal of Neural Systems (2023). https://doi. org/10.1142/S0129065723500387 Hebb, D.O.: The organization of behavior: a neuropsychological theory. John Wiley and Sons, New York (1949) Johnson-Laird, P.N.: Mental Models: Towards a Cognitive Science of Language, Inference, And Consciousness. Harvard University Press (1983) Kim, D.H.: The link between individual and organizational learning. Sloan Manage. Rev. Fall 37–50 (1993); Klein, D.A.: The Strategic Management of Intellectual Capital. Routledge-ButterworthHeinemann, Oxford (1993) De Kleer, J., Brown, J.: Assumptions and ambiguities in mechanistic mental models. In: Gentner, D., Stevens, A. (eds.) Mental Models, pp. 155–190. Lawrence Erlbaum Associates, Hillsdale NJ (1983) Langan-Fox, J., Code, S., Langfield-Smith, K.: Team mental models. Techniques, methods, and analytic approaches. Hum. Factors 42(2), 242–271 (2000) Mathieu, J.E., Hefner, T.S., Goodwin, G.F., Salas, E., Cannon-Bowers, J.A.: The influence of shared mental models on team process and performance. J. Appl. Psychol. 85(2), 273–283 (2000) McShane, S.L., von Glinow, M.A.: Organizational Behavior. McGraw-Hill, Boston (2010) Van Ments, L., Treur, J., Klein, J., Roelofsma, P.H.M.P.: A second-order adaptive network model for shared mental models in hospital teamwork. In: Nguyen, N.T., et al. (eds.) Proceedings of the 13th International Conference on Computational Collective Intelligence, ICCCI’21. Lecture Notes in AI, vol. 12876, pp. 126–140. Springer Nature (2021) Nini, M.: All on the same page: how team mental models (TMM) increase team performance. CQ Net (2019) https://www.ckju.net/en/dossier/team-mental-models-increase-team-performance Shih, Y.F., Alessi, S.M.: Mental models and transfer of learning in computer programming. J. Res. Comput. Educ. 26(2), 154–175 (1993) Stelmaszczyk, M.: Relationship between individual and organizational learning: mediating role of team learning. J. Econ. Manage. 26(4), 1732–1947 (2016). https://doi.org/10.22367/jem.2016. 26.06 Treur, J.: Modeling higher-order adaptivity of a network by multilevel network reification. Netw. Sci. 8, S110–S144 (2020a) Treur, J.: Network-Oriented Modeling for Adaptive Networks: Designing Higher-Order Adaptive Biological, Mental and Social Network Models. Springer Nature, Cham (2020b) Treur, J., Van Ments, L. (eds.).: Mental Models and their Dynamics, Adaptation, and Control: A Self-Modeling Network Modeling Approach. Springer Nature (2022) Van Gog, T., Paas, F., Marcus, N., Ayres, P., Sweller, J.: The mirror neuron system and observational learning: implications for the effectiveness of dynamic visualizations. Educ. Psychol. Rev. 21(1), 21–30 (2009) Van Ments, L., Treur, J.: Reflections on dynamics, adaptation and control: a cognitive architecture for mental models. Cogn. Syst. Res. 70, 1–9 (2021) Wiewiora, A., Chang, A., Smidt, M.: Individual, project and organizational learning flows within a global project-based organization: exploring what, how and who. Int. J. Project Manage. 38, 201–214 (2020) Wiewiora, A., Smidt, M., Chang, A.: The ‘how’ of multilevel learning dynamics: a systematic literature review exploring how mechanisms bridge learning between individuals, teams/projects and the organization. Eur. Manag. Rev. 16, 93–115 (2019) Yi, M.Y., Davis, F.D.: Developing and validating an observational learning model of computer software training and skill acquisition. Inf. Syst. Res. 14(2), 146–169 (2003)

Part II

Background Knowledge

This part gives an overview of elements that were brought together in this book. It provides a review of the Management Science literature with emphasis on organisational learning, learning mechanisms and the multilevel learning framework, which guides the development of most of the models discussed in this book. Furthermore, an introduction of the modeling approach based on self-modeling network models, used throughout the book, is provided. This is followed by an introduction of a threelevel cognitive architecture with levels for dynamics, adaptation and control and how this can be modeled using a self-modeling network.

Chapter 2

Multilevel Organisational Learning Anna Wiewiora

Abstract The multilevel learning is a dynamic process that occurs between individuals, teams and organisation. Multilevel learning can be affected by a range of learning mechanisms that can either promote or restrict the transfer of learning between the levels. This chapter introduces the reader to the notion of organisational learning and multilevel learning. It explains complexities of the learning processes within organisations and mechanisms that trigger learning processes, identified in the literature. The remaining of the chapter discusses how computational modeling of multilevel organisational learning can be used to test and build theories, and to provide useful practical contributions for managers and decision makers. Keywords Learning mechanisms · Learning scenarios · Multilevel learning · Organisational learning

2.1 Introduction Multilevel learning is a dynamic, as opposite to a linear process that occurs between individuals, teams and organisation in the feedback and feed-forward direction. The dynamic nature of the process is evident in multiple directions and trajectories of learning. For example, individuals can learn from each other, and can also learn from teams and the organisation. Similarly, team can learn from other teams, from individuals and organisation. Organisation can learn from individuals as well as from teams. By the same token, individuals, teams and organisation can transfer their own learnings to each other via multiple configurations. The multilevel learning framework introduced in this chapter and used to frame learning scenarios for computational modeling of learning, presented in this volume, was originally developed by Crossan et al. (1999). The framework consists of four A. Wiewiora (B) School of Management, QUT Business School, Queensland University of Technology, Brisbane, Australia e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 G. Canbalo˘glu et al. (eds.), Computational Modeling of Multilevel Organisational Learning and Its Control Using Self-modeling Network Models, Studies in Systems, Decision and Control 468, https://doi.org/10.1007/978-3-031-28735-0_2

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learning processes that link individual, team and organisation in their learning efforts. Our subsequent research further operationalised the framework by identifying mechanisms that promote and/or restrict learning flows between the levels (Wiewiora et al. 2020; Iftikhar and Wiewiora 2020) and by using computational modeling to map the learning processes (Canbalo˘glu et al. 2021, 2022, 2023a). The multilevel learning framework and the learning mechanisms by which the learning is transferred between the levels are discussed in in this chapter in greater details.

2.2 The Nature of Organisational Learning Organisational learning involves developing common understanding and beliefs that are often institutionalised and legitimated (Fiol and Lyles 1985). It is central to organisational survival and renewal (Crossan and Berdrow 2003). This is because learning brings about a new knowledge and capabilities, which can be used to adjust, improve and create new processes, products and services. Learning help individuals, teams and organisation adapt to new environment and adjust to changes. It is now widely acknowledged that organisational learning occurs on individual, team, project and organisational levels (Crossan et al. 1999; Berends and Lammers 2010; Wiewiora et al. 2019). It can even span beyond organisational boundaries, when organisation learns from external environment or via cross-organisational collaborations (Jones and Macpherson 2006). Literature posits that learning begins with an individual who, as a result of the learning process, changes or adjusts their mental models (Kim 1993; Bogenrieder 2002). Individuals learn by observing others, through reading, training or other forms of education and knowledge exchange. Exposed to new information, individuals recognize cognitive differences between their own cognition and the new insights and adjust their own mental models, which results in a learning. This socio-cognitive approach has been promoted by Bogenrieder (2002). Teams or groups also learn, but their process of learning differs to that of individuals. Teams typically learn through interactions between team members (Edmondson 2002). Such interactions can be triggered by the need for problem-solving, discussions about joint tasks and by giving each other feedback. Organisational learning therefore involves the change of cognitions and actions of individuals and teams, which are then embedded and institutionalised in the organisation (Berends and Lammers 2010; Crossan et al. 1999).

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2.3 Multilevel Organisational Learning—Theoretical Underpinning The notion of organisational learning spanning different levels have been long acknowledged in the literature (March 1991), but influential contribution to systematically capture the process of multilevel learning comes from the work of Crossan and colleagues (1999). Their Academy of Management Review 2009 decade award paper developed a multilevel learning framework consisting of four learning sub-processes. These processes of intuiting, interpreting, integrating and institutionalizing connect individuals, teams and organisation in the feedback and feed-forward directions. Intuiting is the process of recognising familiar patterns from past events and situations in order to develop new insights. Intuiting occurs only at the individual level. It is a largely sub-continuous process that involves looking for similarities and differences that occur in the environment and making sense of it. The process of intuiting is deeply rooted in individual experiences and also involves one’s ability to make novel connections and to discover new possibilities. Interpreting is a conscious element of the learning process of sense-making and reshaping new knowledge through individual and collective efforts with the use of metaphors, images and language. In fact, language plays an important role in interpreting, as it allows individuals to name and explain their mental maps, which can then be surfaced and shared with others. As such, interpreting moves beyond the individual and becomes embedded within the workgroup. Individuals can interact and share their understandings with others through the use of language. Integrating is the process of developing shared understanding at the team level, achieved through collective actions, dialogue, shared practices and mutual adjustment. It moved beyond simply sharing individual mental models and focuses on integrating these models into collective learning and action. Integrating takes place through the continuing conversations among team members and results in developing new insights. Institutionalizing refers to individual and collective learning being embedded in the organisation’s systems, structures, strategies, routines and practices. It sets organisational learning apart from individual and group learning. Organisational learning goes beyond just the simple sum of the learning of its members. Organisational learning is institutionalised and deeply embedded in organisational systems, structures, routines, and processes, and constitutes an organisational asset. Learning may begin by spontaneous adjustments of behaviours amongst individuals or teams. Overtime, this change in behaviour may result in a new routine, which become embedded into organisational system and guide actions of many organisational members. More recently, Jones and Macpherson (2006) further extended Crossan et al.’s (1999) model of multilevel learning beyond the organisational boundaries, to include inter-organisational learning process. Using data from three case organisations, Jones and Macpherson (2006) demonstrated how small to medium organisations (SMEs) learn from external knowledge providers. They found that SMEs are frequently sharing learnings with their clients and suppliers, while they are also learning from

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their supply chain. This process of inter-organisational learning is referred to as intertwining (Jones and Macpherson 2006). Building on that work, Iftikhar and Wiewiora (2020) found that the process of intertwining occurs also in the context of interorganisational projects. In such projects, individuals and teams from different organisations bring their own unique expertise and get together to deliver a large-scale project. In such environment, the learning takes place between interorganisational actors involved in the project: consultants, client, contractors and sub-contractors. These actors learn from each other mostly via coordinating work and consulting with each other. The learning processes of intuiting, interpreting, integrating, institutionalizing and intertwining are connected in feed-forward and feedback directions. Feed-forward learning direction relates to the exploration of new knowledge by individuals and teams that eventually becomes institutionalized on the organisational level. As such, through feed-forward processes, new ideas and actions flow from the individual to the group to the organisation levels. Feedback learning direction relates to exploiting existing and institutionalised knowledge and making this knowledge available for teams and individuals (Crossan et al. 1999). This multilevel learning framework has been used to frame learning scenarios, which were used for computational modeling, presented in this volume.

2.4 Mechanisms Facilitating Multilevel Learning Flows Learning mechanisms are the apparatus by which learning can travel between individual, team and organisational levels, in the feedback and feed-forward directions. Wiewiora et al. (2019, 2020) demonstrated that learning mechanisms can work together to enable transfer of learning across organisation. Examples of common learning mechanisms are: organisational culture, leaders, organisational structure and networks. These four mechanisms and how they encourage multilevel learning flows are discussed below. Wiewiora and colleagues, in their systematic literature review (Wiewiora et al. 2019) and subsequent empirical work (Wiewiora et al. 2020; Iftikhar and Wiewiora 2020) offer comprehensive conceptualisation of learning mechanisms that can trigger or restrict learning flows between the levels.

2.4.1 Organisational Culture as a Mechanism Facilitating Multilevel Learning Organisational culture has been recognised as an important mechanism for triggering multilevel leaning flows. Culture is present in the way organisational members interact. It is also captured in organisational artefacts: the way how people great each other, the use of jargon, office lay out, dress code. Culture in also present in the

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shared believes and values of the organisational members (Schein 1990). As such, organisational culture shapes patters and practices for social interaction and influences the way people share knowledge and communicate with each other. Cultural values that promote experimentation, flexibility, risk taking have been found to positively influence learning (Bhatt 2000; Schilling and Kluge 2009). In such cultures, individuals are more likely to share their ideas with others, thus triggering individual to individual, and individual to team learning flows. Similarly, in such environment, the organisation is more likely to consider ideas from their members and use them to modify or develop new processes (Wiewiora et al. 2019).

2.4.2 Leader as a Mechanism Facilitating Multilevel Learning Existing research demonstrated the role of leaders in triggering learning flows between the organisational levels (Edmondson 2002; Vera and Crossan 2004; Hannah and Lester 2009). Hannah and Lester (2009) postulate that leaders are social architects and orchestrators of learning processes. Leaders take specific actions such as promote openness to diverse opinions, provide feedback on performance and increase task challenges, which stimulates individual learning (Vera and Crossan 2004; Hannah and Lester 2009). On the team level, research has found that leaders can influence structure and functioning of social networks (Hannah and Lester 2009). Leaders can also proactively motivate team members to identify and resolve conflicting opinions, jointly reflect on and reframe the problem, work together to develop joint insights and learnings (Chang et al. 2021). These actions promote individual and team learning flows. Leaders also influence social architecture for learning by developing formal or informal networks that open new communication channels. Leaders also influence properties of such networks, by deciding on the frequency and intimacy of those networks. These actions of leaders navigate learning within and between teams (Chang et al. 2021). Finally, at the organisational level, leaders have a power to influence policies and procedures that help foster learning through knowledge creation and diffusion (Hannah and Lester 2009).

2.4.3 Structure as a Mechanism Facilitating Multilevel Learning Organisational structure influences multilevel learning dynamics by shaping the patterns of information flow and communication between organisational units (Wiewiora et al. 2019). One of the most common types of organisational structures are: centralised and decentralised structures. Centralised structures tend to be more hierarchical, where the power and authority is in the hands of senior management. In

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decentralised structures decision-making is distributed across multiple individuals or teams. Research explains how organisational structure influence learning flows between the levels. Decentralised structures are argued to promote development of new learning by facilitating rapid diffusion of ideas between organisational groups (Benner and Tushman 2003). Fang and colleagues (2010) found that weak connections between teams enable novel solutions to be exploited throughout the organisation. Some level of team separation promotes learning by encourages exploration of new ideas and protecting the team from becoming overly exposed to existing organisational routines and norms (Benner and Tushman 2003). Yet, a high level of decentralization inhibits the implementation of new ideas (Kim 1993; Schilling and Kluge 2009). Taken together, decentralised organisational structures tend to encourage free flow of learning more so than centralised structures. However, too much decentralisation can negatively affect institutionalisation of learning on the organisational level.

2.4.4 Networks as a Mechanism Facilitating Multilevel Learning Networks describe relationships between individuals. Both, informal and formal networks have been identified to provide opportunities for learning, where individuals can share ideas and learn from each other (Lee and Roth 2007; McCann et al. 2012). Bogenrieder (2002) outlines specific characteristics affecting learning in networks, such as relational strength (the frequency of communication, the duration of contact over time, intimacy or degree of agreement), legitimacy (a person’s position, e.g. their status, authority) and trust. Formal networks, such as communities of practice, study circles, workshops, offer spaces where individuals can share knowledge and learn from each other (Augustsson et al. 2013). Such networks provide a platform where new learning can be developed through discussion on common interests and exploration of novel ideas. Similarly, informal networks such as casual conversations, coffee, or lunch meetings, can trigger serendipitous learning. Learning via informal networks is more coincidental where people exchange ideas, discuss projects, explore new opportunities at informal gatherings. Facilitating opportunities for formation of informal networks can be beneficial for organisations to encourage learning flows, mostly between individuals.

2.5 Discontinuities of Learning Flows Learning flows between the levels can be disrupted, resulting in discontinuity of learning. A discontinuity of learning occurs where one of the learning processes is interrupted or where learning does not flow from level to level (Berends and Lammers

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2010). This can take place when an organisation fails to institutionalise important learnings from teams or individuals, or when institutionalised learnings in the form of routines or manuals are not being used by individuals, who chose to rely on their own localised practices. Discontinuities of learning can also affect feed-forward learning, as such individual learning may not be transferred to the team or the organisational level. This can occur because of the blockages that restrict learning flow to the next level, such as lack of psychological safety, abuse of power (Edmondson 2002), politics (Berends and Lammers 2010) or having overly bureaucratic culture (Wiewiora et al. 2020). Organisational cultures that promote hierarchy and control, have well-established standards and top-down decision-making have been found to restrict learning flows (Turner et al. 2006; Lin et al. 2013). This is because such cultures promote selfprotective behaviours where individuals are more reluctant to speak up and share their opinions and ideas. Cultures that are focused on blaming others prevent individuals from speaking up and expressing their opinion to the group, thus affecting individual to group learning flows (Edmondson 2002). Research has found that leaders can also restrict learning flows by using their position of power. Edmondson (2002) found that leaders who exhibit behaviours characterized by defensiveness, conflict-avoidance and self-protection, may prevent individuals from experimenting and sharing ideas with others, hence restricting transfer of learning between individuals, and between individual to the team. Furthermore, Turner and colleagues (2006) demonstrated that leaders who abuse their use of power are likely to reinforce an environment where individuals passively execute orders and instructions. In such environment, individuals are less likely to voice their opinions, limiting opportunities for knowledge sharing and learning. Wiewiora and colleagues (2020) observed that in the project-based structures the opportunities for learning can be restricted due to temporality of projects. The interdisciplinary nature of projects means that projects are likely to create new learnings (Bakker 2010). However, despite the ease of knowledge creation, there is a difficulty of transferring knowledge and utilising learnings beyond the project (Bakker 2010). When the project dissolves and participants move on, the created knowledge is likely to disperse (DeFillippi and Sydow 2016). In the project environment, project deliverables and performance are at the forefront of project members and project managers focus. There is often no time or desire to engage in sharing and learning, despite the learning opportunities that project-based organising provides. Time and effort are often spent on the immediate project deliverables—not on the learning activities. Project temporality negatively influences the transfer of learning from the individual to the project level due to the tight project deadlines, which impede the ability to experiment and reflect, and prevent individuals from sharing knowledge. Due to the project temporality, possible learnings generated through working on the project are not being transferred to other project or the organisation, hence restricting feed-forward learning flows, and institutionalisation of learning beyond the project.

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2.6 Multilevel Learning Scenarios Below I outline four illustrative examples, from the empirical management and organisational studies that capture the process of multilevel learning and reveal instances of not learning. All four articles used a qualitative research approach: case study, interviews, field notes and observations. Using qualitative approach allowed researchers to gain rich data on the complexity of the multilevel learning processes.

2.6.1 Learning Scenario 1 The first example, illustrated in the work by Edmondson (2002), demonstrates how individuals and organisation learn through teams and the role of power and psychological safety affecting the team learning. Edmondson (2002) used observations and interviews to study teams in a manufacturing company. Edmondson (2002) observed that teams in the same organisation can have different learning behaviours. There were teams in which members did not reflect together nor tried to fix problems collectively. Members of these teams revealed that they fear to speak up and make mistakes in the group. There were also teams that exhibited effective learning practices. Members of these teams frequently sought feedback, searched for insights from others, and were willing to try new things and experiment. Further analysis revealed that apparent power differences between the team members and their leaders, and a lack of psychological safety disabled individuals’ willingness to actively contribute their ideas and provide suggestions to the team. People rarely enquired or challenged each other, especially the bosses as they feared offending those in the position of power. This in turn inhibited the collective learning process, as the inquiry could have facilitated team’s collective learning. Missed opportunities for sharing ideas and collective reflection, restricted individual and team learning opportunities, leading to learning discontinuities. In contrary, the teams, in which the power difference between the leaders and the team members was minimal or absent, exhibited more effective learning behaviours. Leaders, of those learning teams, encouraged input and debate, provided opportunity for the members to brainstorm ideas and experiment. Team members were proactive in seeking input and ideas even from other departments in the organisation. This in turn had a positive effect on the individual, team and organisational learning.

2.6.2 Learning Scenario 2 The second example describes a learning scenario captured in the research by Wiewiora et al. (2020). Their research investigates multilevel learning in the context of a global project-based organisation, called Theta (pseudo name), using a single

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in-depth case study method. Learning in a global context faces unique opportunities and challenges. Learning across subsidiaries located in different countries is challenging due to the geographical dispersion of the subsidiaries, their diverse national backgrounds and cultural contexts. However, access to the learnings from different locations can give organisation a competitive advantage. Wiewiora and colleagues (2020) research revealed that transfer of learnings between the individual, project and organisational levels occurred via six learning mechanisms of: networks; culture of empowerment; power and politics; coaching and mentoring; organisational initiatives and temporality. I will focus on discussing three most powerful mechanisms— networks, culture of empowerment and leaders. These mechanisms helped facilitating learnings not only across the organisational levels, but also across geographical locations. Networks: Theta strategically provided opportunities for the formation of formal and informal networks, which connected people and units across the organisation. For example, Theta facilitated staff mobility across regions, which encouraged the formation of informal networks that were instrumental for exchanging knowledge across individuals and teams from different geographical locations. Theta also offered opportunities for their employees to work across various regions, which facilitated formation of informal networks. These networks were very powerful, because they linked people and teams across geographical locations and allowed for sharing of experiences and knowledge. Culture: Theta had a strong culture of empowerment underpinned by values of experimentation, self-development, initiative and inclusion. In such environment, individuals felt empowered to voice opinions, action ideas, and share knowledge with their teams. People felt that they were encouraged to provide input and that their contributions were valued. These contributions often reached the organisational level, as the individuals were encouraged to promote and implement their ideas. The third mechanism—senior leaders—influenced multilevel learning flows. In particular, senior leaders influenced implementation of individual or team ideas for organisational improvement, hence facilitating individual/team to organisation learning flows. Senior leaders who had strong position of power, were able to implement and institutionalise ideas which came from individual employees or teams. As employees put forward ideas for enhancements of organisational practices, senior leaders, acted as gate keepers of those ideas, and could either restrict or promote these ideas for wider implementation. Wiewiora et al. (2020) found that learning in a global organisation represents a system of mechanisms and actors that work together and influence each other to facilitate multilevel learning flows. As such, global organisation learns as a system by simultaneously nurturing loosely coupled knowledge networks locally and then strategically connecting these networks across the large geographical spread. For such system to work effectively, there is a need to establish enabling mechanisms to promote learning in the global context and develop the knowledge catalyst at each level.

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2.6.3 Learning Scenario 3 The third example, from Berends and Lammers (2010), draws on an inductive, realtime, longitudinal field study tracking implementation of a knowledge management (KM) project in a bank. The case study captures reasons why learning processes were disrupted or even blocked, which led to discontinuities of multilevel learning and had negative consequences for the success of the KM project. During the project initiation phase, discussions of pros and cons to implement the project took place, triggering interpreting and integrating learning processes. These discussions were settled when director gave green light to support the development of a KM proposal. During project preparation, organising and executing phases, project development team struggled to get the shared understanding of the project, affecting learning process of integrating. There was a power play between KM and IT manager who could not agree on the progress of the project. The misalignment of the project leaders’ agenda and project schedules caused a discontinuity in the feed-forward of ideas. The project was eventually abandoned, as decision was made to discontinue the project, because it has taken too much time, and give priority to other strategic projects. During the project phases, multiple flows of events occurred leading to interruptions, delays or abandoning of learning. On many occasions, interpretative and integrative learning processes were stopped, not because consensus was achieved, but because a deadline forced premature closure. The case study revealed that interruptions to learning or learning discontinuities were triggered by social structuring, temporal aspects, and politics. Temporality of the project meant that the team worked under time pressure, at several moments in the project, learning processes were purposefully interrupted by leaders, who used their position of power and interrupted learning and exploration of ideas in an attempt to speed things up. These interventions helped ensure project progress, but were also a source of learning discontinuities. Berends and Lammers (2010) research revealed messy and dynamic nature of learning processes. The learning processes were blocked at all levels of organisational learning, leading to the ultimate failure of the KM project.

2.6.4 Learning Scenario 4 Fourth example, by Turner et al. (2006), was presented in a case study of the public sector service organisation in the UK. The case organisation was characterised as being hierarchical, traditional and bureaucratic. The case demonstrated how multilevel learning was restricted due to actions of managers and bureaucratic culture focused on control and following rigid rules. The culture in the organisation, characterised by hierarchical relationships encouraged formation of silos between ‘them and us’, and reinforced the ‘master–servant’ relationship between ‘doers’–employees and ‘thinkers’–management. Employees lamented they did not receive constructive feedback, only negative feedback if they made a mistake on a job. Lack of constructive

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feedback restricted learning process between individual mental models and shared mental models; it prevented employees to learn and further develop their skills and capabilities. The case study further revealed that the managers can create an environment, in which employees can be frightened to question established routines, which in turn affect transfer of learning as employees’ thoughts and insights are not shared with the management. Applying Crossan’s model to this case would imply that (1) lack of constrictive feedback from managers, (2) employees’ reluctance to question existing processes and (3) the bureaucratic culture negatively affect a learning process of integrating, which occurs via developing a shared understanding and dialog. It can also affect institutionalising of potentially useful ideas from employees which were never shared or explored due to fear of criticism and management approach to follow prescribed ways of doing things, rather than encouraging sharing of ideas and experimentaiton.

2.7 Computational Modeling of Multilevel Learning Computational simulations can be used to determine the best possible ways to transfer learning between individual, team, and organisation, so to uncover avenues via which learning between the levels can be shared most effectively. In addition to simulating learning flows, computational modeling can observe how learning flows are affected by introducing learning mechanisms and adjusting organisational environment. This makes it a very useful practical tool for organisations. Organisation can explore and test, via simulation, the effectiveness of new learning mechanisms, without needing to first invest and implement costly and untested changes. Secchi (2015) offers an introduction to the use of computational modeling, in particular Agent Based Modeling (ABM) in management studies. Using Secchi’s framework, I will explain elements of the computational modeling for multilevel organisational learning. The most elementary unit in the computational modeling is an agent (Secchi 2015). In modeling multilevel learning this unit may represent: individual, team and organisation. Each agent is autonomous because it has unique individual characteristics, and has specific attributes assigned to capture these individual characteristics. Agents in the units interact with each other. There can be certain level of randomness between these interactions, but also certain level of structure (due to predicted organisational environment such as organisational structure). This helps to achieve more realistic models. In the computational network models, used in this volume, adaptive agents can be modeled by adaptive mental networks. Their interaction can be modeled by social networks. As self-modeling networks are a convenient way to model adaptive networks, they are very useful to model adaptive agents. Agent interacts with other agents in a simulated space—called the environment. The environment can include agents’ actual location and may represent their physical or psychological proximity (Secchi 2015), as well as organisational culture within

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which agents operate. This information about the environment is important for simulating multilevel organisational learning, as the proximity between the agents and the culture within which they operate may determine their opportunity to learn from each other. The other aspect of the computational modeling are the specific rules introduced to the case scenario. For instance, in one of our scenarios presented in this volume, we had an agent (project manager) who had some prior knowledge of project risk management and the agent who did not have that knowledge. Computational simulation of this scenario demonstrated that learning outcomes for the team and for the organisation were different where we introduced the ‘knowledgeable agent’ versus the ‘novice agent’ in the simulations. Finally, time plays a vital role in the computational simulations of multilevel learning. For instance, team learning increases with time, when the team is exposed to changing rules/circumstances. Presence of the multiple agents, some of which represent no only individuals, but also teams consisted of unique individuals, means that computational simulations are complex. Sometimes the simulation needs to be performed multiple times before a clear pattern emerges from the data and can be confidently interpreted (Secchi 2015).

2.8 Benefits of Using Computational Modeling for Testing and Advancing Multilevel Learning Theory Existing research postulates a range of benefits for using computational modeling and simulations in management and organisational studies. Computational modeling is well suited to study complex behavioural systems, such as the one of multilevel learning. In contrast to classic statistical analysis of quantitative data, where typically only a small number of independent variables are varied and can be examined, simulation experiments can deal with hundreds (or even thousands) of independent variables (Baškarada et al. 2016). Computational simulations can be used to gain theoretical insights through developing theories and exploring their consequences, and it can also be used to test theories (Harrison et al. 2007). In the context of multilevel learning, computational modeling can be used to model various learning scenarios and test the influence of various factors on the learning outcomes, which were previously uncovered by using traditional exploratory research methods, such as case studies or interviews. As such, researchers can use mix method approaches in which they can first build a theory through exploratory studies, for example by conducting a case study to uncover new learning mechanisms that trigger feed-back learning, and then apply computational modeling to simulate how the learning mechanisms work and to test their usefulness. New insights into multilevel learning can possibly be gained by studying various learning processes that occur in organisational system and how introduction

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of learning mechanisms at different times, can affect these learning processes over time. Computational modeling brings together theory testing (deduction) and theory building (induction) approaches. “Simulations resemble deduction in that the outcomes follow directly from the assumptions made (without the constraint of analytic tractability). Simulations resemble induction in that relationships among variables may be inferred from analyzing the output data (although the data are generated by simulation programs rather than obtained from “real-world” observations)” (Harrison et al. 2007, p. 1230). Analysis of simulation output may reveal relationships among variables, hence can aid in developing new predictions and hypothesis for further empirical testing. Computational simulation can also be used to discover unexpected consequences of tested behaviours, interactions and processes, hence adding to the theory building. Computational models may also be used to prescribe or suggest a better mode of operation. For example, a better way to connect individuals and teams with the organisation to achieve more effective institutionalisation of learning (Harrison et al. 2007). Despite these clear benefits, in the management studies, computational modeling has had a slow uptake. To the best of our knowledge, computational modeling of multilevel learning has not been done previously. Only recent work by Gülay Canbalo˘glu, Jan Treur, and their colleagues have begun using computational modeling for examining multilevel organisational learning. The reasons for such slow uptake are few. Multilevel organisational learning is a complex phenomenon, affected by a range of mechanisms including culture, leadership, networks, structure, just to name a few. Multilevel learning also depends on the contextual factors, such as internal and external environment of the organisation, which adds to the complexity of the setting within which multilevel learning occurs. Presence of the many organisational variables poses a clear challenge to using computational modeling. Management scholars tend to fear that the computational model can provide only a partial representation of reality, ignoring certain salient characteristics. Furthermore, computational modeling requires use of a new language and a new methodology, which is outside of the common methodological approaches for the management scholars that typically involve conducing interviews, case studies, survey, or observational studies. Those common research methods, used in management studies have its own language, analytical approaches, and guidelines to achieve validity and reliability of the research findings. Computational modeling is still considered outside of this realm and requires considerable time and investment to learn the new method and new language, hence many management scholars may be reluctant to use it. In this book, we offer a pathway towards a better understanding of computational modeling of complex organisational behaviours, focusing predominantly on multilevel learning involving individuals, teams and organisation, as well as factors influencing the learning such as organisational culture and leadership.

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2.9 Conclusion The key insights from this chapter are: • The multilevel learning is a dynamic process that occurs between individuals, teams and organisation who can transfer learnings to each other via multiple configurations. • Multilevel learning consists of four learning sub-processes of intuiting, interpreting, integrating and institutionalizing that connect individuals, teams and organisation in the feedback and feed-forward directions. • Learning can be affected by a range of learning mechanisms that can either promote the transfer of learning between the levels or block the learning flows. • Learning mechanisms are the apparatus by which learning can travel between individual, team and organisational levels, in the feedback and feed-forward directions. Some examples include: organisational culture, leaders, organisational structure and networks. • Discontinuities of learning can occur when the learning is disrupted or is blocked, so that the learning cannot easily flow from one level to another. • Computational modeling can be used to model various learning scenarios and test the influence of various factors on the learning outcomes. • Computational modeling and simulation of multilevel learning scenarios can be used to explore how learning flows between the levels and test the effectiveness of learning mechanisms. • Computational modeling and simulation of multilevel learning makes a very useful practical tool for organisations so that learning scenarios and the effectiveness of new learning mechanisms can be tested without needing to first invest and implement costly and untested changes.

References Augustsson, H., Törnquist, A., Hasson, H.: Challenges in transferring individual learning to organizational learning in the residential care of older people. J. Health Organ. Manag. 27(3), 390–408 (2013) Baškarada, S., Chandran, A., Shokr, M., Stewart, C.: Facilitating organisational learning through agent-based modeling and simulation experimentation. Learn. Organ. 23(6), 429–443 (2016) Bakker, R.M.: Taking stock of temporary organizational forms: a systematic review and research agenda. Int. J. Manag. Rev. 12(4), 466–486 (2010) Benner, M.J., Tushman, M.L.: Exploitation, exploration, and process management: the productivity dilemma revisited. Acad. Manag. Rev. 28(2), 238–256 (2003) Berends, H., Lammers, I.: Explaining discontinuity in organisational learning: a process analysis. Organ. Stud. 31(8), 1045–1068 (2010)

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Bhatt, G.D.: Information dynamics, learning and knowledge creation in organizations. Learn. Organ. 7(2), 89–99 (2000) Bogenrieder, I.: Social architecture as a prerequisite for organizational learning. Manag. Learn. 33(2), 197–212 (2002) Canbalo˘glu, G., Treur, J., Roelofsma, P.H.M.P.: Computational modeling of organisational learning by self-modeling networks. Cogn. Syst. Res. 73, 51–64 (2022) Canbalo˘glu, G., Treur, J., Wiewiora, A.: Computational modeling of the role of leadership style for its context-sensitive control over multilevel organisational learning. In: Proceedings of the 7th International Congress on Information and Communication Technology, ICICT’22. Lecture Notes in Networks and Systems, vol. 447, pp. 223–239. Springer Nature Switzerland AG (2023a) Chang, A., Wiewiora, A., Liu, Y.: A socio-cognitive approach to leading a learning project team: a proposed model and scale development. Int. J. Project Manage. 39(6), 646–657 (2021) Crossan, M.M., Berdrow, I.: Organisational learning and strategic renewal. Strateg. Manag. J. 24(11), 1087–1105 (2003) Crossan, M.M., Lane, H.W., White, R.E.: An organizational learning framework: from intuition to institution. Acad. Manag. Rev. 24(3), 522–537 (1999) DeFillippi, R., Sydow, J.: Project networks: governance choices and paradoxical tensions. Proj. Manag. J. 47(5), 6–17 (2016) Edmondson, A.C.: The local and variegated nature of learning in organisations: a group-level perspective. Organ. Sci. 13(2), 128–146 (2002) Fang, C., Lee, J., Schilling, M.A.: Balancing exploration and exploitation through structural design: the isolation of subgroups and organizational learning. Organ. Sci. 21(3), 625–642 (2010) Fiol, C.M., Lyles, M.A.: Organisational learning. Acad. Manag. Rev. 10, 803–813 (1985) Hannah, S.T., Lester, P.B.: A multilevel approach to building and leading learning organizations. The leadership quarterly, 20(1), 34–48 (2009) Harrison, J.R., Lin, Z., Carroll, G.R., Carley, K.M.: Simulation modeling in organisational and management research. Acad. Manag. Rev. 32(4), 1229–1245 (2007) Iftikhar, R., Wiewiora, A.: Learning processes and mechanisms for interorganisational projects: insights from the Islamabad–Rawalpindi metro bus project. IEEE Trans. Eng. Manage. (2020) Jones, O., Macpherson, A.: Inter-organisational learning and strategic renewal in SMEs: extending the 4I framework. Long Range Plan. 39(2), 155–175 (2006) Kim, D.H.: The link between individual and organizational learning. Sloan Manage. Rev. 35, 37–50 (1993) Lee, Y.J., Roth, W.M.: The individual|collective dialectic in the learning organization. Learn. Organ. 14(2), 92–107 (2007) Lin, H.E., McDonough, E.F., III., Lin, S.J., Lin, C.Y.Y.: Managing the exploitation/exploration paradox: the role of a learning capability and innovation ambidexterity. J. Prod. Innov. Manag. 30(2), 262–278 (2013) March, J.G.: Exploration and exploitation in organisational learning. Organ. Sci. 2(1), 71–87 (1991) McCann, C., Asenova, D., Bailey, S.J.: Organisational risk-learning: a case study of social care capital projects in Scottish local authorities. J. Risk Gov. 3(1), 1 (2012) Schein, E.H.: Organizational culture. Am. Psychol. Assoc. 45, 109–119 (1990) Schilling, J., Kluge, A.: Barriers to organizational learning: an integration of theory and research. Int. J. Manag. Rev. 11(3), 337–360 (2009) Secchi, D.: A case for agent-based models in organisational behavior and team research. Team Perform. Manage. 12(1–2), 37–50 (2015) Turner, J., Mavin, S., Minocha, S.: We will teach you the steps but you will never learn to dance. Learn. Organ. 13(4), 398–412 (2006) Vera, D., Crossan, M.: Strategic leadership and organizational learning. Acad. Manag. Rev. 29(2), 222–240 (2004) Wiewiora, A., Smidt, M., Chang, A.: The ‘how’ of multilevel learning dynamics: a systematic literature review exploring how mechanisms bridge learning between individuals, teams/projects and the organization. Eur. Manag. Rev. 16(1), 93–115 (2019)

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Wiewiora, A., Chang, A., Smidt, M.: Individual, project and organisational learning flows within a global project-based organisation: exploring what, how and who. Int. J. Project Manage. 38(4), 201–214 (2020)

Chapter 3

Modeling Dynamics, Adaptivity and Control by Self-modeling Networks Jan Treur

Abstract Networks provide an intuitive, declarative way of modeling which has turned out to be suitable for many types of applications that involve complex dynamics. In many cases also adaptivity plays a role. By using algorithmic or procedural descriptions for the adaptation processes as is often the approach followed, easily leads to less declarative and transparent forms of modeling. This chapter exploits the notion of self-modeling network that has been developed recently to avoid this. According to this approach, adaptivity is obtained by adding a self-model to a given base network, with states that represent part of the network’s structure. This results in a two-level network. The self-modeling construction can easily be iterated so that multiple orders of adaptation can be covered as well. In particular, a three-level self-modeling network can be used to integrate dynamics, adaptivity and control in one network. In this chapter, it is shown how this can provide useful building blocks to design network models for learning within an organisation. Keywords Network-oriented modeling · Self-modeling network · Network reification · Adaptive network model · Controlled adaptation

3.1 Introduction A network modeling approach based on self-modeling can be used to model not only the dynamics of nodes or states of a network but also the adaptation of its network structure and the control of that adaptation. In this chapter, it will be discussed how such self-modeling networks (Treur 2020a, b) can be designed.

J. Treur (B) Social AI Group, Department of Computer Science, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 G. Canbalo˘glu et al. (eds.), Computational Modeling of Multilevel Organisational Learning and Its Control Using Self-modeling Network Models, Studies in Systems, Decision and Control 468, https://doi.org/10.1007/978-3-031-28735-0_3

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Self-modeling networks are networks that include a self-model for part of their own network structure based on nodes that represent certain network structure characteristics, for example, connection weights or excitability thresholds. Such a selfmodeling process for a network is also called network reification. This relates to a long-standing tradition in other areas of AI, namely that of meta-programming and metalevel architectures; e.g., Bowen and Kowalski (1982), Demers and Malenfant (1995), Sterling and Shapiro (1996), Sterling and Beer (1989), Weyhrauch (1980). By using self-models within a network, adaptation of the network structure can be modeled by the dynamics of the self-model states representing the network structure. The latter can be specified by declarative means in a network-oriented manner in the form of mathematical relations and functions; thus, adaptivity of the network structure can be specified in a declarative manner. To support the modeler, a dedicated software environment for self-modeling networks is available; see Treur (2020b, Chap. 9, 2022a). In this chapter, in Sect. 3.2 the network-oriented modeling approach based on self-modeling networks will be briefly introduced. In Sect. 3.3 it is discussed how various adaptation principles can be modeled. In Sect. 3.4, it is briefly pointed out how this approach can be applied to a number of concepts concerning learning within and of an organisation. Finally, Sect. 3.5 is a discussion.

3.2 Modeling Adaptivity by Self-modeling Networks In this section, the network-oriented modeling approach by self-modeling networks used is briefly introduced in two steps.

3.2.1 Network-Oriented Modeling by Temporal-Causal Networks In this approach nodes Y in a network have activation values Y (t) that are dynamic over time t; therefore, they serve as state variables and will usually be called states. To specify these dynamics, the states are considered to causally affect each other by the connections within the network. Following Treur (2016, 2020b), a basic network structure is characterised by: • connectivity characteristics Connections from a state X to a state Y and their weights ωX,Y • aggregation characteristics For any state Y, some combination function cY (..) defines aggregation that is applied to the single impacts ω X i ,Y X i (t) on Y from its incoming connections from states X 1 , . . . , X k • timing characteristics

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Each state Y has a speed factor ηY defining how fast it changes upon given impact Here, the states X i and Y have activation levels X i (t) and Y (t) that vary (often within the [0, 1] interval) over time, described by real numbers t. The dynamics of such networks are described by the following difference (or differential) equations that incorporate in a canonical manner the network characteristics ωX,Y , cY (..), ηY : Y (t + /\t) = Y (t) + ηY [cY (ω X 1 ,Y X 1 (t), . . . , ω X k ,Y X k (t)) − Y (t)]/\t

(3.1)

for any state Y and where X 1 , . . . , X k are the states from which Y gets its incoming connections. The Eq. (3.1) is useful for simulation purposes and also for analysis of properties of the emerging behaviour of such network models. The overall combination function cY (..) for state Y is taken as the weighted average of some of the available basic combination functions cj (..) by specified weights γj,Y , and parameters π1, j,Y , π2, j,Y of cj (..), for Y: cY (V1 , . . . , Vk ) =

γ1,Y c1 (V1 , . . . , Vk ) + · · · + γm,Y cm (V1 , . . . , Vk ) γ1,Y + · · · + γm,Y

(3.2)

Such Eqs. (3.1), (3.2) are hidden in the dedicated software environment that can be used for simulation and analysis; see Treur (2020b, Chap. 9). This software environment is freely downloadable from URL https://www.researchgate.net/publication/368775720_Network-Oriented_Mod eling_Software. Combination functions are similar to the functions used in a static manner in the deterministic Structural Causal Model perspective described, for example, in Pearl (2000), Wright (1921), Mooij et al. (2013). However, in the Network-Oriented Modeling approach described here they are used in a dynamic manner. For example, Pearl (2000, p. 203), denotes nodes by V i and combination functions by f i (although he uses a different term for these functions). In the following quote he points at the issue of under-specification concerning aggregation of multiple connections, as in the often used graph representations the specification of combination functions f i for nodes V i , is lacking: Every causal model M can be associated with a directed graph (…) This graph merely identifies the endogenous and background variables that have a direct influence on each V i ; it does not specify the functional form of f i (Pearl 2000, p. 203).

Therefore, to obtain a full specification of a network model in addition to graph representations for connectivity, at least aggregation in terms of combination functions has to be addressed. Indeed, this is done for the way network models are specified here, to avoid this problem of under-specification. Therefore, aggregation in terms of combination functions is part of the definition of the network structure, in addition to connectivity in terms of connections and their weights and timing in terms of speed factors. As part of the software environment, a large number >65 of useful basic combination functions are included in a Combination Function Library, and also a facility

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Table 3.1 Examples of basic combination functions from the library Name

Notation

Formula

Parameters

Identity

id(V )

V

–

Scaled sum

ssumλ (V 1 , …, V k )

V1 +···+Vk λ

Scaling factor λ

/

n V1 n +···+Vk n

Euclidean

eucln,λ (V 1 , …, V k )

Advanced logistic

alogisticσ,τ (V 1 , …, V k )

[

Stepmod

stepmodρ,δ (V 1 , …,V k )

0 if t mod ρ < δ, else 1

Order n Scaling factor λ

λ

1 1+e−σ(V1 +···+Vk −τ) −στ +e )

−

1 1+eστ ](1

Steepness σ > 0 Threshold τ Repetition ρ Duration δ

to easily indicate any function composition of any available basic combination functions in the library. For a few examples of basic combination functions, see Table 3.1. Here V 1 , …, V k are variables for the single impacts ω X i ,Y X i (t). The above characteristics ωX,Y , γj,Y , πi,j,Y , ηY enable to design network models and their dynamics in a declarative manner, based on mathematically defined functions and relations for them. Note that for each state Y, all characteristics ωX,Y , γj,Y , πi,j,Y , ηY mentioned above causally affect the activation level of Y, as also can be seen from Eqs. (3.1) and (3.2). Each of these characteristics has that influence in its own way from a specific role, either for connectivity, for aggregation or for timing.

3.2.2 Using Self-modeling Networks to Model Adaptive Networks Realistic network models are usually adaptive: often some of their network characteristics ωX,Y , γj,Y , πi,j,Y , ηY change over time. For example, for mental networks often the connections are assumed to change by Hebbian learning (Hebb 1949) and for social networks, it is often assumed that connections between persons change, for example through a bonding by homophily principle (McPherson et al. 2001; Pearson et al. 2006; Sharpanskykh and Treur 2014). Adaptive networks are often modeled in a hybrid manner by considering two different types of separate models that interact with each other: a network model for the base network and its within-network dynamics, and a separate numerical model for the adaptivity of (some of) the network structure characteristics of the base network. The latter dynamic model is usually specified in a format outside the context of network modeling: in the form of some adaptation-specific procedural or algorithmic programming specification used to run the difference or differential equations underlying the network adaptation process. In contrast, by including self-models, a network-oriented conceptualisation like what was described above, is

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applied to obtain adaptive networks as well using declarative descriptions based on mathematically defined functions and relations. The approach using self-models was inspired in a metaphorical sense by the more general idea of self-referencing or ‘Mise en abyme’, sometimes also called ‘the Droste-effect’ after the famous Dutch chocolate brand who uses this effect in packaging and advertising of their products since 1904. For some examples, see Fig. 3.1. For more explanation, see for example, https://en.wikipedia.org/wiki/ Mise_en_abyme, https://en.wikipedia.org/wiki/Droste_effect. This effect occurs in art when within artwork a small copy of the same artwork is included. This can be applied graphically in paintings or photographs, or in sculptures. In these cases, such self-models are static, they cannot change over time. But how about cases in which self-models can change over time? And even more, about cases in which changes for such self-models also magically change the real situation that is modeled by the self-model? There are actually cases in art where a self-model can change. More specifically, the idea of self-modeling is sometimes used within literature (story-within-the-story), theater (theater-within-the-theater), or movies (movie-within-the-movie). In each of these cases the self-model extends over time and can change. But can such a change also magically change the real situation modeled by the self-model? As an example, imagine that a writer is writing a novel with as main character (to a certain extent autobiographically) a writer writing a novel. Then some development of this main character while writing a novel may take place because of new insights obtained by the deepened reflection and analysis performed for this novel. In fact the real writer may use the main character as some alter ego that explores possibilities for the real writer in a kind of fantasy or internal simulation format that would be one bridge too far to try them out in real life. In that case the main character in its development

culturfemale

Fig. 3.1 Three examples of the Mise en abyme or Droste-effect. http://michel.parpere.pagesp erso-orange.fr/pedago/voc/mise%20en%20abyme.htm. https://www.instagram.com/culturfemale/. https://www.instagram.com/p/CCYmVLMpGPo/

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may come to new insights and changes that in turn provide new insights for the real writer too, so that he or she also changes accordingly. This idea of self-models that change over time and where these changes magically lead to similar changes of the real situation has actually been applied to develop the notion of self-modeling network model. Such networks contain self-models as subnetworks with states that can change over time, and changes of these states make the network structure change accordingly. This idea was applied to model adaptation for a network by adding self-models to it by the approach introduced in Treur (2020a, b, c), resulting in self-modeling networks, also called reified networks. This works through the addition of new states to the network (called self-model states) which represent network characteristics by network states, e.g., connection weights or excitability thresholds. Then the impacts of these characteristics on a state Y as mentioned above can be modeled as impacts from such self-model states. This brings the impacts from these characteristics on a state Y in the standard form of a network model where via connections nodes causally affect other nodes. More specifically, adding a self-model for a base network can be done in the way that for some of the network structure characteristics ωX,Y , γj,Y , πi,j,Y , ηY for connectivity, aggregation and timing, additional network states WX,Y , Cj,Y , Pi,j,Y , HY (self-model states or reification states) are introduced and connected to the other states: (a) Connectivity self-model • Self-model states WX,Y are added representing connectivity characteristics, in particular connection weights ωX,Y (b) Aggregation self-model • Self-model states Cj,Y are added representing aggregation characteristics, in particular combination function weights γj,Y • Self-model states Pi,j,Y are added representing aggregation characteristics, in particular combination function parameters πi,j,Y (c) Timing self-model • Self-model states HY are added representing timing characteristics, in particular speed factors ηY Note that the names using the letters W, C, P and H can also be chosen in a different manner. For example, for combination function parameter self-model states often names are used that refer to the specific parameter, for example, T for excitability threshold parameter τ, and M for persistence parameter μ. The process of adding a self-model to a base network is also called network reification and the resulting selfmodeling network is sometimes called a reified network. If such self-model states are dynamic, they describe adaptive network characteristics. In a graphical 3D-format, such self-model states are depicted at a next level (also called self-model level or reification level), where the original network is at a base level.

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Having self-model states to model a specific form of adaptation in a networkoriented manner is only a first step. To fully specify a certain adaptation principle by a self-modeling network, the dynamics of each self-model state itself and its effect on a corresponding target state Y have to be specified in a network-oriented manner by the three general standard types of network characteristics (a) connectivity, (b) aggregation, and (c) timing: (a) Specifying connectivity for the self-model states in a self-modeling network For the self-model states, their connectivity in terms of their incoming and outgoing connections has two different functions: • Effectuating its special effect from its specific role The outgoing downward connections from the self-model states WX,Y , Cj,Y , Pi,j,Y , HY to state Y represent the specific impact (their special effect from their specific role) each of these self-model states has on Y. These downward impacts are standard per role, and make that the dynamic values WX,Y (t), Cj,Y (t), Pi,j,Y (t), HY (t) at t are actually used for the adaptive characteristics of the base network in Eqs. (3.1) and (3.2). • Indicating the input for the adaptation principle as specified in (b) The incoming upward or leveled connections to a self-model state are used to specify the input needed for the particular adaptation principle that is addressed. (b) Specifying aggregation for the self-model states in a self-modeling network For the self-model states, specification of their aggregation characteristics has one main aim: • Expressing the adaptation principle by a mathematical function For the aggregation of the incoming impacts for a self-model state, provided as indicated in (a), a specific combination function is chosen to express the adaptation principle in a declarative mathematical manner. (c) Specifying timing for the self-model states in a self-modeling network For the self-model states, specification of their timing characteristics has one main aim: • Expressing the adaptation speed for the adaptation principle by a value Finally, like any other state, self-model states have their own timing in terms of speed factors. These speed factors are used as the means to express the adaptation speed. As a base network extended by including a self-model is also a network model itself, as has been illustrated in Treur (2020b, Chap. 10), this self-modeling construction can easily be applied iteratively to include self-models of multiple self-modeling (or reification) levels. This can provide higher-order adaptive network models and has turned out quite useful to model context-sensitive control of adaptation in a unified form by a second-order self-model. For example, within Cognitive Neuroscience

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such context-sensitive control is described by the notions plasticity and metaplasticity (e.g., Abraham and Bear 1996; Garcia 2002; Magerl et al. 2018; Robinson et al. 2016). Also, for learning within or of organisations such context-sensitive control of learning is a crucial concept, e.g. Canbalo˘glu et al. (2023a).

3.3 Modeling Adaptation Principles by Self-models In this section, it will be pointed out how the modeling approach for self-modeling network models described in Sect. 3.2 can be applied to model adaptation principles as found in several disciplines. By making self-model states change over time in a proper manner, a useful method to model any adaptation principle is obtained. This does not only apply to first-order adaptive networks, but also to second- or higher-order adaptive networks, for example to model control by using second-order self-models.

3.3.1 Modeling First-Order Adaptation Principles by First-Order Self-models In the neuroscientific literature, a distinction is made between synaptic and nonsynaptic (intrinsic) adaptation. The classical notion of synaptic plasticity is described, e.g., in Hebb (1949), Shatz (1992). The nonsynaptic adaptation of intrinsic excitability of (neural) states has been addressed in more detail more recently, e.g., Chandra and Barkai (2018), Debanne et al. (2019), Zhang et al. (2021). For example: Learning-related cellular changes can be divided into two general groups: modifications that occur at synapses and modifications in the intrinsic properties of the neurons. While it is commonly agreed that changes in strength of connections between neurons in the relevant networks underlie memory storage, ample evidence suggests that modifications in intrinsic neuronal properties may also account for learning related behavioral changes (Chandra and Barkai 2018, p. 30).

In this chapter for these two types of adaptivity, two examples of first-order adaptation principles are considered: Hebbian Learning for connection weights (synaptic) and Excitability Modulation for the excitability threshold of states (nonsynaptic). The latter form of adaptation has been related, for example, to homeostatic regulation (Williams et al. 2013) and also to how deviant dopamin levels during sleep make that dreams can make use of more associations due to easier excitable neurons; e.g., Boot et al. (2017). Moreover, both (synaptic and nonsynaptic) forms of adaptation can easily work together, e.g., Lisman et al. (2018). The Hebbian Learning adaptation principle A well-known adaptation principle of the first type (addressing adaptive connectivity) is Hebbian Learning (Hebb 1949), which can be explained by:

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When an axon of cell A is near enough to excite B and repeatedly or persistently takes part in firing it, some growth process or metabolic change takes place in one or both cells such that A’s efficiency, as one of the cells firing B, is increased. (Hebb 1949, p. 62) (3)

This is sometimes simplified (neglecting the phrase ‘as one of the cells firing B’) to: What fires together, wires together (Shatz 1992) (4)

Within a self-modeling network, this can be modeled by using a connectivity self-model based on self-model states WX,Y representing connection weights ωX,Y . These self-model states need incoming and outgoing connections to let them function within the network. To incorporate the ‘firing together’ part, for the self-model’s connectivity, incoming connections from the connected states X and Y to WX,Y are used; see Fig. 3.2 (upward arrows in blue). These upward connections have weight 1 here. Also a connection from WX,Y to itself with weight 1 is used to model persistence of the learnt effect; in pictures they are usually left out. In addition, an outgoing connection from WX,Y to state Y is used to indicate where this self-model state WX,Y has its effect; see in Fig. 3.2 the (pink) downward arrow. The downward connection indicates that the at the base level the value of WX,Y is actually used for the connection weight of the connection from X to Y. For the aggregation characteristics of the self-model, one of the options for a learning rule is defined by combination function hebbμ (V 1 , V 2 , W ) from Table 3.2. The Excitability Modulation adaptation principle Although connectivity adaptation is most often addressed in the literature, it more recently has been pointed out that also other characteristics can be made adaptive, such as excitability thresholds. For example, the following quote indicates that synaptic activity induces long-lasting modifications in excitability of neurons: Long-lasting modifications in intrinsic excitability are manifested in changes in the neuron’s response to a given extrinsic current (generated by synaptic activity or applied via the recording electrode). (Chandra and Barkai 2018, p. 30) (5)

For more literature on this form of learning or adaptation (called here the Excitability Modulation adaptation principle), see, for example, Aizenman and Linden (2000), Daoudal and Debanne (2003), Debanne et al. (2019), Lisman et al. (2018), Scheler (2014), Titley et al. (2017), Zhang and Linden (2003). As here Fig. 3.2 Connectivity characteristics of the self-model for the Hebbian learning adaptation principle

WX,Y

X

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Table 3.2 Combination functions for self-models modeling first- and second-order adaptation principles used here in the illustrative examples Name and self-model state

Combination functions

Variables and parameters

Hebbian learning WX,Y

hebbμ (V 1 , V 2 , W ) = V1 V2 (1 − W ) + μW V 1 ,V 2 activation levels of the connected states W activation level of self-model state WX,Y μ persistence factor

Excitability modulation alogisticσ,τ (V 1 , …, V k ) TY

V 1 , …, V k single impacts from base states

Exposure accelerates adaptation HWT X,Y

V 1 , …, V k single impacts from base states and first-order self-model states

alogisticσ,τ (V 1 , …, V k )

Fig. 3.3 Connectivity characteristics of a self-model for the excitability modulation adaptation principle

TY

X

Y Z

the adaptation depends on activation of a base state Y and the base states (here X, Z) from which it gets its incoming connections, this can be modeled in a self-modeling network in a similar form as above, but this time using a self-model state TY ; see Fig. 3.3. In this case, based on literature as referred above it is assumed that exposure enhances excitability, which means that it decreases the excitability threshold. To achieve this, for the self-model state TY a monotonically increasing combination function can be used, while the connection weights from X, Y, Z to TY are negative; examples of monotonically increasing combination functions are the logistic sum functions and the Euclidean function (with odd order n) from Table 3.1. In this case, the (pink) downward connection from TY to Y indicates that the value of TY is used for the threshold value of the logistic sum function of base state Y.

3.3.2 Modeling Second-Order Adaptation Principles for Control of Adaptation by Second-Order Self-models The two first-order adaptation principles discussed in Sect. 3.3.1 refer to what in neuroscientific literature is called plasticity. It was shown how they can be described

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by a first-order self-model for connectivity or aggregation characteristics of the base network, in this case in particular for the connection weights or the excitability thresholds used in aggregation. For an organism, in some circumstances it is better to learn (and change) fast, but in other circumstances, it is better to stay stable and let what has been learnt in the past persist: the Plasticity Versus Stability Conundrum (Sjöström et al. 2008, p. 773). Under which circumstances and to which extent such plasticity actually takes place is controlled by a form of socalled metaplasticity; e.g., Abraham and Bear (1996), Garcia (2002), Magerl et al. (2018), Robinson et al. (2016), Sjöström et al. (2008). Such control can address ‘The Plasticity Versus Stability Conundrum’ by only making plasticity happen in contextual circumstances when it is important for the person to change and otherwise stabelize it. In literature as mentioned, various studies show how adaptation (as described, for example, by Hebbian learning), is modulated by accelerating the adaptation process or decelerating or even blocking it. Among the reported factors affecting plasticity in such a way are stimulus exposure, activation, previous experiences, and stress. Here we consider three specific second-order adaptation principles for such control of first-order adaptation: the Exposure Accelerates Adaptation, Exposure Modulates Persistence, and Stress Reduces Adaptation adaptation principles. The Adaptation Accelerates with Increasing Exposure Adaptation Principle For example, in Robinson et al. (2016) the following compact quote is found summarizing that increasing stimulus exposure makes that the adaptation speed increases: Adaptation accelerates with increasing stimulus exposure (Robinson et al. 2016, p. 2) (6)

This indeed describes a form of metaplasticity that controls the speed of adaptation (learning rate). This principle can be modeled by a (dynamic) second-order selfmodel for timing characteristics (speed factors) of a first-order self-model for the first-order adaptation. Such a second-order is based on self-model states HW X,Y or HTY for adaptive learning speed of any of the two types of (synaptic or intrinsic) learning discussed in Sect. 3.1, or HWT X,Y for both types combined. The principle formulated by (6) indicates that the activation level of these second-order self-model states should depend in a monotonically increasing manner on the activation levels of the base states involved: these base states are Y itself and the states X, Z from which Y gets incoming connections. This makes that the connectivity of this timing self-model (for both forms of learning) is as shown in Fig. 3.4: the (positive, blue) upward connections from the base states X, Y and Z to the self-model state HWT X,Y are used to express the part of the principle in (6) referring to ‘stimulus exposure’. For the aggregation, for HWT X,Y , a Euclidean combination function (with odd order n) or a logistic sum combination function can be used to get the monotonic effect as needed. The (blue) upward connections from WX,Y and TY (with negative and positive weight, respectively) to the self-model state HWT X,Y indicate a counterbalancing effect that makes that the learning speed is limited depending on a high learnt level as represented by a high value of WX,Y and a low value of TY . The downward (pink)

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J. Treur HWTY Second-Order Self-Model First-Order Self-Model

TY

WX,Y

X

Base Level

Y Z

Fig. 3.4 Connectivity of a second-order self-model for the second-order exposure accelerates adaptation adaptation principle for control of first-order self-models for Hebbian learning and excitability modulation

connections from HWT X,Y to WX,Y and TY indicate that the value of HWT X,Y is actually used as speed factor for WX,Y and TY . The Exposure Modulates Persistence Adaptation Principle A similar perspective can be applied to obtain a principle for modulation of persistence. Stimulus exposure modulates persistence of adaptation. (7)

Depending on further context factors, this can be applied in different ways. Reduced persistence can be used in order to be able to get rid of earlier learnt connections that do not apply anymore. However, enhanced persistence can be used to keep what has been learnt. This also is a form of metaplasticity, which can be described by a second-order adaptive network that is modeled using a dynamic second-order aggregation self-model, for persistence characteristics of a first-order self-model for the first-order adaptation, based on self-model states MW X,Y for an adaptive persistence factor (Fig. 3.5). This second-order adaptation principle will be illustrated by the example adaptive network model discussed in Sect. 3.4.

Fig. 3.5 Connectivity of a second-order self-model for the exposure modulates persistence adaptation principle with a first-order self-model for Hebbian learning

MWX,Y

WX,Y

X

Y Z

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The Stress Reduces Adaptation Adaptation Principle In Garcia (2002) the focus is on the role of stress in reducing or blocking plasticity. Many mental and physical disorders are stress-related and are hard to overcome due to poor or even blocked plasticity that comes with the stress. Garcia (2002) describes the negative role of stress-related metaplasticity for this, which often becomes a situation that a patient is locked in his or her disorder by that negative pattern. However, he also shows that by some form of therapy this negative cycle may be broken: At the cellular level, evidence has emerged indicating neuronal atrophy and cell loss in response to stress and in depression. At the molecular level, it has been suggested that these cellular deficiencies, mostly detected in the hippocampus, result from a decrease in the expression of brain-derived neurotrophic factor (BDNF) associated with elevation of glucocorticoids (Garcia 2002, p. 629). …modifications in the threshold for synaptic plasticity that enhances cognitive function is referred here to as ‘positive’ metaplasticity. In contrast, changes in the threshold for synaptic plasticity that yield impairment of cognitive functions, for example (..) in response to stress (..), is referred to as ‘negative’ metaplasticity (Garcia 2002, pp. 630–631). In summary, depressive-like behavior in animals and human depression are associated with high plasma levels of glucocorticoids that produce ‘negative’ metaplasticity in limbic structures (…). This stress-related metaplasticity impairs performance on certain hippocampal-dependent tasks. Antidepressant treatments act by increasing expression of BDNF in the hippocampus. This antidepressant effect can trigger, in turn, the suppression of stress-related metaplasticity in hippocampal-hypothalamic pathways thus restoring physiological levels of glucocorticoids (Garcia 2002, p. 634).

For this second-order adaptation principle, a picture similar to what is shown in Fig. 3.4 can be drawn, but then for the case that one of the base states represents the stress level and the upward connection of that base state to the H-state at the second-order self-model level has a negative weight.

3.4 Examples from the Organisational Learning Context In this section we discuss some examples that are often used when modeling learning processes within or of an organisation. Note that they are just briefly sketched here in a summarized form. They will be discussed and illustrated in much more detail in later chapters in this volume (Canbalo˘glu et al. 2023b).

3.4.1 Examples for Individual Learning As a first example, suppose that person A has knowledge that state a in the world causally affects state b with some weight. This knowledge involves a connection from mental state a_A to mental state b_A with weight indicated by ωa_A,b_A . This can be represented (at a next self-model level) by a first-order self-model state named

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Wa_A,b_A ; such states are shortly called W-states, in this case W-states for A’s knowledge. Now, individual learning (or forgetting) for A can be modeled by making such a W-state change over time by adding causal connections to it, for example, by Hebbian learning as shown in Sect. 3.3.1 and Fig. 3.2. This can be done through internal mental simulation, but it can also be combined with observing the own actions by A. Such individual learning processes usually are controlled, which for example can be modeled using a second-order self-model state HWa_A,b_A . By causal connections (or pathways) to HWa_A,b_A context-sensitive control of adaptation can be modeled as discussed in Sect. 3.3.2.

3.4.2 Examples for Dyad or Group Learning Within a dyad or group, the example of Sect. 3.4.1 can also be extended by interaction with another person B. A first form of this involves observation of the other person’s actions while applying his/her knowledge. Suppose this person B has knowledge indicated by a W-state Wa_B,b_B . If B uses this knowledge by making a step from a to b and A observes this (described by horizontal causal connections at the base level from the observed states a and b to A’s corresponding mental states a_A and b_A), this observation can also activate Hebbian learning for A, like the case described in Sect. 3.4.1. This can be used to model observational learning in dyads or groups; see also Chaps. 5 and 13 in this volume (Canbalo˘glu et al. 2023b). Another form of learning in dyads or groups occurs when a person B directly communicates his/her knowledge to person A. This can be modeled by a (horizontal) causal connection (or pathway) at the first-order self-model level from Wa_B,b_B to Wa_A,b_A . Also these dyad or group learning processes usually are controlled, which like in Sect. 3.4.1 can be modeled using a second-order self-model state HWa_A,b_A as discussed in Sect. 3.3.2. However, another way of controlling the learning is by using WW -states, representing the weights of the horizontal (communication) channels at the first-order self-model level. For example, WWa_B,b_B ,Wa_A,b_A indicates a secondorder self-model state that represents weight of the communication channel from Wa_B,b_B to Wa_A,b_A . If this weight is 0 no communication takes place, if it is 1 full communication takes place. By causal connections (or pathways) to WWa_B,b_B ,Wa_A,b_A from relevant context factors, context-sensitive control can be modeled.

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3.4.3 Examples for Feed Forward and Feedback Organisational Learning As discussed in Chaps. 2 and 5 of this volume (Canbalo˘glu et al. 2023b), well-known forms of multilevel organisational learning are feed forward learning and feedback learning. According to the same idea as discussed in Sect. 3.4.2, these can be modeled by horizontal causal connections (or pathways) on the first-order self-modeling level. For example, to obtain feed forward learning the knowledge elements Wa_A1 ,b_A1 , …, Wa_Ak ,b_Ak of a number of persons A1 ,.., Ak can be aggregated into shared organisational knowledge represented by Wa_O,b_O using horizontal connections from each of Wa_A1 ,b_A1 , …, Wa_Ak ,b_Ak to Wa_O,b_O at the first-order self-model level. Similarly, feedback learning can be obtained by using horizontal connections on the first-order self-modeling level in the opposite direction: from Wa_O,b_O to each of Wa_A1 ,b_A1 , …, Wa_Ak ,b_Ak . This models how each individual can learn from the organisational knowledge. Also these feed forward and feedback learning processes usually are controlled, which like in Sect. 3.4.1 can be modeled using second-order self-model states HWa_Ai ,b_Ai and HWa_O,b_O similarly as what was discussed in Sect. 3.4.2. Again, as described in Sect. 3.4.2 another way of controlling the learning is by using WW states, representing the weights of the horizontal (communication) channels at the first-order self-model level. For more details and illustrations of these multilevel organisational learning modeling forms, see for example, Chaps. 6–8 in this volume (Canbalo˘glu et al. 2023b).

3.5 Discussion Most material for this chapter came from Treur (2020b, c). For many domains network models provide an intuitive, declarative way of modeling supported by graphical representations. Connections between nodes in a network can be used as a format to model different types of relations occurring in real-world situations. Once network models are represented within a computing device, these relations can be used for some types of computational processes to generate within-network dynamics. However, as relations in real-world domains often change over time themselves too, network models for realistic situations also need facilities to change their structure: network adaptation. Self-modeling networks enable to model such changes in network structure relatively easily. They include nodes that represent specific network characteristics of the network itself and in this way form a selfmodel of part of the network’s own structure. By using a self-model, the adaptation of the network structure can be modeled through within-network dynamics of this self-model.

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In Sect. 3.4 it has been pointed out how a number of concepts that are crucial for learning within or of organisations can be described by first-order and second-order self-model states. For example, first-order self-model states can be used to represent connection weights that define knowledge elements and the change over time of these self-model states model adaptation or learning. Moreover, second-order selfmodel states can be used to model the quite relevant context-sensitive control of such learning, e.g., Canbalo˘glu et al. (2023a, b); see also Carley (2002, 2006). To analyse the scope of applicability of this network-oriented modeling approach based on self-modeling networks following Ashby (1960) in Treur (2017), Sect. 3.1 it has been shown that any (state-determined) dynamical system as defined in Ashby (1960) and also used in Port and van Gelder (1995) can be described by a set of first-order differential equations, and conversely; see also Treur (2021a, 2022d). Moreover, in Treur (2017), Sect. 3.2 it has also been shown how any set of first-order differential equations can be (re)modeled by a network model. These methods can also be applied to adaptive processes: any description of an adaptation process by a dynamical system or by first-order differential equations can be rewritten as a selfmodel in a self-modeling network. This has been used in Hendrikse, Treur, Koole (2023) to show that any smooth adaptive dynamical system can be represented in a canonical manner as a self-modeling network; see also Treur (2022d) or Chap. 16 of this volume (Canbalo˘glu et al. 2023b). Finally, analysis of stationary points and equilibria for self-modeling network models has been addressed in Treur (2016, Chap. 12, 2020b, Chaps. 11–14, 2021a, 2022b). Validation and parameter tuning has been addressed (Treur 2016, Chap. 14, 2022c).

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Carley, K.M.: Inhibiting adaptation. In: Proceedings of the 2002 Command and Control Research and Technology Symposium, pp. 1–10. Naval Postgraduate School, Monterey, CA (2002) Carley, K.M.: Destabilization of covert networks. Comput. Math. Org. Theory 12, 51–66 (2006) Chandra, N., Barkai, E.: A non-synaptic mechanism of complex learning: modulation of intrinsic neuronal excitability. Neurobiol. Learn. Mem. 154, 30–36 (2018) Daoudal, G., Debanne, D.: Long-term plasticity of intrinsic excitability: learning rules and mechanisms. Learn. Mem. 10, 456–465 (2003) Debanne, D., Inglebert, Y., Russier, M.: Plasticity of intrinsic neuronal excitability. Curr. Opin. Neurobiol. 54, 73–82 (2019) Demers, F.N., Malenfant, J.: Reflection in logic, functional and objectoriented programming: a short comparative study. In: IJCAI’95 Workshop on Reflection and Meta-Level Architecture and Their Application in AI, pp. 29–38 (1995) Garcia, R.: Stress, metaplasticity, and antidepressants. Curr. Mol. Med. 2, 629–638 (2002) Hebb, D.O.: The Organisation of Behavior: A Neuropsychological Theory. Wiley (1949) Hendrikse, S.C.F., Treur, J., Koole, S.L.: Modeling Emerging Interpersonal Synchrony and its Related Adaptive Short-Term Affiliation and Long-Term Bonding: A Second-Order MultiAdaptive Neural Agent Model. International Journal of Neural Systems (2023). https://doi. org/10.1142/S0129065723500387 Lisman, J., Cooper, K., Sehgal, M., Silva, A.J.: Memory formation depends on both synapse-specific modifications of synaptic strength and cell-specific increases in excitability. Nat. Neurosci. 21, 309–314 (2018) Magerl, W., Hansen, N., Treede, R.D., Klein, T.: The human pain system exhibits higher-order plasticity (metaplasticity). Neurobiol. Learn. Mem. 154, 112–120 (2018) McPherson, M., Smith-Lovin, L., Cook, J.M.: Birds of a feather: homophily in social networks. Annu. Rev. Sociol. 27, 415–444 (2001) Mooij, J.M., Janzing, D., Schölkopf, B.: From differential equations to structural causal models: the deterministic case. In: Nicholson, A., Smyth, P. (eds.) Proceedings of the 29th Annual Conference on Uncertainty in Artificial Intelligence (UAI-13), pp. 440–448. AUAI Press (2013) Pearl, J.: Causality. Cambridge University Press (2000) Pearson, M., Steglich, C., Snijders, T.: Homophily and assimilation among sport-active adolescent substance users. Connections 27(1), 47–63 (2006) Port, R.F., Van Gelder, T.: Mind as Motion: Explorations in the Dynamics of Cognition. MIT Press, Cambridge, MA (1995) Robinson, B.L., Harper, N.S., McAlpine, D.: Meta-adaptation in the auditory midbrain under cortical influence. Nat. Commun. 7, 13442 (2016) Scheler, G.: Learning intrinsic excitability in medium spiny neurons. F1000Research 2, 88 (2014). https://doi.org/10.12688/f1000research.2-88.v2 Sharpanskykh, A., Treur, J.: Modeling and analysis of social contagion in dynamic networks. Neurocomputing 146, 140–150 (2014) Shatz, C.J.: The developing brain. Sci. Am. 267, 60–67 (1992). https://doi.org/10.1038/scientificam erican0992-60 Sjöström, P.J., Rancz, E.A., Roth, A., Hausser, M.: Dendritic excitability and synaptic plasticity. Physiol. Rev. 88, 769–840 (2008) Sterling, L., Beer, R.: Metainterpreters for expert system construction. J. Log. Program. 6, 163–178 (1989) Sterling, L., Shapiro, E.: The Art of Prolog, Chap. 17, pp. 319–356. MIT Press (1996) Titley, H.K., Brunel, N., Hansel, C.: Toward a neurocentric view of learning. Neuron 95, 19–32 (2017) Treur, J.: Network-Oriented Modeling: Addressing Complexity of Cognitive, Affective and Social Interactions. Springer Publishers (2016) Treur, J.: On the applicability of network-oriented modeling based on temporal-causal networks: why network models do not just model networks. J. Inf. Telecommun. 1(1), 23–40 (2017)

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Treur, J.: Modeling higher-order adaptivity of a network by multilevel network reification. Netw. Sci. 8, S110–S144 (2020a) Treur, J.: Network-Oriented Modeling for Adaptive Networks: Designing Higher-Order Adaptive Biological, Mental and Social Network Models. Springer Nature Cham, Cham (2020b) Treur, J.: Modeling multi-order adaptive processes by self-modeling networks (keynote speech). In: Tallon-Ballesteros, A.J., Chen, C.-H. (eds.) Machine Learning and Intelligent Systems: Proceedings of MLIS 2020. Frontiers in Artificial Intelligence and Applications, vol. 332, pp. 206–217. IOS Press (2020c) Treur, J.: On the dynamics and adaptivity of mental processes: relating adaptive dynamical systems and self-modeling network models by mathematical analysis. Cogn. Syst. Res. 70, 93–100 (2021a) Treur, J.: With a little help: a modeling environment for self-modeling network models. In: Treur, J., van Ments, L. (eds.) Mental Models and Their Dynamics, Adaptation and Control: A Selfmodeling Network Modeling Approach, Chap. 17. Springer Nature Switzerland (2022a) Treur, J.: Where is this leading me: stationary point and equilibrium analysis of self-modeling network models. In: Treur, J., van Ments, L. (eds.) Mental Models and Their Dynamics, Adaptation and Control: A Self-modeling Network Modeling Approach, Chap. 18. Springer Nature Switzerland (2022b) Treur, J.: Does this suit me: validation of self-modeling network models by parameter tuning. In: Treur, J., van Ments, L. (eds.) Mental Models and Their Dynamics, Adaptation and Control: A Self-modeling Network Modeling Approach, Chap. 19. Springer Nature Switzerland (2022c) Treur, J.: How far do self-modeling network models reach: relating them to adaptive dynamical systems. In: Treur, J., van Ments, L. (eds.) Mental Models and Their Dynamics, Adaptation and Control: A Self-modeling Network Modeling Approach, Chap. 20. Springer Nature Switzerland (2022d) Weyhrauch, R.W.: Prolegomena to a theory of mechanized formal reasoning. Artif. Intell. 13, 133–170 (1980) Williams, A.H., O’Leary, T., Marder, E.: Homeostatic regulation of neuronal excitability. Scholarpedia 8, 1656 (2013) Wright, S.: Correlation and causation. J. Agric. Res. 20, 557–585 (1921) Zhang, W., Linden, D.J.: The other side of the engram: experience-driven changes in neuronal intrinsic excitability. Nat. Rev. Neurosci. 4, 885–900 (2003) Zhang, A., Li, X., Gao, Y., Niu, Y.: Event-driven intrinsic plasticity for spiking convolutional neural networks. IEEE Trans. Neural Netw. Learn. Syst. (2021). https://doi.org/10.1109/tnnls.2021. 3084955

Chapter 4

Modeling Mental Models: Their Use, Adaptation and Control Gülay Canbalo˘glu and Jan Treur

Abstract Using a proper mental model during mental processes is often crucial. Such a mental model has to be learnt and maintained; this involves mental model adaptation. Metacognition is applied to control use and adaptating in a contextsensitive manner. In this chapter, a second-order adaptive network model for handling mental models, covering their use, adaptation and control, is discussed and used to illustrate these processes. Keywords Adaptive network models · Mental models

4.1 Introduction Mental processes often use specific mental models, e.g., Gentner and Stevens (1983), Greca and Moreira (2000), Skemp (1971), Seel (2006), Treur and Van Ments (2022). Learning or adaptation of a mental model has a decisive effect on the process of using it. Moreover, metacognitive control determines when and how to focus on learning. Metacognition (Darling-Hammond et al. 2008; Shannon 2008; Mahdavi 2014; Flavell 1979; Koriat 2007; Pintrich 2000) is a form of cognition about cognition. In Koriat (2007) it is described as what people know about their own cognitive processes and how they put that knowledge to use in regulating their cognitive processing and behavior. So, metacognition can be used to control one’s own cognitive processes. In the context of mental models such control can apply to the use of a mental model or to its learning or adaptation. A sometimes used closely related term is self-regulation and when the cognitive processes addressed by metacognition concern learning, the term self-regulated learning is used. For example, in Pintrich G. Canbalo˘glu · J. Treur (B) Social AI Group, Department of Computer Science, Vrije Universiteit Amsterdam, Amsterdam, Netherlands e-mail: [email protected] G. Canbalo˘glu e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 G. Canbalo˘glu et al. (eds.), Computational Modeling of Multilevel Organisational Learning and Its Control Using Self-modeling Network Models, Studies in Systems, Decision and Control 468, https://doi.org/10.1007/978-3-031-28735-0_4

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(2000), self-regulated learning is described as an active, constructive process whereby learners set goals for their learning and then attempt to monitor, regulate, and control their cognition, motivation, and behavior, guided and constrained by their goals and context. From a network-oriented modeling perspective, adaptation of mental models can be described by adaptive network models, where some of the network characteristics such as connection weights or excitability thresholds change over time. If, in addition, metacognition is used to regulate or control the change process, this implies that the adaptation of the mental network is itself adaptive as well, which is called secondorder adaptation. Thus, a network model for these processes has to address such complex second-order adaptive behaviour; e.g., Bhalwankar and Treur (2021), Van Ments and Treur (2021), Treur and Van Ments (2022). Following this line in the current chapter, using the self-modeling network modeling approach for higher-order adaptive networks from Treur (2018, 2020a, b), a second-order adaptive network model is introduced for metacognitive control over adaptation of a specific mental model. In this chapter, first in Sect. 4.2 more background knowledge is discussed on metacognition and its role in controlling mental processes and a three-level cognitive architecture for it. In Sect. 4.3 the network-oriented modeling approach used is briefly explained and in Sect. 4.4 it is shown how it can be used to formalize the cognitive architecture as a self-modeling network. Next, in Sect. 4.5 the introduced secondorder adaptive network model is described in some detail. In Sect. 4.6, it is shown how this model was used to perform simulations for the illustrative example scenario. Finally, Sect. 4.7 is a discussion and Sect. 4.8 is an Appendix with the full specification of the introduced adaptive network model.

4.2 A Three-Level Cognitive Architecture for Mental Models and Their Use, Adaptation and Control For the history of the mental model area, often Kenneth Craik is mentioned as a central person. In his book (Craik 1943), he describes a mental model as a small-scale model that is carried by an organism within its head as follows: If the organism carries a “small-scale model” of external reality and of its own possible actions within its head, it is able to try out various alternatives, conclude which is the best of them, react to future situations before they arise, utilize the knowledge of past events in dealing with the present and future, and in every way to react in a much fuller, safer, and more competent manner to the emergencies which face it (Craik 1943, p. 61)

This quote mentions both the usage of a mental model by internal mental simulation (‘try out various alternatives’) and the learning of the mental model (‘utilize the knowledge of past events’). Shih and Alessi (1993, p. 157) indicate that mental models are relational structures consisting of states and causal relationships between them:

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Control of adaptation of mental models

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Fig. 4.1 Cognitive architecture for mental model handling with three levels of mental processing for mental models where each next level is monitoring and modulating or controlling the processes at the level below it: (1) the adaptation on the middle level is decisive for the use of a mental model on the base level, and (2) the adaptation itself on the middle level is controlled by the upper level

By a mental model we mean a person’s understanding of the environment. It can represent different states of the problem and the causal relationships among states.

By Van Ments and Treur (2021), an analysis of different types and uses of mental models is provided. This analysis resulted into a three-level cognitive architecture (see Fig. 4.1): • base level: internal simulation of a mental model • middle level: the adaptation of the mental model (e.g., formation, learning, revising, and forgetting); this adaptation modulates or controls the internal simulation processes at the base level • upper level: the (metacognitive) control over the adaptation processes Learning of mental models can involve observational and instructional learning (Yi and Davis 2003; Van Gog et al. 2009) and combinations thereof, but also learning by mental simulation or by just using a mental model in practice can take place. Literature on metacognition, sometimes also called self-regulation, can be found, for example in Darling-Hammond et al. (2008), Shannon (2008), Mahdavi (2014), Flavell (1979), Koriat (2007), Pintrich (2000). The focus is here on the role of metacognition applied to learning or adaptation. For example, in Pintrich (2000, pp. 452–453) the following assumptions for self-regulated learning are described by ‘Learners can monitor, control, and regulate certain aspects of their own cognition, motivation, and behavior, and some elements of their environment.’. In Koriat (2007, p. 290), metacognition is described by what people know about cognition and their own cognitive processes, and how they use that in regulating their cognitive processes and behavior. It is emphasized that there is a causal relation from monitoring to control (Koriat 2007), p. 315. So, in both descriptions of Pintrich (2000) and Koriat (2007) on metacognition (as well as in most other literature on metacognition), monitoring and control of the own cognitive processes are central concepts. These processes work through a causal cycle where the own cognitive processes affect the metacognitive monitoring, this

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monitoring in turn affects the metacognitive control, and this control affects the own cognitive processes. Such a causal cycle is indicated by the upward and downward arrows in Fig. 4.1.

4.3 Higher-Order Adaptive Network Models In this section, the network-oriented modeling approach used is briefly introduced. Following Treur (2016, 2020b), a temporal-causal network model is characterised by (here X and Y denote nodes of the network, also called states): • Connectivity characteristics • Connections from a state X to a state Y and their weights ωX,Y • Aggregation characteristics For any state Y, some combination function cY (..) defines the aggregation that is applied to the impacts ωX,Y X(t) on Y from its incoming connections from states X • Timing characteristics Each state Y has a speed factor ηY defining how fast it changes for given causal impact. The following difference (or related differential) equations that are used for simulation purposes and also for analysis of temporal-causal networks, incorporate these network characteristics ωX,Y , cY (..), ηY in a standard numerical format: Y (t + /\t) = Y (t) + ηY [cY (ω X 1 ,Y X 1 (t), . . . , ω X k ,Y X k (t)) − Y (t)]/\t

(4.1)

for any state Y and where X 1 to X k are the states from which Y gets its incoming connections. Within the software environment described in Treur (2020b, Chap. 9), a large number of around 70 useful basic combination functions are included in a combination function library. The above concepts enable us to design network models and their dynamics in a declarative manner, based on mathematically defined functions and relations. Realistic network models are usually adaptive: often not only their states but also some of their network characteristics change over time. By using a self-modeling network (also called a reified network), a similar network-oriented conceptualisation can also be applied to adaptive networks to obtain a declarative description using mathematically defined functions and relations for them as well, for more details, see Treur (2018, 2020a, b), see also Chap. 3 of this volume (Canbalo˘glu et al. 2023). In brief, this works through the addition of new states to the network (called self-model states) which represent (adaptive) network characteristics. In the graphical 3D-format as shown in Sect. 4.4, such additional states are depicted at a next level (called selfmodel level or reification level), where the original network is at the base level. As an example, the weight ωX,Y of a connection from state X to state Y can be represented

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(at a next self-model level) by a self-model state named WX,Y . Similarly, all other network characteristics from ωX,Y , cY (..), ηY can be made adaptive by including selfmodel states for them. For example, an adaptive speed factor ηY can be represented by a self-model state named HY and an adaptive excitability threshold parameter τY can be represented by a self-model state named TY . Moreover, a persistence factor μ of a state Y of used for adaptation can be represented by a self-model state MY . As the outcome of such a process of network reification is also a temporal-causal network model itself, as has been shown in Treur (2020b, Chap. 10), this selfmodeling network construction can easily be applied iteratively to obtain multiple orders of self-models at multiple (first-order, second-order, …) self-model levels. In the current chapter, this multi-level self-modeling network perspective will be applied to obtain a second-order adaptive network model addressing metacognitive control of adaptation as needed to learn and use a specific mental model.

4.4 Modeling Adaptation of a Mental Model and Its Metacognitive Control by Self-Modeling Networks In this section, the adaptive self-modeling network model for mental models is introduced. This adaptive network model follows the cognitive architecture that has processes at three levels (Van Ments and Treur 2021), described in Sect. 4.3. By using the notion of self-modeling network (or reified network) from Treur (2020a, b), recently this cognitive architecture has been formalized computationally and used in computer simulations for applications of mental models; for an overview of this approach and various applications of it, see Treur and Van Ments (2022). This cognitive architecture can be formalized as a self-modeling network model as shown in Fig. 4.2. More specifically, the mapping from the three levels of the cognitive architecture to this self-modeling network architecture is as follows (see also Fig. 4.2):

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Fig. 4.2 Modeling the three-level cognitive architecture for mental model handling by a selfmodeling network

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• Lower level: a mental model as a subnetwork The mental model as a relational structure at the base level within the cognitive architecture is modeled as a (sub)network structure of states (nodes) and connections between them at the base level of the self-modeling network; the dynamics of the states of this subnetwork model internal simulation of the mental model. • Middle level: a first-order self-model of the mental model representing adaptation of its network structure The level for adaptation of the mental model within the cognitive architecture is modeled as a first-order self-model of the mental model structure by the base level network; the dynamics of the states of this first-order self-model model adaptation makes changes in the structure of the mental model. • Upper level: a second-order self-model of a mental model representing control of adaptation of its network structure The level for control of adaptation of a mental model is modeled as a second-order self-model of the base network for the mental model, which is a self-model for the self-model for adaptation of the mental model; the dynamics of the states of this second-order self-model model control of adaptation by making changes in the structure of the first-order self-model that describes the adaptation of the mental model. So, mental models and the way they are handled can be considered as being described through multiple representations: they can be viewed from three levels of representation according to the three planes depicted in Fig. 4.2, right hand side. At the lower, base level depicted by the lower (pink) plane, a mental model, which in general essentially is considered a relational structure, is represented by nodes and connections between these nodes. For internal simulation, the nodes have activation levels that vary over time. Based on the relations between the nodes, these activation levels affect each other over time. Next, at the adaptation level depicted in Fig. 4.2 right-hand side by the middle (blue) plane, it is represented how the network connections representing the mental model relations, change over time by some adaptation model. Finally, at the top level depicted by the upper (purple) plane in Fig. 4.2 it is indicated how the adaptation at the middle level is controlled. In this way, to model mental processes in which mental models play a role, within the self-modeling network these mental models do not get a single but a three-fold representation by which the different uses and operations on the mental model are distinguished like they are distinguished by the levels in the cognitive architecture.

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4.5 A Second-Order Adaptive Mental Network Model for Metacognitive Control of Adaptation of a Mental Model The three-level architecture for mental model handling discussed in Sect. 4.4 (see Fig. 4.2) is illustrated in more detail by an example second-order adaptive selfmodeling network model. The connectivity of this network model is depicted (according to three different views) in Figs. 4.3, 4.5 and 4.6. The states used are explained in Fig. 4.4. As a case study, in this second-order self-modeling network model, mental models for indirect (big blue ovals in Fig. 4.3) and direct (big purple ovals in Fig. 4.3) communication scenarios are modeled addressing the learning process of people trying to communicate with each other. Direct communication means the direct interaction between two people via asking a question and replying to it. On the other hand, indirect communication requires one or more intermediary people to interact with the target person. The scenario was constructed in the form of a request for an appointment to focus on the understanding of the process. For indirect communication, in the example scenario a mental model is used in which person A asks the personal assistant PA of person B for an appointment. PA relays the request to B and receives the reply of B. Then PA transfers B’s reply to A and gets A’s notification receipt to let B know about this notification. In contrast, for direct communication, a mental model is used in which A and B interact with each other, therefore, there is no need for a personal assistant. A directly asks B for the appointment and can get the answer immediately. In the introduced adaptive network model, mental model connections are represented by adaptive first-order self-model states called W-states. Control of the adaptation uses second-order self-model states (called HW -states) for the adaptation speed of the W-states. A W-state can change when the corresponding HW -state representing the adaptation speed becomes nonzero; when this HW -state is 0, no change can take place. The HW -states can become nonzero in a context-sensitive manner because the context states have connections to them. This is how the context-sensitive metacognitive control over the change of a mental model takes place, thereby following the second-order adaptation principle ‘Adaptation accelerates with increasing stimulus exposure’ as formulated by Robinson et al. (2016). The second-order self-model states called MW -states model the persistence of the mental model connections represented by the related W-states. If MW -states have activation level 1, there is full persistence, if they have level 0 there is no persistence at all. These second-order self-model states (together with the HW -states) model in a context-sensitive manner the ‘Plasticity versus Stability Conundrum’ described, for example, in Sjöström et al. (2008). They are used for the Hebbian learning (and forgetting) that takes place during the use of a mental model for internal mental simulation and to change the mental model in focus to another mental model. Figure 4.3 depicts the view on the base level and first-order self-model level and the interactions between these two levels. From the context state for the indirect interaction case, by upward connections (in blue) the W-states for the mental model

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for the indirect case are activated (thereby assuming that these W-states have a nonzero adaptation speed, see below and Fig. 4.5) and similarly for the direct case. Within the base level, the two context states also have connections to the first state of these mental models, so that these mental models are actually used for internal simulation. Figure 4.5 shows the view on the interactions of the second-order self-model level with the other two levels for the HW -states. It can be seen here that by upward connections (in blue), the adaptation speed as represented by the HW -states depends on activation of the related mental model states at the base level and the related connection representation W-states at the first-order self-model level. This follows the secondorder adaptation principle ‘Adaptation accelerates with increasing stimulus exposure’ (Robinson et al. 2016) mentioned above and makes that by the downward connections (in pink) from the HW -states to the W-states, these W-states indeed can change. All this depends on the context state that triggers activation of these specific base states and W-states for a mental model, which makes it a context-sensitive form of control of adaptation. Figure 4.6 shows the view on the interactions of the second-order self-model level with the other levels in particular for the MW -states. The MW -states have values 1 when the related W-states needs to be fully persistent and lower values when these W-states should not be (fully) persistent. As mentioned above, this models in a

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Explanation Mental model state for person A asks PA for appointment to personal assistant of person B Mental model state for personal assistant asks B for appointment for person A Mental model state for person B replies to PA for appointment Mental model state for personal assistant replies to person A for appointment Mental model state for person A notifies receipt to personal assistant of B Mental model state for personal assistant transfers receipt of A to person B Mental model state for person A directly asks person B for appointment Mental model state for person B directly replies to person A for appointment Mental model state for person A directly notifies receipt to person B Context state for the indirect communication (option 1) Context state for the direct communication (option 2) Self-model state for speed factor for connection weight between X1 and X2 Self-model state for speed factor for connection weight between X2 and X3 Self-model state for speed factor for connection weight between X3 and X4 Self-model state for speed factor for connection weight between X4 and X5 Self-model state for speed factor for connection weight between X5 and X6 Self-model state for speed factor for connection weight between X7 and X8 Self-model state for speed factor for connection weight between X8 and X9 Self-model state for speed factor for self-model state X12 Self-model state for speed factor for self-model state X13 Self-model state for speed factor for self-model state X14 Self-model state for speed factor for self-model state X15 Self-model state for speed factor for self-model state X16 Self-model state for speed factor for self-model state X17 Self-model state for speed factor for self-model state X18 Self-model state for persistence factor for self-model state X12 Self-model state for persistence factor for self-model state X13 Self-model state for persistence factor for self-model state X14 Self-model state for persistence factor for self-model state X15 Self-model state for persistence factor for self-model state X16 Self-model state for persistence factor for self-model state X17 Self-model state for persistence factor for self-model state X18

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Fig. 4.4 The states in the adaptive network model

context-sensitive manner the ‘Plasticity versus Stability Conundrum’ described, for example, in Sjöström et al. (2008). The context-dependence of this form of control is modeled specifically by the upward connections (in blue) from the two context states at the base level to their related MW -states. The combination functions from the library used in the introduced network model are defined as follows: • The advanced logistic sum combination function alogisticσ,τ (V 1 , …, V k ) is defined by: | alogisticσ,τ (V1 , . . . , Vk ) =

1 1 + e−σ(V1 +···+Vk −τ)

| ( ) 1 1 + e−στ (4.2) − 1 + eστ

where σ is a steepness parameter and τ a threshold parameter and V 1 , …, V k are the impacts from the states from which the considered state Y gets incoming connections

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• The composed max-hebbian learning combination function is defined by maxhebbμ (V1 , V2 , V3 , V4 , V5 ) = max(V1 ∗ V2 (1 − V3 ) + μV3 , max(V4 , V5 )) (4.3) where μ is a persistence parameter, V3 represents the weight of the connection, and V 1 , V 2 are the activation levels of the connected states. • The steponceα,β (..) function is 1 between time points α and β and 0 else. The full specification can be found in the Appendix Sect. 4.7; see also the Linked Data at URL https://www.researchgate.net/publication/353667091.

4.6 Example Simulation Scenario The introduced second-order self-modeling network model is illustrated for an example case concerning indirect and direct communication scenarios, as described in Sect. 4.5. In this section, a simulation example of the adaptive mental network model is discussed displaying the learning process of people trying to communicate with each other. Not so surprisingly, direct communication is much faster than indirect communication, so when that is an option, it is not efficient to apply a mental model for indirection communication. The designed network model can be characterized in terms of connectivity, aggregation and timing. Two matrices for connectivity, mb for base connectivity and mcw for connection weights characterize the connections of the network model. Two matrices for aggregation, mcfw for weights of combination functions and mcfp for parameters of the combination functions specify aggregation. And finally, one matrix ms for speed factors characterizes the timing. The full specification of these matrices can be found in Appendix Sect. 4.8. As briefly indicated in Sect. 4.3 and 4.4, the self-modeling feature of the modeling method adds higher-order levels above the base level. In our model, the base level includes the mental models for interaction states between people and in addition two context states for switching between the mental models for indirect and direct cases, beginning from X1 to X11 inclusive. In the base level, for the indirect case, there is a mental model of 6 states that can be seen as the steps of the communication (big blue oval in the base level in Fig. 4.3), and for the mental model for the direct case there are 3 (big purple oval in the base level in Fig. 4.3). It indeed shows that indirect communication is a longer process. At the first-order self-model level, there are 7 W-states (in the big blue and purple ovals in the middle level plane in Fig. 4.3) for all connections of the two mental models shown at the base level both for the direct and indirect cases. This level makes the model adaptive in terms of the connections between base level states. For

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these W-states Hebbian learning is used to provide learning (and forgetting), and the W-states are changed to obtain focusing on them. At the second-order self-model level, HW -states and MW -states are used to control the mentioned forms of adaptation itself in the first-order self-model level. In our model, there are 7 HW -states and 7 MW -states (in the big blue and purple ovals in the upper-level plane in Fig. 4.3) for all of the 7 W-states from the middle level plane. The simulation outcomes depicted in the overall graphs in Fig. 4.7 and the partial graphs in Figs. 4.8, 4.9 and 4.10 show how the process runs. In each of the periods from 25 to 125 and from 200 to 300, a different mental model comes in focus. In both cases the mental model is not perfect as its connection weights are only 0.8. However, by using the mental model for internal mental simulation, Hebbian learning (Hebb 1949) takes place by which the weights increase to 1 or close to it. The first context state finishes at time 125 and the next, other context state starts at time 200. In the meantime, the weights of the mental model that was first in focus drop to 0 (so, it is not used anymore) and instead, after time 200 the other mental model relating to the new context gets high weights and is used then. The steponce function was used in our model to do the indirect-direct context case shift. In Figs. 4.7, 4.8, 4.9 and 4.10 the time interval 25–125 demonstrates the first case (indirect communication) and the time interval 200–300 demonstrates the second one (direct communication). As it can be seen, base states become higher in their level after the increase of the W-states because of the learning that takes place. Each different W-state affects its corresponding base states, thus, also in harmony with real life, within a mental model the represented communication steps do not trace the same route, they follow each other with a small time difference. Learning is a process; it does not happen all of a sudden. X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17 X18 X19 X20 X21 X22 X23 X24 X25 X26 X27 X28 X29 X30 X31 X32

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The learning process of indirect communication only takes place in the first time interval (25–125) with the help of the context states based on the steponce function. All the base and adaptation states of the indirect case get increased, but between time 125 and time 150, all become 0 because the context state of this case becomes 0 after time 125. During the gap between the cases, until the second case context state becomes nonzero, everything is zero except the W-states of the second case. A minimal nonzero weight is used for the initialization of the learning of direct

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Fig. 4.10 Picture for the second-order self-model states in the simulation exerting context-sensitive control both over the focusing on a mental model and the learning of it

communication. Then the second case starts and the learning process of this direct communication only happens in the second time interval from time 200 to about 300. Similar to the first case, adaptation states such as W-, HW - and MW -states increase hand in hand with the base states and that corresponds to the learning process.

4.7 Discussion Part of the content of this chapter is based on Canbalo˘glu and Treur (2021). Within mental processes, often mental models are used for internal simulation to obtain predictions. These mental models are also often adapted. Adaptation processes can be described by adaptive network models. If metacognition is used to regulate adaptation, for example during learning (Pintrich 2000), the adaptation becomes itself adaptive as well, so then it involves second-order adaptation. In this chapter, a second-order adaptive network model was introduced for metacognitive control of adaptation processes needed for learning of a specific mental model and using this mental model. It was shown how a second-order self-modeling network model provides adequate means to model the different aspects that make the addressed topic complex: the network has a self-model about its own structure, it models mental models and adaptation of them, and it models context-sensitive

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metacognitive control of this adaptation. The model was applied to simulate an illustrative example scenario that explains what the model does. In further work other scenarios have been addressed as well, in particular for the use of mental models in teams in hospitals, building further, for example, on Van Ments et al. (2021) and Treur and Van Ments (2022).

4.8 Appendix: Full Specification by Role Matrices In Figs. 4.11, 4.12, 4.13, 4.14 and 4.15, the different role matrices are shown that provide a full specification of the network characteristics defining the network model in a standardised table format. Here in each role matrix, each state has its row where it is listed which are the impacts on it from that role. Fig. 4.11 Role matrices for the connectivity: mb for base connectivity

mb base connectivity X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17 X18 X19 X20 X21 X22 X23 X24 X25 X26 X27 X28 X29 X30 X31 X32

AaskPA PAaskB BreplyPA PAreplyA AnotifytoPA PAtransfertoB AaskB BreplyA AnotifytoB indirectcase directcase WAaskPA,PAaskB WPAaskB,BreplyPA WBreplyPA,PAreplyA WPAreplyA,AnotifytoPA WAnotifytoPA,PAtransfertoB WAaskB,BreplyA WBreplyA,AnotifytoB HWAaskPA,PAaskB HWPAaskB,BreplyPA HWBreplyPA,PAreplyA HWPAreplyA,AnotifytoPA HWAnotifytoPA,PAtransfertoB HWAaskB,BreplyPA HWBreplyA,AnotifytoB MWAaskPA,PAaskB MWPAaskB,BreplyPA MWBreplyPA,PAreplyA MWPAreplyA,AnotifytoPA MWAnotifytoPA,PAtransfertoB MWAaskB,BreplyPA MWBreplyA,AnotifytoB

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X12 X13 X14 X15 X16 X17 X18 X12 X13 X14 X15 X16 X17 X18 X12 X13 X14 X15 X16 X17 X18

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4.8.1 Role Matrices for Connectivity Characteristics The connectivity characteristics are specified by role matrices mb and mcw shown in Figs. 4.11 and 4.12. Role matrix mb lists the other states (at the same or lower level) from which the state gets its incoming connections, whereas in role matrix mcw the connection weights are listed for these connections. Nonadaptive connection weights are indicated in mcw by a number (in a green shaded cell), but adaptive connection weights are indicated by a reference to the (self-model) state representing the adaptive value (in a peach-red shaded cell). This can be seen for states X2 to X6 (with self-model states X12 to X16 ) and states X8 and X9 (with self-model states X17 and X18 ). Fig. 4.12 Role matrices for the connectivity: mcw for connection weights

mcw X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17 X18 X19 X20 X21 X22 X23 X24 X25 X26 X27 X28 X29 X30 X31 X32

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AaskPA PAaskB BreplyPA PAreplyA AnotifytoPA PAtransfertoB AaskB BreplyA AnotifytoB indirectcase directcase WAaskPA,PAaskB WPAaskB,BreplyPA WBreplyPA,PAreplyA WPAreplyA,AnotifytoPA WAnotifytoPA,PAtransfertoB WAaskB,BreplyA WBreplyA,AnotifytoB HWAaskPA,PAaskB HWPAaskB,BreplyPA HWBreplyPA,PAreplyA HWPAreplyA,AnotifytoPA HWAnotifytoPA,PAtransfertoB HWAaskB,BreplyPA HWBreplyA,AnotifytoB MWAaskPA,PAaskB MWPAaskB,BreplyPA MWBreplyPA,PAreplyA MWPAreplyA,AnotifytoPA MWAnotifytoPA,PAtransfertoB MWAaskB,BreplyPA MWBreplyA,AnotifytoB

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4.8.2 Role Matrices for Aggregation Characteristics The network characteristics for aggregation are defined by the selection of combination functions from the library and values for their parameters. In role matrix mcfw it is specified by weights which state uses which combination function; see Fig. 4.13. In role matrix mcfp (see Fig. 4.14) it is indicated what the parameter values are for the chosen combination functions. Some of them are adaptive, as can be seen in the rows from X12 to X18 (see the indications for the persistence factors μ represented by the self-model states X26 to X32 ). Fig. 4.13 Role matrices for the aggregation characteristics: combination function weights

mcfw X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17 X18 X19 X20 X21 X22 X23 X24 X25 X26 X27 X28 X29 X30 X31 X32

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AaskPA PAaskB BreplyPA PAreplyA AnotifytoPA PAtransfertoB AaskB BreplyA AnotifytoB indirectcase directcase WAaskPA,PAaskB WPAaskB,BreplyPA WBreplyPA,PAreplyA WPAreplyA,AnotifytoPA WAnotifytoPA,PAtransfertoB WAaskB,BreplyA WBreplyA,AnotifytoB HWAaskPA,PAaskB HWPAaskB,BreplyPA HWBreplyPA,PAreplyA HWPAreplyA,AnotifytoPA HWAnotifytoPA,PAtransfertoB HWAaskB,BreplyPA HWBreplyA,AnotifytoB MWAaskPA,PAaskB MWPAaskB,BreplyPA MWBreplyPA,PAreplyA MWPAreplyA,AnotifytoPA MWAnotifytoPA,PAtransfertoB MWAaskB,BreplyPA MWBreplyA,AnotifytoB

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Fig. 4.14 Role matrices for the aggregation characteristics: combination function parameters

4.8.3 Role Matrices for Timing Characteristics In Fig. 4.15, the role matrix ms for speed factors is shown, which lists all speed factors. Next to it the list of initial values can be found. Also here, a few them are adaptive: the speed factors of X12 to X18 are represented by self-model states X19 to X25 . In Fig. 4.15, also the initial values of all states used in the example simulation are shown.

4 Modeling Mental Models: Their Use, Adaptation and Control Fig. 4.15 Role matrices for the timing characteristics and initial values: ms for speed factors

ms

speed factors

X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17 X18 X19 X20 X21 X22 X23 X24 X25 X26 X27 X28 X29 X30 X31 X32

AaskPA PAaskB BreplyPA PAreplyA AnotifytoPA PAtransfertoB AaskB BreplyA AnotifytoB indirectcase directcase WAaskPA,PAaskB WPAaskB,BreplyPA WBreplyPA,PAreplyA WPAreplyA,AnotifytoPA WAnotifytoPA,PAtransfertoB WAaskB,BreplyA WBreplyA,AnotifytoB HWAaskPA,PAaskB HWPAaskB,BreplyPA HWBreplyPA,PAreplyA HWPAreplyA,AnotifytoPA HWAnotifytoPA,PAtransfertoB HWAaskB,BreplyPA HWBreplyA,AnotifytoB MWAaskPA,PAaskB MWPAaskB,BreplyPA MWBreplyPA,PAreplyA MWPAreplyA,AnotifytoPA MWAnotifytoPA,PAtransfertoB MWAaskB,BreplyPA MWBreplyA,AnotifytoB

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1 1 1 1 1 1 1 1 1 1 1 X19 X20 X21 X22 X23 X24 X25 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17 X18 X19 X20 X21 X22 X23 X24 X25 X26 X27 X28 X29 X30 X31 X32

AaskPA PAaskB BreplyPA PAreplyA AnotifytoPA PAtransfertoB AaskB BreplyA AnotifytoB indirectcase directcase WAaskPA,PAaskB WPAaskB,BreplyPA WBreplyPA,PAreplyA WPAreplyA,AnotifytoPA WAnotifytoPA,PAtransfertoB WAaskB,BreplyA WBreplyA,AnotifytoB HWAaskPA,PAaskB HWPAaskB,BreplyPA HWBreplyPA,PAreplyA HWPAreplyA,AnotifytoPA HWAnotifytoPA,PAtransfertoB HWAaskB,BreplyPA HWBreplyA,AnotifytoB MWAaskPA,PAaskB MWPAaskB,BreplyPA MWBreplyPA,PAreplyA MWPAreplyA,AnotifytoPA MWAnotifytoPA,PAtransfertoB MWAaskB,BreplyPA MWBreplyA,AnotifytoB

1 0 0 0 0 0 0 0 0 0 0 0 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0 0 0 0 0 0 0 0 0 0 0 0 0 0

References Abraham, W.C., Bear, M.F.: Metaplasticity: the plasticity of synaptic plasticity. Trends Neurosci. 19(4), 126–130 (1996) Bhalwankar, R., Treur, J.: Modeling learner-controlled mental model learning processes by a secondorder adaptive network model. PLoS ONE 16(8): e0255503 (2021) Canbalo˘glu, G., Treur, J.: Modeling context-sensitive metacognitive control of focusing on a mental model during a mental process. In: Silhavy, R., Silhavy, P., Prokopova, Z. (eds.) Data Science and Intelligent Systems. Proceedings of CoMeSySo 2021. Lecture Notes in Networks and Systems, vol. 231, pp. 992–1009. Springer Nature (2021). https://www.researchgate.net/publication/353 667091 Canbalo˘glu, G., Treur, J., Wiewiora, A. (eds.).: Computational Modeling of Multilevel Organizational Learning and its Control Using Self-Modeling Network Models. Springer Nature (2023) (this volume) Craik, K.J.W.: The nature of explanation. Cambridge, MA: University Press. (1943). Darling-Hammond, L., Austin, K., Cheung, M., Martin, D.: Thinking about Thinking: Metacognition (2008) Flavell, J.H.: Metacognition and cognitive monitoring: a new area of cognitive–developmental inquiry. Am. Psychol. 34(10), 906–911 (1979) Gentner, D., Stevens, A.L.: Mental Models. Erlbaum, Hillsdale NJ (1983) Greca, I.M., Moreira, M.A.: Mental models, conceptual models, and modelling. Int. J. Sci. Educ. 22(1), 1–11 (2000) Hebb, D.O.: The Organization of Behavior: A Neuropsychological Theory. Wiley (1949)

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Koriat, A.: Metacognition and consciousness. In: Zelavo, P.D., Moscovitch, M., Thompson, E. (eds.) Cambridge Handbook of Consciousness. Cambridge University Press, New York (2007) Magerl, W., Hansen, N., Treede, R.D., Klein, T.: The human pain system exhibits higher-order plasticity (metaplasticity). Neurobiol. Learn. Mem. 154, 112–120 (2018) Mahdavi, M.: An overview: metacognition in education. Int. J. Multidisc. Curr. Res. 2, 529–535 (2014) Pintrich, P.R.: The role of goal orientation in self-regulated learning. In: Boekaerts, M., Pintrich, P., Zeidner, M. (eds.) Handbook of Self-Regulation Research and Applications, pp. 451–502. Academic Press, Orlando, FL (2000) Robinson, B.L., Harper, N.S., McAlpine, D.: Meta-adaptation in the auditory midbrain under cortical influence. Nat. Commun. 7, 13442 (2016) Seel, N.M.: Mental models in learning situations. In: Advances in Psychology, vol. 138, pp. 85–107. North-Holland, Amsterdam (2006) Shannon, S.V.: Using metacognitive strategies and learning styles to create self-directed learners. Inst. Learn. Styles J. 1, 14–28 (2008) Shih, Y.F. Alessi, S.M.: Mental models and transfer of learning in computer programming. Journal of Research in Computing Education, 26(2), 154–175 (1993) Sjöström, P.J., Rancz, E.A., Roth, A., Hausser, M.: Dendritic excitability and synaptic plasticity. Physiol. Rev. 88(769–840), 2008 (2008) Skemp, R.R.: The Psychology of Learning Mathematics. Penguin Books, Harmondsworth (1971) Treur, J.: Network-Oriented Modeling: Addressing Complexity of Cognitive. Springer Publishers, Affective and Social Interactions (2016) Treur, J.: Multilevel network reification: representing higher order adaptivity in a network. In: Aiello, L., Cherifi, C., Cherifi, H., Lambiotte, R., Lió, P., Rocha, L. (eds.) Proceedings of the 7th International Conference on Complex Networks and their Applications, Complex Networks’18, vol. 1. Studies in Computational Intelligence, vol. 812, pp. 635–651, Springer Nature (2018) Treur, J.: Modeling higher-order adaptivity of a network by multilevel network reification. Netw. Sci. 8, S110–S144 (2020a) Treur, J.: Network-Oriented Modeling for Adaptive Networks: Designing Higher-Order Adaptive Biological, Mental and Social Network Models. Springer Nature Publishing, Cham, Switzerland (2020b) Treur, J.: An adaptive network model covering metacognition to control adaptation for multiple mental models. Cogn. Syst. Res. 67, 18–27 (2021) Treur, J., Van Ments, L. (eds.): Mental Models and their Dynamics, Adaptation and Control: A Self-Modeling Network Modeling Approach. Springer Nature, Cham, Switzerland (2022) Van Gog, T., Paas, F., Marcus, N., Ayres, P., Sweller, J.: The mirror neuron system and observational learning: Implications for the effectiveness of dynamic visualizations. Educational Psychology Review 21(1), 21-30 (2009) Van Ments, L., Treur, J.: Reflections on dynamics, adaptation and control: a cognitive architecture for mental models. Cogn. Syst. Res. 70, 1–9 (2021) Van Ments, L., Treur, J., Klein, J., Roelofsma, P.H.M.P.: A second-order adaptive network model for shared mental models in hospital teamwork. In: Nguyen, N.T., et al. (eds.) Proceedings of the 13th International Conference on Computational Collective Intelligence, ICCCI’21. Lecture Notes in AI, vol 12876, pp 126–140. Springer Nature (2021) Yi, M.Y., Davis, F.D.: Developing and validating an observational learning model of computer software training and skill acquisition. Information Systems Research 14(2), 146–169 (2003)

Part III

Overall Computational Network Models of Organisational Learning

This part provides an introduction and illustration of the first basic models. It addresses first steps in formalisation and computational modeling of multilevel organisational learning, which is one of the major challenges for the area of organisational learning. Various conceptual learning mechanisms, identified in the literature, are formalised as computational mechanisms that provide mathematical formalisations to enable computer simulation. The formalisations have been expressed using the self-modeling network modeling approach introduced in Part II. Mental models, also introduced in Part II, are considered as a vehicle for both individual learning and organisational learning.

Chapter 5

From Conceptual to Computational Mechanisms for Multilevel Organisational Learning Gülay Canbalo˘glu, Jan Treur, and Anna Wiewiora

Abstract This chapter addresses formalisation and computational modeling of multilevel organisational learning, which is one of the major challenges for the area of organisational learning. It is discussed how various conceptual mechanisms in multilevel organisational learning as identified in the literature, can be formalised by computational mechanisms which provide mathematical formalisations that enable computer simulation. The formalisations have been expressed using a self-modeling network modeling approach. Keywords Organisational learning · Mechanisms · Computational modeling · Self-modeling networks

5.1 Introduction Multilevel organisational learning is a complex adaptive process with multiple levels and nested cycles between them. As discussed in Chaps. 2 and 4 of this volume (Canbalo˘glu et al. 2023b), much literature is available analysing and describing in a conceptual manner the different conceptual mechanisms involved, e.g., (Kim 1993; Crossan Lane White 1999; Wiewiora et al. 2019, 2020; Iftikhar and Wiewiora 2021). However, mathematical or computational formalisation of organisational learning in G. Canbalo˘glu · J. Treur (B) Social AI Group, Department of Computer Science, Vrije Universiteit Amsterdam, Amsterdam, Netherlands e-mail: [email protected] G. Canbalo˘glu e-mail: [email protected] A. Wiewiora School of Management, QUT Business School, Queensland University of Technology, Brisbane, Australia e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 G. Canbalo˘glu et al. (eds.), Computational Modeling of Multilevel Organisational Learning and Its Control Using Self-modeling Network Models, Studies in Systems, Decision and Control 468, https://doi.org/10.1007/978-3-031-28735-0_5

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a systematic manner was a serious challenge. Successfully addressing this challenge requires: • An overall mathematical and computational modeling approach able to handle the interplay of the different levels, adaptations and mechanisms involved • For the conceptual mechanisms involved mathematical and computational formalisation as computational mechanisms A progress has been made in recent years to develop a mathematical and computational model to handle multilevel dynamics via the self-modeling network approach described in (Treur 2020a, b). This approach has successfully been applied to the use, adaptation and control of mental models in (Treur and Van Ments 2022). For the second bullet, for many of the identified conceptual mechanisms from the literature, it is discussed in the current chapter how they can be modeled mathematically and computationally as computational mechanisms within a self-modeling network format. In Sect. 5.2 an overview is given of conceptual mechanisms and how they can be related to computational mechanisms. Section 5.3 briefly describes the self-modeling network modeling approach used for computational formalisation. In Sect. 5.4, a few examples of computational mechanisms for the level of individuals are described more in detail. Section 5.5 discusses more complex examples of computational models for feed forward and feedback learning that form bridges between the levels.

5.2 Overview: From Conceptual to Computational Mechanisms In this section, a global overview of conceptual organisational learning mechanisms is described and supported by relevant references. Some of these conceptual mechanisms do not have pointers yet to computational mechanisms and can be considered items for a research agenda. Organisations operate as a system or organism of interconnected parts. Similarly, organisational learning is considered a multilevel phenomenon involving dynamic connections between individuals, teams or projects and organisation (Fiol and Lyles 1985; Crossan et al. 1999); see Fig. 5.1. Due to the complex and changing environment within which organisations operate, the learning constantly evolves and some learning may become obsolete. Organisational learning is a vital means of achieving strategic renewal and continuous improvement, as it allows an organisation to explore new possibilities as well as exploit what they have already learned (March 1991). Organisational learning is a dynamic process that occurs in feed forward and feedback directions. Feed forward learning assists in exploring new knowledge by individuals and teams and institutionalizing this knowledge at the organisational level (Crossan et al. 1999). Feedback learning helps in exploiting existing and institutionalized knowledge, making it available for

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Fig. 5.1 Organisational learning: multiple levels and nested cycles (with depth 3) of interactions

teams and individuals. The essence of organisational learning is best captured in the following quote: Organisations are more than simply a collection of individuals; organisational learning is different from the simple sum of the learning of its members. Although individuals may come and go, what they have learned as individuals or in groups does not necessarily leave with them. Some learning is embedded in the systems, structures, strategy, routines, prescribed practices of the organisation, and investments in information systems and infrastructure. (Crossan et al. 1999, p. 529).

Individuals can learn by reflecting on their own past experiences, learn on the job (learning by doing), by observing others and from others, or by exploiting existing knowledge and applying that knowledge to other situations and contexts. Individuals can also learn by exploring new insights through pattern recognition, deep evaluation of a problem at hand, materialised in the ‘aha’ moment, when a new discovery is made. It is highly subjective and deeply rooted in individual experiences (Crossan et al. 1999). Teams learn by interpreting and integrating individual learnings by interpreting and sharing knowledge through the use of language, mind maps, images, or metaphors and thus jointly developing new shared mental models (Crossan et al. 1999). Team level learning encompasses integration of possibly diverse, conflicting meanings, in order to obtain a shared understanding of a state or a situation. The developed shared understanding results in taking coordinated action by the team members (Crossan et al. 1999). Eventually, these shared actions by individuals and teams are turned into established routines, deeply embedded into organisational cultures, and/or captured in new processes or norms. From a computational perspective, such a process of shared mental model formation out of a number of individual mental models may be considered to relate to some specific form of knowledge integration or (feedforward) aggregation of the individual mental models. In order for the organisational learning to occur, it has to be triggered by learning mechanisms, which are defined as apparatus for enabling learning. A recent review

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by Wiewiora et al. (2019) and their subsequent empirical investigation (Wiewiora et al. 2020) identified organisational and situational mechanisms affecting project learning in a project-based context. Organisational learning mechanisms include culture, practices, systems, leadership and structure. From the organisational learning perspective, organisational systems are designed to capture knowledge, which was developed locally by teams or projects, and captured into manuals or guidelines. These can represent knowledge management systems such as centralised knowledge repositories or specialised software used to collect, store and access organisational knowledge. Future learnings of individuals based on this in general may be considered another specific form of (feedback) aggregation, this time of the organisation level mental model with the already available individual mental model; an extreme form of this is fully replacing the own mental model by the organisation mental model. Organisational practices include coaching and mentoring sessions for building competencies. Coaching and mentoring occurs on individual level, where individuals have opportunities to learn from more experienced peers or teachers. Coaching and mentoring can also facilitate organisational to individual level learning. These experts have often accumulated, through the years, a vast of organisational knowledge and experiences, in which case they can be also sharing organisational learnings. Furthermore, training sessions provide opportunities for developing soft and technical skills. During the sessions, a facilitator shares their own soft or technical skills or organisational knowledge with individuals or teams. Leaders have been described as social architects and orchestrators of learning processes (Hannah and Lester 2009). Leaders who limit power-distances and encourage input and debate promote an environment conducive to openness and sharing, hence facilitating individual to team learning (Edmondson 2002). Meanwhile, self-protected leaders are more likely to use their position of power and impose control, hence restricting collective learning opportunities. When it comes to the organisational structure, decentralised structures promote rapid diffusion of ideas and encourage the exploration of a more diverse range of solutions (Benner and Tushman 2003). The ideal structure appears to be the one that is loosely coupled, providing some degree of team separation, while ensuring weak connections between teams and the organisation (Fang et al. 2010). A situational mechanism affecting multilevel learning is occurrence of major events (Wiewiora et al. 2019): significant situations, positive or negative, that trigger immediate reaction (Madsen 2009). There is limited research that systematically and empirically investigates mechanisms that trigger learning flows within and between levels. Tables 5.1, 5.2, 5.3 synthesise existing research into multilevel learning and offers (in the first three columns of Tables 5.1, 5.2, 5.3) a list of learning mechanisms facilitating multilevel learning flows. This chapter demonstrates one of the first attempts to translate these (conceptual) mechanisms into computational mechanisms (in the last three columns of Tables 5.1, 5.2, 5.3) and propose a new computational modeling approach (briefly summarized in Sect. 5.3) that can handle the interplay between the levels and consider learning mechanisms that trigger learning flows between the levels. Table 5.1 addresses the learning at the individual level, in Fig. 5.1 indicated by the circular arrow from Individuals to Individuals. A number of examples of conceptual

Examples

Individuals are observing themselves while they are performing a task

Individuals are learning by reflecting on their own past experiences

Learning by observing oneself during own task execution

Learning from past experiences

Wiewiora et al. (2019, 2020)

Learning from internal communication channels and aggregation

Learning from more senior and experienced people their individual ‘tricks of the trade’ via coaching and mentoring

Coaching and mentoring

Learning based on counterfactual thinking

Hebbian learning for mirroring and internal simulation of an individual mental model

Hebbian learning during internal simulation of an individual mental model

Computational mechanisms

Hebbian learning for mirroring and internal simulation of an individual mental model

Iftikhar and Wiewiora (2021)

Iftikhar and Wiewiora (2021)

Relevant references

Learning by observing Individuals are observing how Iftikhar and others during their task their peers are performing a Wiewiora (2021) execution task

Individual: between persons

Mental simulation (sometimes called visualisation) of individual mental models to memorize them better

Learning by internal simulation

Individual: within persons

Conceptual mechanisms

Table 5.1 Conceptual and computational mechanisms for learning at the level of individuals Relevant references

Doctor explains own mental model to nurse as preparation for surgery

Observation each others’ task execution by nurses and doctors in a hospital operation room

Counterfactual internal what-if simulation of nearest alternative scenarios

Observation own task execution by nurses and doctors in a hospital operation room

(continued)

Bhalwankar and Treur (2021a); Van Ments et al. (2021)

Bhalwankar and Treur (2021a); Van Ments et al. (2021, 2022)

Bhalwankar and Treur (2021b)

Bhalwankar and Treur (2021a); Van Ments et al. (2021, 2022)

Mental simulation of Canbalo˘glu et al. individual mental models (2022, 2023a) for surgery in a hospital before shared mental model formation and after learning from a shared mental model

Examples

5 From Conceptual to Computational Mechanisms for Multilevel … 77

Training sessions in which a Wiewiora et al. facilitator shares their own soft (2019, 2020) and technical skills with individuals

Training sessions

Relevant references

Examples

Conceptual mechanisms

Table 5.1 (continued)

Learning from internal communication channels and aggregation

Computational mechanisms Experienced doctor explains own mental model to team

Examples

Bhalwankar and Treur (2021a); Van Ments et al. (2021)

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78 G. Canbalo˘glu et al.

Examples

Individuals mobilise to Wiewiora et al. (2019) react and find solutions to major events. The best solution is selected and institutionalised by the organisation

Occurrence of major events

Training sessions

Training sessions in Wiewiora et al. (2019, which a facilitator shares 2020) their own soft and technical skills with teams or projects

From individuals to teams or projects

Individuals share their mental models and institutionalise a shared mental model for the organisation

Wiewiora et al. (2019, 2020)

Relevant references

Shared organisation mental model formation and improvement based on individual mental models

From individuals to organisation

Feedforward learning

Conceptual mechanisms

Feedforward aggregation of individual mental models (and perhaps an existing shared organisation mental model)

Feedforward aggregation of individual mental models for formation or improvement of shared mental models

Feedforward aggregation of individual mental models for formation or improvement of shared mental models

Computational mechanisms

Relevant references

(continued)

Aggregating individual Canbalo˘glu et al. (2023a) mental models for surgery by hospital teams to form a shared team or project mental model

Aggregating individual Canbalo˘glu and Treur mental models from a (2021, 2022); nurse and a doctor to Canbalo˘glu et al. (2022) form a shared mental model of an intubation

Aggregating individual Canbalo˘glu and Treur mental models from a (2021, 2022); nurse and a doctor to Canbalo˘glu et al. (2022) form a shared mental model of an intubation

Examples

Table 5.2 Conceptual and computational mechanisms for feedforward learning: from individual to teams or projects or to the organisation and from teams or projects to the organisation

5 From Conceptual to Computational Mechanisms for Multilevel … 79

Teams mobilise to react and find solutions to major events. The best solution is selected and institutionalised by the organisation

Occurrence of major events

Feedforward aggregation of team or project mental models to obtain a shared organisation mental model

Feedforward aggregation of individual mental models (and perhaps an existing shared organisation mental model)

Computational mechanisms

Wiewiora et al. (2019) Feedforward aggregation of team or project mental models to obtain a shared organisation mental model

Teams capture their Crossan et al. (1999); learnings into manuals or Iftikhar and Wiewiora guidelines, which then (2020) inform new organisational practices

Formalising team learnings

From teams or projects to organisation

Individuals of a team Kim (1993); Iftikhar while working together and Wiewiora (2021) are sharing their individual mental models and creating a new shared mental model by discussing and jointly solving a problem in hand

Learning by working together and joint-problem solving

Relevant references

Examples

Conceptual mechanisms

Table 5.2 (continued) Relevant references

Aggregating team or project mental models for surgery by hospital teams to form a shared organisation mental model

Aggregating team or project mental models for surgery by hospital teams to form a shared team or project mental model

Canbalo˘glu et al. (2023a)

Canbalo˘glu et al. (2023a)

Aggregating individual Canbalo˘glu et al. (2023a) mental models for surgery by hospital teams to form a shared organisation mental model

Examples

80 G. Canbalo˘glu et al.

Examples

Relevant references

Crossan et al. (1999); Iftikhar and Wiewiora (2021)

Individuals access organisational knowledge management systems, policies and procedures to inform their practices

Provision of courses during Wiewiora et al., (2019; Learning from internal which a facilitator shares communication channels 2020) organisational knowledge to and feedback aggregation individuals

Organisational systems

Training sessions

Training sessions

Provision of courses during Wiewiora et al., (2019; Learning from internal which a facilitator shares communication channels 2020) organisational knowledge to and feedback aggregation teams or projects

Teams of doctors and nurses learning a team mental model from a shared organisation mental model for intubation

Individuals (doctors and nurses) learning an own mental model from a shared organisation mental model for intubation

Learning from internal Individuals (doctors and communication channels nurses) learning an own and feedback aggregation mental model from a shared organisation mental model for intubation

Wiewiora et al. (2019, 2020)

Learning from experienced people who have through years accumulated organisational knowledge

From organisation to teams or projects

Examples

Learning from internal Individuals (doctors and communication channels nurses) learning an own and feedback aggregation mental model from a shared organisation mental model for intubation

Computational mechanisms

Coaching and mentoring

Instructional learning from a shared organisation mental model

From organisation to individuals

Feedback learning

Conceptual mechanisms

(continued)

Canbalo˘glu et al. (2023a)

Canbalo˘glu et al. (2022)

Canbalo˘glu et al. (2022)

Canbalo˘glu et al. (2022)

Relevant references

Table 5.3 Conceptual and computational mechanisms for feedback learning: from the organisation to individuals and to teams or projects and from teams or projects to individuals

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Examples

Individuals of a team while working together are sharing their individual mental models and creating a new shared mental model by discussing and jointly solving a problem in hand

Provision of courses during which a facilitator shares team knowledge to individuals

Learning by working together and joint-problem solving

Training sessions

From teams or projects to individuals

Conceptual mechanisms

Table 5.3 (continued)

Wiewiora et al. (2019; 2020)

Kim (1993); Iftikhar and Wiewiora (2021)

Relevant references

Examples

Learning from internal Individuals (doctors and communication channels nurses) learning an own and feedback aggregation mental model from a shared team mental model for intubation

Learning from internal Individuals (doctors and communication channels nurses) learning an own and feedback aggregation mental model from a shared team mental model for intubation

Computational mechanisms

Canbalo˘glu et al. (2022)

Canbalo˘glu et al. (2023a)

Relevant references

82 G. Canbalo˘glu et al.

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mechanisms are shown in the different rows and for each of them it is indicated which computational mechanisms have been found that can be associated to them. These computational mechanisms are based on findings from neuroscience, such as Hebbian learning (Hebb 1949) and mirroring, e.g., (Iacoboni 2008; Keysers and Gazzola 2014; Rizzolatti and Sinigaglia 2008; Van Gog et al. 2009). Tables 5.2 and 5.3 address the mechanisms behind the arrows from left to right and vice versa connecting different levels in Fig. 5.1. Here the arrows from left to right indicate feedforward learning (see Table 5.2) and the arrows from right to left indicate feedback learning (Table 5.3). The three different sections in Table 5.2, relate to arrows from individuals to teams or projects, from teams or projects to the organisation, and from individuals directly to the organisation level. Similarly, the three different sections in Table 5.3, relate to the arrows in Fig. 5.1 from the organisation to teams or projects, from teams or projects to individuals, and from the organisation level directly to individuals. After introducing the computational modeling approach based on self-modeling networks in Sect. 5.3, in the subsequent Sects. 5.4 and 5.5 for a number of the computational mechanisms indicated in Tables 5.1, 5.2, 5.3 more details will be given.

5.3 The Self-Modeling Network Modeling Approach Used In this section, the network-oriented modeling approach used is briefly introduced. A temporal-causal network model is characterised by the following; here X and Y denote nodes of the network that have activation levels that can change over time, also called states (Treur 2020b): • Connectivity characteristics: Connections from a state X to a state Y and their weights ωX,Y • Aggregation characteristics: For any state Y, some combination function cY (..) defines the aggregation that is applied to the impacts ωX,Y X(t) on Y by its incoming connections from states X • Timing characteristics: Each state Y has a speed factor ηY defining how fast it changes for given causal impact. The following canonical difference (or related differential) equations are used for simulation; they incorporate these network characteristics ωX,Y , cY (..), ηY in a standard numerical format: Y (t + /\t) = Y (t) + ηY [cY (ω X 1 ,Y X 1 (t), . . . , ω X k ,Y X k (t)) − Y (t)]/\t

(5.1)

for any state Y, where X 1 to X k are the states from which Y gets incoming connections. Modeling and simulation are supported by a dedicated software environment described in (Treur 2020b, Ch. 9). It comes with a combination function library with currently around 65 combination functions. Some examples of these combination functions that are used here can be found in Table 5.4.

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Table 5.4 Examples of combination functions for aggregation available in the library Name

Formula

Advanced logistic sum alogisticσ,τ (V 1 , …,V k )

[

Scaled maximum smaxλ (V 1 , …, V k )

max(V 1 , …, V k )/λ

Euclidean eucln,λ (V 1 , …, Vk) Scaled geometric mean sgeomeanλ (V 1 , …, V k )

Parameters 1

1+e−σ(V1 +···+Vk −τ)

 n

 k

−

1 ] 1+eστ)

(1 + e−στ ) Steepness σ > 0; excitability threshold τ Scaling factor λ

V1 n +···+Vk n λ

Order n; scaling factor λ

V1 ∗···∗Vk λ

Scaling factor λ

Hebbian learning hebbμ (V 1 , V 2 , V 3 )

V1 ∗ V2 (1 − V3 ) + μV3

V 1 ,V 2 activation levels of the connected states; V 3 activation level of the self-model state for the connection weight; persistence factor μ

Maximum composed with Hebbian learning max-hebbμ (V 1 , …, V k )

max(hebbμ (V1 , V2 , V3 ), V4 , . . . , V k )

V 1 ,V 2 activation levels of the connected states; V 3 activation level of the self-model state for the connection weight; persistence factor μ

Applying the concept of self-modeling network, the network-oriented approach can also be used to model adaptive networks easily; see (Treur 2020a, b, c). By the addition of new states to the network which represent certain network characteristics, such characteristics become adaptive. These additional states are called self-model states (or reification states) and they are depicted at a next level, distinguished from the base level of the network. For instance, the weight ωX,Y of a connection from one state X to another state Y is represented by an additional self-model state WX,Y . In such a way, by including self-model states any network characteristic can be made adaptive. As another example, an adaptive speed factor ηY can be modeled by a self-model state HY . The self-modeling network concept can be applied iteratively, thus creating multiple orders of self-models (Treur 2020a, b, c). A second-order selfmodel can model an adaptive speed factor ηW X,Y of a first-order self-model state WX,Y by a second-order self-model state HW X,Y . Moreover, a persistence factor μW X,Y of WX,Y used for Hebbian learning can be modeled by a second-order self-model state MW X,Y .

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5.4 Some Examples of Computational Mechanisms In this section and the next one, for a number of conceptual mechanisms it will be shown in more detail how they can be related to computational mechanisms in terms of the self-modeling network format. Some examples from (Canbalo˘glu and Treur 2021, 2022; Canbalo˘glu et al. 2021, 2023a) will be briefly discussed, e.g. (see also Fig. 5.1 and Tables 5.1, 5.2, 5.3): • Learning by internal simulation: individual mental model learning based on internal simulation (conceptual) modeled by Hebbian learning (computational) • Learning by observation: individual mental model learning based on observation (conceptual) and mirroring combined with Hebbian learning (computational) • Learning by communication: individual mental model learning based on communication with another individual (conceptual) modeled by aggregation of communicated information with already available information (computational) • Feedforward learning: shared team or organisation mental model learning based on an individual or shared team mental model (conceptual) modeled by aggregation of multiple individual mental models • Feedback learning: individual mental model learning based on a shared team or organisation mental model (conceptual) modeled by aggregation of multiple shared team mental models In the current section the first three bullets (all relating to Table 5.1) are addressed as mechanisms. In Sect. 5.5 the last two bullets (relating to Tables 5.2 and 5.3, respectively) are addressed and it is also shown how the mechanisms involved can play their role in an overall multilevel organisation learning process. The mental models used as example are kept simple, they concern tasks a, b, c, d which are assumed to be linearly connected. Learning by internal simulation: Hebbian learning for an individual mental model In Fig. 5.2a (see also Table 5.1) it is shown how internal simulation (Hesslow 2002, 2012) of a mental model by person B (triggered by context state con1 ) activates subsequently the mental model states a_B to d_B of B and these activations in turn activate Hebbian learning of their mutual conection weights. Here for the Hebbian learning (Hebb 1949), the self-model state WX,Y for the weight of the connection from X to Y, uses the combination function hebbμ (V 1 , V 2 , W ) shown in Table 5.4. More specifically, this function hebbμ (V 1 , V 2 , W ) is applied to the activation values V 1 , V 2 of X and Y and the current value W of WX,Y . To this end upward (blue) connections are included in Fig. 5.2a (also a connection to WX,Y itself is assumed but usually such connections are not depicted). The (pink) downward arrow from WX,Y to Y depicts how the obtained value of WX,Y is actually used in activation of Y. Thus, the mental model is learnt. If the persistence parameter μ is 1, the learning result persists forever; if μ < 1, then forgetting takes place. For example, when μ = 0.9, per time unit 10% of the learnt result is lost.

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Fig. 5.2 a Upper. Learning by internal simulation: Hebbian learning during internal simulation b Middle. Learning by observation: Hebbian learning after mirroring of the world states, c Lower. Learning by communication and by observation combined: learning by communication from person A to person B combined with Hebbian learning based on mirroring within person B

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Learning by observation: observing, mirroring and Hebbian learning of an individual mental model For learning by observation, see Fig. 5.2b (see also Table 1). Here mirror links are included: the (black) horizontal links from World States a_WS to d_WS to mental model states a_B to d_B within the base (pink) plane. When the world states are activated, through these mirror links they in turn activate B’s mental model states which in their turn activate Hebbian learning like above; this is modeled, e.g., in (Bhalwankar and Treur 2021a). Learning by communication: receiving communication and aggregation in an individual mental model See Fig. 5.2c for a combined form of learning by communication and by observation as modeled, e.g., in (Bhalwankar and Treur 2021a); see also Table 5.1. The horizontal links within the upper (blue) plane model communication from A to B. This communication provides input from the mental model self-model states Wa_A,b_A to Wa_A,b_A of A to the mental model self-model states Wa_B,b_B to Wa_B,b_B of B; this input is aggregated within these self-model states of B’s mental model using the maxhebbμ combination function (see Table 5.4). This function takes the maximum of the communicated value originating from Wx_A,y_A and the current value of Wx_B,y_B that is being learnt by B through Hebbian learning. More complex examples covering multiple mechanisms for feedforward and feedback learning relating to Table 5.2 and 5.3 are shown in Sect. 5.5.

5.5 Computational Models for Feed Forward and Feedback Learning In this section, feed forward and feedback learning mechanisms (see also Fig. 5.1) in computational models in self-modeling network format will be explained with two examples from (Canbalo˘glu et al. 2023a) and (Canbalo˘glu and Treur 2022); see the network pictures in Figs. 5.3 and 5.4. For more details of these two examples, see also Chap. 7 (Canbalo˘glu et al. 2023b) and Chap. 10 (Canbalo˘glu and Treur 2023b) of this volume. These are the mechanisms listed as the last two bullets of the list of building blocks of organisational learning process in the first paragraph of the Sect. 4. Feedforward learning: formation of a shared mental model by individuals or teams In Fig. 5.3, self-model W-states representing the weights of connections between mental model states at the base level and horizontal W-to-W connections between them are depicted in the first-order self-model level (blue plane). The rightward connections from W-states of individuals’ mental models to W-states of teams’ shared mental models and from W-states of teams’ shared mental models to W-states

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Second-order self-model level for control of network adaptation

First-order self-model level for network adaptation

Base level

Fig. 5.3 The connectivity within the first-order self-model level for the adaptation of the mental models by formation of shared team and organisation mental models (links from left to right: feedforward learning) and by instructional learning of individual mental models and shared team mental models from these shared mental models (links from right to left: feedback learning). (Canbalo˘glu et al. 2023a)

Fig. 5.4 An example involving context-sensitive control of aggregation in the process of shared mental model formation based on 16 context states (grey ovals) and four options of combination functions for aggregation (Canbalo˘glu and Treur 2021)

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of the organisation’s shared mental model trigger the formation (by a form of aggregation) of shared mental models for teams and for the organisation by feedforward learning. Feedback learning: learning of individuals from shared mental models In Fig. 5.3, self-model W-states of individuals’ mental models (on the left) have connections coming from self-model W-states of their corresponding teams’ shared mental models, and these team W-states have connections coming from self-model W-states of the organisation’s shared mental model. These leftward connections are used for individuals’ improvements on their knowledge with the help of the shared mental models: the aggregated knowledge returns to the individuals by feedback learning. Feedforward learning requires a combination function for aggregation of separate individual mental models to form a team’s shared mental model, and a combination function for aggregation of different team mental models to form the organisation’s shared mental model. This aggregation can take place always according to one and the same method (modeled by one combination function), like in Fig. 5.3, or it can be adaptive according to the context. For real-life cases, the formation of a shared mental model is not same for different scenarios. Thus, making the aggregation adaptive improves the model in terms of applicability and accuracy. In Fig. 5.4, context factors placed in the first-order self-model level (grey ovals in the blue plane) determine the choice of combination function during the aggregation of different mental models. Here the combination function is dynamically chosen according to the activation status of the context factors that by their activation values characterise the context. In the second-order self-model level, C-states represent the choice of combination function for different mental model connections (between tasks a to d). Each C-state has (1) an incoming connection from each of the relevant context factors for the corresponding task connection it addresses (upward connections), and (2) one (downward) outward connection to the corresponding W-state. Thus, the control of the selection of the combination function is realised by the connections between context factors and C-states. Therefore, this approach makes the choice of combination function for the aggregation context-sensitive. This makes the aggregation adaptive.

5.6 Discussion Formalisation and computational modeling of multilevel organisational learning is one of the major challenges for the area of organisational learning. The current chapter addresses this challenge. It is based on material from (Canbalo˘glu et al. 2023a). Various conceptual mechanisms in multilevel organisational learning as identified in the literature were discussed. Moreover, it was shown how they can be formalised by computational mechanisms. For example, it has been discussed how formation of a shared mental model on the basis of a number of individual mental models, from

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a computational perspective can be considered a form of (feed forward) aggregation of these individual mental models. The formalisations have been expressed using the self-modeling network modeling approach introduced in (Treur 2020a, b) and used as a basis for modeling dynamics, adaptation and control of mental models in (Treur and Van Ments 2022). The obtained computational mechanisms provide mathematical formalisations that form a basis for simulation experiments for the area of organisational learning, as has been shown in (Canbalo˘glu and Treur 2021, 2022; Canbalo˘glu et al. 2022, 2023a). For example, in (Canbalo˘glu and Treur 2021, 2022) it is shown how specific forms of context-sensitivity of feedforward aggregation to obtain shared mental models can be modeled by second-order adaptive self-modeling networks according to the self-modeling network modeling approach applied to mental models from (Treur 2020b; Treur and Van Ments 2022). The different types of mechanisms addressed cover almost all of the overall picture of multilevel organisational learning shown in Fig. 1, but by no means cover all relevant mechanisms. For example, for the sake of shortness factors that affect all levels, such as leaders, organisation structure and culture, have been left out of consideration here. However, the modeling approach described here provides a promising basis to address in the future also the ones that were not addressed yet.

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and Communication Technology, ICICT’22, vol. 2. Lecture Notes in Networks and Systems, vol 448, pp. 179–191. Springer Nature (2023a) Canbalo˘glu, G., Treur, J., Roelofsma, P.H.M.P.: A controlled adaptive self-modeling network model of multilevel organisational learning for individuals, teams or projects, and organisation. In: Canbalo˘glu, G., Treur, J., Wiewiora, A., (eds.) Computational Modeling of Multilevel Organisational Learning and its Control Using Self-Modeling Network Models, Ch 7. (this volume). Springer Nature (2023b) Canbalo˘glu, G., Treur, J., Wiewiora, A.: Computational modeling of multilevel organisational learning: from conceptual to computational mechanisms. In: Shukla, A., Murthy, B.K., Hasteer, N., Van Belle, JP. (eds) Computational Intelligence. Proceedings of the Second International Conference InCITe’22. Lecture Notes in Electrical Engineering, vol. 968, pp. 1-17. Springer Nature (2023a) Canbalo˘glu, G., Treur, J., Wiewiora, A. (eds.): Computational Modeling of Multilevel Organisational Learning and its Control Using Self-Modeling Network Models (this volume). Springer Nature (2023b) Crossan, M.M., Lane, H.W., White, R.E.: An organizational learning framework: from intuition to institution. Acad. Manag. Rev. 24, 522–537 (1999) Edmondson, A.C.: The local and variegated nature of learning in organisations: a group-level perspective. Organ. Sci. 13, 128–146 (2002) Fang, C., Lee, J., Schilling, M.A.: Balancing exploration and exploitation through structural design: The isolation of subgroups and organizational learning. Organ. Sci. 21, 625–642 (2010) Fiol, C.M., Lyles, M.A.: Organizational learning. Acad. Manag. Rev. 10, 803–813 (1985) March, J.G.: Exploration and exploitation in organizational learning. Organization Science 2, 71–87 (1991) Hannah, S. T., & Lester, P. B.: A multilevel approach to building and leading learning organizations. The Leadership Quarterly 20(1), 34-48 (2009). https://doi.org/10.1016/j.leaqua.2008.11.003 Hebb, D.O.: The organization of behavior: A neuropsychological theory. John Wiley and Sons, New York (1949) Hesslow, G.: Conscious thought as simulation of behaviour and perception. Trends Cogn. Sci. 6, 242–247 (2002) Hesslow, G.: The current status of the simulation theory of cognition. Brain Res. 1428, 71–79 (2012) Iacoboni, M.: Mirroring People: The New Science of How We Connect with Others. Farrar, Straus & Giroux, New York (2008) Iftikhar, R., Wiewiora, A.: Learning processes and mechanisms for interorganisational projects: insights from the Islamabad-Rawalpindi metro bus project. IEEE Trans. Eng. Manage. (2021). https://doi.org/10.1109/TEM.2020.3042252 Keysers, C., Gazzola, V.: Hebbian learning and predictive mirror neurons for actions, sensations and emotions. Philos. Trans. R Soc. Lond. B Biol. Sci. 369, 20130175 (2014) Kim, D.H.: The link between individual and organizational learning. sloan management review, Fall 1993, pp. 37–50. Reprinted in: Klein, D.A. (ed.) The Strategic Management of Intellectual Capital. Routledge-Butterworth-Heinemann, Oxford (1993) Madsen, P. M.: These lives will not be lost in vain: Organizational learning from disaster in US coal mining. Organization Science, 20(5), 861-875 (2009) Rizzolatti, G., Sinigaglia, C.: Mirrors in the Brain: How Our Minds Share Actions and Emotions. Oxford University Press (2008) Treur, J.: Modeling higher-order adaptivity of a network by multilevel network reification. Netw. Sci. 8, S110–S144 (2020a) Treur, J.: Network-Oriented Modeling for Adaptive Networks: Designing Higher-Order Adaptive Biological, Mental and Social Network Models. Springer Nature, Cham (2020b) Treur, J.: Modeling multi-order adaptive processes by self-modeling networks (keynote speech). In: A.J. Tallón-Ballesteros, C.-H. Chen (eds.) Proceedings of the 2nd International Conference on Machine Learning and Intelligent Systems, MLIS’20. Frontiers in Artificial Intelligence and Applications, vol. 332, pp. 206–217. IOS Press (2020c)

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Chapter 6

Using Self-modeling Networks to Model Organisational Learning Gülay Canbalo˘glu, Jan Treur, and Peter H. M. P. Roelofsma

Abstract Within organisational learning literature, mental models are considered a vehicle for both individual learning and organisational learning. By learning individual mental models (and making them explicit), a basis for formation of shared mental models for the level of the organisation is created, which after its formation can then be adopted by individuals. This provides mechanisms for organisational learning. These mechanisms have been used as a basis for an adaptive computational network model. The model is illustrated by a not too complex but realistic case study. Keywords Adaptive computational network model · Mental models · Organisational learning mechanisms

6.1 Introduction Learning is an essential part of survival and has been a topic intensively studied. Organisational learning is a dynamic, multilevel and non-linear type of learning both involving individuals and independent of individuals. It is dynamic because it involves people, it is multilevel because the learning of organisation is different than all the individuals in the organisation, and it is non-linear because it has feedback mechanisms which provide individuals to learn from organisation. The concept of organisational learning has been addressed, for example, in (Argyris 1978; Bogenrieder 2002; Crossan 1999; Fischhof 1997; Kim 1993; McShane 2010; Stelmaszczyk G. Canbalo˘glu (B) · J. Treur Social AI Group, Department of Computer Science, Vrije Universiteit Amsterdam, Amsterdam, Netherlands e-mail: [email protected] J. Treur e-mail: [email protected] P. H. M. P. Roelofsma Center for Safety in Healthcare, Delft University of Technology, Delft, The Netherlands e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 G. Canbalo˘glu et al. (eds.), Computational Modeling of Multilevel Organisational Learning and Its Control Using Self-modeling Network Models, Studies in Systems, Decision and Control 468, https://doi.org/10.1007/978-3-031-28735-0_6

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2016; Wiewiora 2019). Until recently the extensive literature on the concept of organisational learning had some deficiencies when it comes to computational models for it. However, in recent years a more detailed computational formalization of a clearly defined organisational learning process from beginning to end was developed. The study described in the current chapter, was the first in which a self-modeling network perspective was used to model the different processes and phases of organisational learning. The transitions between individual and organisational learning are key points of understanding and directing the learning process of organisations (Kim 1993). Without any doubt, one of the most influential papers on organisational learning is (Kim 1993) with an impressive number of around 5000 citations in Google Scholar in 2022. The following quote illustrates in a summarized form the perspective sketched by Kim (1993): Organisational learning is dependent on individuals improving their mental models; making those mental models explicit is crucial to developing new shared mental models. This process allows organisational learning to be independent of any specific individual. Why put so much emphasis on mental models? Because the mental models in individuals’ heads are where a vast majority of an organisation’s knowledge (both know-how and know-why) lies. (Kim 1993), p. 44

According to Kim, although there is a huge amount of previous research on learning, we are not able to fully understand the process itself (Kim 1993). Therefore, to comprehend and manage the formation of the common unified mental potential of a group, we need to work on organisational learning and its processes and phases. Computational odelling of organisational learning provides a more observable formalization of development steps of unified shared mental models. To this end, the network-oriented modeling approach based on self-modeling networks introduced in (Treur 2020a, b) that will be explained in detail in Sect. 6.3 was used in this current chapter. This modeling approach is at least as general as any other adaptive dynamical system modeling approach, as in (Hendrikse, Treur, Koole, 2023) it has been proven that any smooth adaptive dynamical system has a canonical representation as a self-modeling network. The paper by Kim (1993) was used as a point of departure and main source of inspiration for this chapter. First, Sect. 6.2 presents how and in what aspects literature provides ideas on mental models and their role in organisational learning. Then, Sect. 6.3 explains the characteristics and details of adaptive self-modeling network models and how they can be used to model the different processes concerning dynamics, adaptation and control of mental models. In Sect. 6.4 the controlled adaptive network model for organisational learning is introduced. Then in Sect. 6.5, an example simulation scenario is explained in detail. In Sect. 6.6 equilibrium analysis of the introduced adaptive network model is provided. Section 6.7 is a Discussion section. Lastly, Sect. 6.8 is an appendix with a full specification of the model.

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6.2 Background Literature The topic addressed in this chapter involves a number of concepts and processes such as individual mental models and shared mental models, and how they are handled in order to obtain organisational learning. In this section, some of the multidisciplinary literature about these concepts and processes is briefly discussed. This provides a basis for the design choices made for the adaptive network model that will be presented in Sect. 6.4 and accordingly for the scientific justification of the model based on this multidisciplinary literature.

6.2.1 Mental Models For the history of the mental model area, often Kenneth Craik is mentioned as a central person. In his book (Craik 1943), he describes a mental model as a small-scale model that is carried by an organism within its head as follows; see also (Williams 2018): If the organism carries a “small-scale model” of external reality and of its own possible actions within its head, it is able to try out various alternatives, conclude which is the best of them, react to future situations before they arise, utilize the knowledge of past events in dealing with the present and future, and in every way to react in a much fuller, safer, and more competent manner to the emergencies which face it. (Craik 1943, p. 61)

Note that this quote covers both the usage of a mental model based on socalled internal mental simulation (‘try out various alternatives’) and the learning of it (‘utilize the knowledge of past events’). Moreover, it also indicates how this contributes to safety when facing emergencies. Other authors also have formulated what mental models are. For example, with an emphasis on causal relations, Shih and Alessi (1993, p. 157) explain that. By a mental model we mean a person’s understanding of the environment. It can represent different states of the problem and the causal relationships among states.

De Kleer and Brown (1983) describe a mental model as the envisioning of a system, including a topological representation of the system components, the possible states of each of the components, and the structural relations between these components, the running or execution of the causal model based on basic operational rules and on general scientific principles. An analysis of various types of mental models and the types of mental processes processing them can found in (Van Ments and Treur 2021). This analysis has led to a three-level cognitive architecture as depicted in Fig. 6.1 where: • The base level models internal simulation of a mental model • The middle level models the adaptation of the mental model (formation, learning, revising, and forgetting a mental model, for example) • The upper-level models the (metacognitive) control over these processes

96 Fig. 6.1 Cognitive architecture for mental model handling with three levels of mental processing for mental models

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Control of adaptation of mental models

Adaptation of mental models

Use of mental models

Specific forms of learning that can be applied to mental models are observational learning (Yi and Davis 2003; Van Gog et al. 2009), instructional learning (Hogan 1997) and combinations thereof. By using the notion of self-modeling network (or reified network) from (Treur 2020a, b), recently this cognitive architecture has been formalized computationally and used in computer simulations for many applications of mental models; for an overview of this approach and various applications of it, see (Treur and Van Ments 2022); see also Sect. 6.3.

6.2.2 Shared Mental Models Mental models also play an important role when people work together in teams. When every team member has a different individual mental model of the task that is performed, then this will stand in the way of good teamwork. Therefore, ideally these mental models should be aligned to such an extent that it becomes one shared mental model for all team members. Team errors have often been linked to inadequacies of the shared mental model and the lack of adaptivity of it (Fisschoff and Johnson 1997; Jones and Roelofsma 2000; Mathieu et al. 2000; Burthscher et al. 2011; Wilson 2019; Todd 2018). This has major implications for health care and patent safety in the operation room, e.g., concerning open heart operation and tracheal intubation (Higgs et al. 2018; Seo et al. 2021). Jones and Roelofsma (2000) discuss four types of team errors resulting from inadequate shared mental models. The first is called ‘false consensus’. The false consensus effect (Ross et al. 1977; Kreuger 1998) refers to the tendency to overestimate the degree of similarity between self and other team members and this may result in biased judgements or team decisions. It is often described as people’s tendency to ‘see their own behavioural choices and judgements as relatively common and appropriate to existing circumstances while viewing alternative responses as uncommon, deviant, or inappropriate’. A second type of team error and perhaps the most well-known is ‘groupthink’; e.g., (Janis 1972; Kleindorfer et al. 1993). It is often described as a mode of thinking that people engage in when they are deeply involved in a cohesive in-group, when the

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members’ striving for unanimity overrides their motivation to realistically appraise alternative courses of action. Groupthink refers to a deterioration of mental efficiency and reality testing that results from in-group pressures. A third type of team error resulting from inadequate shared mental model is group polarization, e.g., (Lamm and Myers 1978; Isenberg 1986). This refers to the phenomenon that occurs when the position that is held on an issue by the majority of the group members is intensified as a result of discussion. For example, if group members are initially generally in favour of a particular preference of action, then group discussion will further enhance the favorability of this preference at an individual level. There are two special cases of group polarization. One is termed risky shift and occurs when a group, overall, becomes more risk seeking than the initial average risk seeking tendencies of the individual members. The other is termed cautious shift and occurs when groups become more risk averse than the initial average risk averse tendencies of the individual members. In both cases the average response of the individual group members is more extreme after discussion. Such shifts in preference have been demonstrated by an overwhelming number of studies. A fourth team error is labelled escalation of commitment, e.g., (Bazerman 1984). This refers to the tendency for individuals or groups to continue to support a course of action despite evidence that it is failing. In other words, it is the tendency for a decision to support a previous decision for which there was a negative outcome. The specific concern is with non-rational escalation of commitment with a degree to which an individual escalates commitment to a previously selected course of action beyond a rational one. An example of a computational model of a shared mental model and how imperfections in it work out can be found in (Van Ments et al. 2021). The model also uses the cognitive architecture for mental models depicted in Fig. 6.1 and its computational formalization addressed in (Treur and Van Ments 2022).

6.2.3 Organisational Learning: From Individual to Shared Mental Models and Back Organisational learning is an area which has received much attention over time; see, for example, (Argyris 1978; Bogenrieder 2002; Crossan 1999; Fischhof 1997; Kim 1993; McShane 2010; Stelmaszczyk 2016; Wiewiora et al. 2019). However, contributions to computational formalization of organisational learning are very rare. The quote in the introduction section illustrates the perspective sketched by Kim (1993). Here, mental models are considered a vehicle for both individual learning and organisational learning. By learning individual mental models (and making them explicit), a basis for formation of shared mental models for the level of the organisation is created, which provides a mechanism for organisational learning. Inspired by this, the overall process consists of the following main processes and interactions (see also (Kim 1993), Fig. 6.8):

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(a) Individual level (1) (2) (3) (4)

Creating and maintaining individual mental models Choosing for a specific context a suitable individual mental model as focus Applying a chosen individual mental model for internal simulation Improving individual mental models (individual mental model learning)

(b) From individual level to organisation level (1) Deciding about creation of shared mental models (2) Creating shared mental models based on developed individual mental models (c) Organisation level (1) Creating and maintaining shared mental models (2) Associating to a specific context a suitable shared mental model as focus (3) Improving shared mental models (shared mental model refinement or revision) (d) From organisation level to individual level (1) Deciding about individuals to adopt shared mental models (2) Individuals adopting shared mental models by learning them In terms of the cognitive architecture depicted in Fig. 6.1, applying a chosen individual mental model for internal simulation relates to the base level, improving the individual mental model relates to the middle level and choosing an individual mental model as focus relates to the upper level. Moreover, both interactions from individual to organisation level and vice versa involve changing (individual or shared) mental models and therefore relate to the middle level, while the deciding actions as a form of control relate to the upper level. This overview will provide useful input to the design of the computational network model for organisational learning that will be introduced in Sect. 6.4.

6.3 The Self-Modeling Network Modeling Approach Used In this section, the network-oriented modeling approach used is briefly introduced. Following (Treur 2020b), a temporal-causal network model is characterised by (here X and Y denote nodes of the network, also called states): • Connectivity characteristics Connections from a state X to a state Y and their weights ωX,Y • Aggregation characteristics For any state Y, some combination function cY (..) defines the aggregation that is applied to the impacts ωX,Y X(t) on Y from its incoming connections from states X

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• Timing characteristics Each state Y has a speed factor ηY defining how fast it changes for given causal impact. The following difference (or related differential) equations that are used for simulation purposes and also for analysis of temporal-causal networks, incorporate these network characteristics ωX,Y , cY (..), ηY in a standard numerical format: Y (t + /\t) = Y (t) + ηY [cY (ω X 1 ,Y X 1 (t), . . . , ω X k ,Y X k (t)) − Y (t)]/\t

(6.1)

for any state Y and where X 1 to X k are the states from which Y gets its incoming connections. Within the software environment described in (Treur 2020b, Ch. 9), a large number of currently around 65 useful basic combination functions are included in a combination function library. The above concepts enable to design network models and their dynamics in a declarative manner, based on mathematically defined functions and relations. The examples of combination functions that are applied in the model introduced here can be found in Table 6.1. Realistic network models are usually adaptive: Often not only their states but also some of their network characteristics change over time. By using a self-modeling network (also called a reified network), a similar network-oriented conceptualisation can also be applied to adaptive networks to obtain a declarative description using mathematically defined functions and relations for them as well; see (Treur 2020a, b). This works through the addition of new states to the network (called self-model states) which represent (adaptive) network characteristics. In the graphical 3D-format as shown in Sect. 6.4, such additional states are depicted at a next level (called self-model level or reification level), where the original network is at the base level. As an example, the weight ωX,Y of a connection from state X to state Y can be represented (at a next self-model level) by a self-model state named WX,Y . Similarly, all other network characteristics from ωX,Y , cY (..), ηY can be made adaptive by including self-model states for them. For example, an adaptive speed factor ηY can be represented by a self-model state named HY . As the outcome of such a process of network reification is also a temporal-causal network model itself, as has been shown in (Treur 2020b, Ch 10), this self-modeling network construction can easily be applied iteratively to obtain multiple orders of self-models at multiple (first-order, second-order, …) self-model levels. For example, a second-order self-model may include a second-order self-model state HW X,Y representing the speed factor ηW X,Y for the dynamics of first-order self-model state WX,Y which in turn represents the adaptation of connection weight ωX,Y . Similarly, a persistence factor μW X,Y of such a first-order self-model state WX,Y used for adaptation (e.g., based on Hebbian learning) can be represented by a second-order self-model state MW X,Y . In the current chapter, this multi-level self-modeling network perspective will be applied to obtain a second-order adaptive mental network architecture addressing the mental and social processes underlying organisational learning by proper handling of individual mental models and shared mental models. In this self-modeling network

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Table 6.1 The combination functions used in the introduced network model Notation

Formula

Parameters −

1 1+eστ ]

(1 + e−στ ) Steepness σ > 0 Excitability threshold τ

Advanced alogisticσ,τ (V 1 ,…,V k ) logistic sum

[

Steponce

steponceα,β (..)

1 if time t is between α and β, else 0

Start time α End time β

Hebbian learning

hebbμ (V 1 , V 2 , V 3 )

V1 ∗ V2 (1 − V3 ) + μV3

V 1 ,V 2 activation levels of the connected states; V 3 activation level of the self-model state for the connection weight Persistence factor μ

1

1+e−σ(V1 +···+Vk −τ)

Maximum max-hebbμ (V 1 , …, V k ) max(hebbμ (V1 , V2 , V3 ), V4 , . . . , V k ) composed with Hebbian learning

V 1 ,V 2 activation levels of the connected states; V 3 activation level of the self-model state for the connection weight Persistence factor μ

Scaled smaxλ (V 1 , …, V k ) maximum

Scaling factor λ

max(V 1 , …, V k )/λ

architecture the base level addresses the use of a mental model by internal simulation, the first-order self-model the adaptation of the mental model, and the second-order self-model level the control over this; see Fig. 6.2. In this way the three-level cognitive architecture depicted in Fig. 6.1 is formalized computationally in the form of a self-modeling network architecture. In (Bhalwankar and Treur 2021a, b) it is shown how specific forms of learning and their control can be modeled based on this self-modeling network architecture, in particular observational learning (Yi and Davis 2003; Van Gog et al. 2009) and instructional learning (Hogan 1997) and combinations thereof. Such forms of learning will also be applied in the model for organisational learning introduced here in Sect. 6.4.

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Control of adaptation of a mental model

Second-order self-model of a mental model

Adaptation of a mental model

First-order self-model of a mental model

Internal simulation by a mental model Three-level cognitive architecture

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Base level with a mental model as subnetwork

Self-modeling network architecture

Fig. 6.2 Computational formalization of the three-level cognitive architecture for mental model handling from Fig. 6.1 by a self-modeling network architecture

6.4 The Adaptive Network Model for Organisational Learning The case study addressed to illustrate the introduced model was adopted from the more extensive case study in an intubation process from (Van Ments et al. 2021a, b). Here only the part of the mental models is used that addresses four mental states; see the red outlined parts in Fig. 6.3 and the explanations in Table 6.2. In the case study addressed here, initially the mental models of the nurse (person A) and doctor (person B) are different and based on weak connections; they don’t use a stronger shared mental model as that does not exist yet. The organisational learning addressed to improve the situation covers:

Fig. 6.3 The example mental model from (Van Ments et al. 2021a, b) with indicated the part used in the current chapter

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Table 6.2 The mental model used for the simple case study States for mental models of persons A, B and organisation O

Short notation

Explanation

a_A

a_B

a_O

Prep_eq_N

Preparation of the intubation equipment by the nurse

b_A

b_B

b_O

Prep_d_N

Nurse prepares drugs for the patient

c_A

c_B

c_O

Pre_oy_D

Doctor executes pre oxygenation

d_A

d_B

d_O

Prep_team_D

Doctor prepares the team for intubation

1. Individual learning by A and B of their mental models through internal simulation which results in stronger but still incomplete and different mental models (by Hebbian learning). Person A’s mental model has no connection from c_A to d_A and person B’s mental model has no connection from a_B to b_B. 2. Formation of a shared organisation mental model based on the two individual mental models. A process of unification takes place. 3. Learning individual mental models from the shared mental model, e.g., a form of instructional learning. 4. Strengthening these individual mental models by individual learning through internal simulation which results in stronger and now complete mental models (by Hebbian learning). Now person A’s mental model has a connection from c_A to d_A and person B’s mental model has a connection from a_B to b_B. The connectivity of the designed network model is depicted in Fig. 6.4; for an overview of the states, see Figs. 6.5, 6.6, 6.7. For more details about the connections and how they relate to (a) to (d) from Sect. 6.2.3, see Fig. 6.8. In this model, at the base level individual mental states of persons and shared mental model states of the organisation involving these people are placed. The context states used for initiation of different processes or phases are also in this base level plane. These states can be considered as the core of the model representing knowledge of people and organisation’s general level of knowledge on separate tasks. The mental states of persons are connected to each other, which reflects the knowledge about the temporal order between tasks and the first ones have a connection from the first context state to be initiated in the first phase. Their ‘hollow’ mental states, the tasks that they do not know, have connections also from the fourth context state to be able to observe the progress of these states. First- and second-order self-model states are used to bring multi-order adaptivity to the network model. The first-order adaptation level provides adaptivity of the base level and the second-order one controls this adaptivity. In the first-order self-model level, W-states for all the weights of the connections between the base level states are placed. In the first place, these are the adaptive weights of the base level individual mental state connections of persons. In addition, there are W-states of the developed shared organisation mental model states. At this first-order adaptation level there are (intralevel) connections from all the W-states (two for this case) that specify the

6 Using Self-modeling Networks to Model Organisational Learning HWc_A,d_A HWb_A,c_A HWa_A,b_A MWa_A,b_A

HWc_B,d_B HWb_B,c_B HWa_B,b_B

MWc_A,d_A HWc_O,d_O HWb_O,c_O HWa_O,b_O MWb_A,c_A WWb_O,c_O,Wb_A,c_A WWa_O,b_O,Wa_A,b_A WWc_O,d_O,Wc_A,d_A

MWc_B,d_B

MWb_B,c_B MWa_B,b_B Wb_A,c_A

103

Second-order self-model level for control of network adaptation

WWb_O,c_O,Wb_B,c_B WWa_O,b_O,Wa_B,b_B

WWc_O,d_O,Wc_B,d_B

Wc_A,d_A

Wa_A,b_A

Wc_B,d_B Wb_B,c_B

First-order self-model level for network adaptation

Wc_O,d_O Wb_O,c_O

Wa_B,b_B Wa_O,b_O

conph3 a_A

b_A

conph2

d_A

c_A

Base level conph4

a_B

a_O b_B

c_B

b_O

c_O

d_O

d_B

conph1

Fig. 6.4 The connectivity of the second-order adaptive network model

Nr X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14

State a_A b_A c_A d_A a_B b_B c_B d_B a_O b_O c_O d_O conph1 conph2

X15

conph3

X16

conph4

Explanation Individual mental model state for person A for task a Individual mental model state for person A for task b Individual mental model state for person A for task c Individual mental model state for person A for task d Individual mental model state for person B for task a Individual mental model state for person B for task b Individual mental model state for person B for task c Individual mental model state for person B for task d Shared mental model state for organisation O for task a Shared mental model state for organisation O for task b Shared mental model state for organisation O for task c Shared mental model state for organisation O for task d Context state for Phase 1: individual mental model simulation and learning Context state for Phase 2: creation of a shared mental model for organisation O Context state for Phase 3: learning individual mental models from the shared mental model for organisation O Context state for Phase 4: individual mental model simulation and learning

Fig. 6.5 Base level states of the introduced adaptive network model

weight of a connection between the same tasks for all people (two for this case) to the W-states representing the weights of the connections of the shared organisation model (for the formation of the shared organisation mental model) and vice versa (for the learning of the shared organisation mental model by the individuals). At the second-order self-model level, there are W-states specifying the weights of the connections from the W-states to the individual ones (to initiate and control the learning of the shared organisation mental model by the individuals), HW -states for

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Nr X17

State Wa_A,b_A

X18

Wb_A,c_A

X19

Wc_A,d_A

X20

Wa_B,b_B

X21

Wb_B,c_B

X22

Wc_B,d_B

X23

Wa_O,b_O

X24

Wb_O,c_O

X25

Wc_O,d_O

Explanation First-order self-model state for the weight of the connection from a to b within the individual mental model of person A First-order self-model state for the weight of the connection from b to c within the individual mental model of person A First-order self-model state for the weight of the connection from c to d within the individual mental model of person A First-order self-model state for the weight of the connection from a to b within the individual mental model of person B First-order self-model state for the weight of the connection from b to c within the individual mental model of person B First-order self-model state for the weight of the connection from c to d within the individual mental model of person B First-order self-model state for the weight of the connection from a to b within the shared mental model of the organisation O First-order self-model state for the weight of the connection from b to c within the shared mental model of the organisation O First-order self-model state for the weight of the connection from c to d within the shared mental model of the organisation O

Fig. 6.6 First-order self-model states of the introduced adaptive network model

adaptation speeds of connection weights in the first-order adaptation level, and MW states for persistence of adaptation. This provides the speed and persistence control of the adaptation.

6.5 Example Simulation Scenario In this scenario, a multi-phase approach is applied to observe two separate individual mental models first, formation and effects of the created shared mental model for the organisation then. Thus, it is possible to explore how organisational learning progresses. Note that these processes are structured in phases to get a clear picture of what happens. In practice and also in the model, these processes also can overlap or take place entirely simultaneously. The four phases were designed as follows: • Phase 1: Individual mental model usage and learning This relates to (a) in Sect. 6.2.3. Two distinct mental models representing two different employees in the same group or organisation are constructed here. Persons have both common and special characteristics and knowledge. For the specific scenario, persons A and B are the employees of an organisation. Initially they have a weak mental model for their job considered here but by (Hebbian) learning their mental models strengthen over time during usage of them for internal simulation. They are involved in the same job, but A does the first part of the job while B finishes it. Therefore, in this phase A does not have the knowledge of the end part of the job, and B does not know how to start the job. Moreover, their characteristics are different in terms of persistence of the learning. The values of

6 Using Self-modeling Networks to Model Organisational Learning Nr X26

X27

X28

X29

X30

X31

X32 X33 X34 X35 X36 X37 X38 X39 X40 X41 X42 X43 X44 X45 X46

105

State Explanation WWa_O,b_O,Wa_A,b_A Second-order self-model state for the weight of the connection from shared mental model connection weight self-model state Wa_O,b_O to individual mental model connection weight self-model state Wa_A,b_A for instructional learning of the shared mental model WWb_O,c_O,Wb_A,c_A Second-order self-model state for the weight of the connection from shared mental model connection weight self-model state Wb_O,c_O to individual mental model connection weight self-model state Wb_A,c_A for instructional learning of the shared mental model WWc_O,d_O,Wc_A,d_A Second-order self-model state for the weight of the connection from shared mental model connection weight self-model state Wc_O,d_O to individual mental model connection weight self-model state Wc_A,d_A for instructional learning of the shared mental model WWa_O,b_O,Wa_B,b_B Second-order self-model state for the weight of the connection from shared mental model connection weight self-model state Wa_O,b_O to individual mental model connection weight self-model state Wa_B,b_B for instructional learning of the shared mental model WWb_O,c_O,Wb_B,c_B Second-order self-model state for the weight of the connection from shared mental model connection weight self-model state Wb_O,c_O to individual mental model connection weight self-model state Wb_B,c_B for instructional learning of the shared mental model WWc_O,d_O,Wc_B,d_B Second-order self-model state for the weight of the connection from shared mental model connection weight self-model state Wc_O,d_O to individual mental model connection weight self-model state Wc_B,d_B for instructional learning of the shared mental model HWa_A,b_A Second-order self-model state for the adaptation speed of individual mental model connection weight self-model state Wa A,b A HWb_A,c_A Second-order self-model state for the adaptation speed of individual mental model connection weight self-model state Wb A,c A HWc_A,d_A Second-order self-model state for the adaptation speed of individual mental model connection weight self-model state Wc A,d A HWa_B,b_B Second-order self-model state for the adaptation speed of individual mental model connection weight self-model state Wa B,b B HWb_B,c_B Second-order self-model state for the adaptation speed of individual mental model connection weight self-model state Wb B,c B HWc_B,d_B Second-order self-model state for the adaptation speed of individual mental model connection weight self-model state Wc B,d B HWa_O,b_O Second-order self-model state for the adaptation speed of shared mental model connection weight self-model state Wa_O,b_O for formation or revision of the shared mental model HWb_O,c_O Second-order self-model state for the adaptation speed of shared mental model connection weight self-model state Wb_O,c_O for formation or revision of the shared mental model HWc_O,d_O Second-order self-model state for the adaptation speed of shared mental model connection weight self-model state Wc_O,d_O for formation or revision of the shared mental model MWa_A,b_A Second-order self-model state for persistence of adaptation of individual mental model connection weight self-model state Wa A,b A MWb_A,c_A Second-order self-model state for persistence of adaptation of individual mental model connection weight self-model state Wb A,c A MWc_A,d_A Second-order self-model state for persistence of adaptation of individual mental model connection weight self-model state Wc A,d A MWa_B,b_B Second-order self-model state for persistence of adaptation of individual mental model connection weight self-model state Wa B,b B MWb_B,c_B Second-order self-model state for persistence of adaptation of individual mental model connection weight self-model state Wb B,c B MWc_B,d_B Second-order self-model state for persistence of adaptation of individual mental model connection weight self-model state Wc B,d B

Fig. 6.7 Second-order self-model states of the introduced adaptive network model

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x_Z - y_ Z x_O - y_O conp - x_Z

G. Canbalo˘glu et al. Intralevel connections Connection from x to y in individual mental model of person Z: (a) from Sect. 2.3. Connection from x to y in shared mental model of organisation O: (a) from Sect. 2.3.

Connection from context state conp for phase p {ph1, ph4} to activate mental model state x of person Z: (c) from Sect. 2.3. Wx_Z,y_Z - Wx_O,y_O Connection for person Z’s contribution from the weight of the connection from x to y in the individual mental model of Z to the weight of the connection from x to y in the shared mental model of O: (b) from Sect. 2.3. Wx_O,y_O - Wx_Z,y_Z Connection for O’s contribution from the weight of the connection from x to y in the shared mental model of O to the weight of the connection from x to y in the individual mental model of person Z: (d) from Sect. 2.3. Wx_Z,y_Z - Wx_Z,y_Z Persistence connection for Z’s mental model connections: (a) from Sect. 2.3. Interlevel connections Connection for individual Hebbian learning from state x in person Z’s x_Z - Wx_Z,y_Z individual mental model to self-model state Wx_A,y_A for Z’s individual mental model: (a) from Sect. 2.3. Upward Connection for individual Hebbian learning from state y in person Z’s y_Z - Wx_Z,y_Z from base individual mental model to self-model state Wx_A,y_A for Z’s individual level to first mental model: (a) from Sect. 2.3. self-model Connection for Hebbian learning from state x in O’s shared mental model to level x_O - Wx_O,y_O self-model state Wx A,y A for O’s shared mental model: (c) from Sect. 2.3. Connection for Hebbian learning from state y in O’s shared mental model to y_O - Wx_O,y_O self-model state Wx A,y A for O’s shared mental model: (c) from Sect. 2.3. Connection for the effect of self-model state Wx_Z,y_Z for person Z’s Wx_Z,y_Z - y_Z Downward individual mental model on state y in Z’s individual mental model: (a) from from firstSect. 2.3. order selfConnection for the effect of self-model state Wx_O,y_O for O’s shared mental model level Wx_O,y_O - y_O to base level model on state y in O’s shared mental model: (c) from Sect. 2.3. Connection from the context state for Phase 2 to second-order self-model conph2 - HWx_O,y_O state HWa_O,b_O representing the adaptation speed of first-order self-model state Wx_O,y_O for the weight of the connection from x to y in the shared mental model of O in order to trigger this adaptation speed for shared Upward mental model formation: (b) from Sect. 2.3. from base level to conph3Connection from the context state for Phase 3 to second-order self-model WWx_O,y_O,Wx_Z,y_Z state WWx_O,y_O,Wx_Z,y_Z representing the weight of the connection from first- second-order order self-model state Wx_O,y_O for the weight of the connection from x to y self-model in the shared mental model of O to first-order self-model state Wx_Z,y_Z for level the weight of the connection from x to y in the individual mental model of person Z in order to activate this connection for instructional learning of Z from the shared mental model: (d) from Sect. 2.3. HWx_O,y_O - Wx_O,y_O Effectuation of control of the adaptation of O’s shared mental model connection weight Wx_O,y_O for shared mental model formation based on Z’s Downward from secondindividual mental model: (b), (c) from Sect. 2.3. to first-order WWx_O,y_O,Wx_Z,y_Z - Effectuation of control of the adaptation of person Z’s individual mental self-model model connection weight Wx_Z,y_Z for instructional learning of Z’s individual level Wx_Z,y_Z mental model from O’s shared mental model: (d) from Sect. 2.3.

Fig. 6.8 Types of connections in the adaptive network model and how they relate to (a) to (d) identified in Sect. 6.2.3. For the example scenario, x and y are states from {a, b, c, d} and Z is a person from {A, B}

person A’s M-states are slightly higher than B’s. It means that B forgets things faster than A. • Phase 2: Shared mental model formation

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This relates to (b) and (c) in Sect. 6.2.3. Formation of the unified shared mental model of the employees occurs in this phase. This takes place by a form of aggregation and unification of the individual mental models. The collaboration of the employees starts the process of organisational learning, and the values of the Wstates of the shared mental model for the general (non-personal) states for the job (a_O to d_O) increase. Then this shared mental model is maintained by the organisation. • Phase 3: Instructional learning of the shared mental model by the individuals This relates to (d) in Sect. 6.2.3. The connections from the general W-states of the shared mental model to the personal W-states of the individuals are activated, and knowledge from the shared mental model is received here as a form of instructional learning. Persons start to learn from the organisation’s unified shared mental model, for this scenario, which can be considered as learning from each other in an indirect manner via the shared mental model. Since there is only one shared mental model, this does not require many mutual one-to-one interactions between employees. • Phase 4: Individual mental model usage and learning This relates to (d) in Sect. 6.2.3. In this phase, employees have the chance of further improving their mental models (in Phase 3 already improved based on the shared mental model) by the help of Hebbian learning during usage of the mental model for internal simulation. Person A starts to learn about task d (state d_A) by using the knowledge of person B (obtained via the shared mental model) and similarly B learns about task a (state a_B) that they did not know in the beginning. Therefore, these ‘hollow’ states become meaningful for the individuals. The individuals take advantage of the organisational learning. Figure 6.9 shows an overview of all states of the simulation; Figs. 6.10, 6.11 focus on part of the states (for the same simulation) to get a more detailed view. In Fig. 6.10 it can be seen that the activation levels of person A’s mental model states X1 , X2 and X3 (a_A to c_A) increase in Phase 1 between time 10 and 300 while the activation level of X4 (d_A) remains at zero because A does not have knowledge on this state d in the beginning. The latter state will increase in Phase 4 after learning in Phase 3 from the unified shared mental model developed in Phase 2. Person B’s mental model states X6 , X7 and X8 (b_B to d_B) increase just like A’s in phase 1, while the activation level of X5 (a_B) remains at zero because B does not have knowledge of this state a in the beginning. It will also increase in Phase 4 after learning in Phase 3 from the unified shared model developed in Phase 2. The values of person A’s W-states X17 and X18 representing A’s mental model connection weights Wa_A,b_A and Wb_A,c_A increase in the first phase, meaning that A learns the mental model better by using it for internal simulation (Hebbian learning). However, they slightly decrease in the second phase at about 300–400 since the persistence factor self-model M-state of A has not the perfect value 1, meaning that A forgets. Person B’s W-states X21 and X22 representing B’s mental model

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Shared Mental Model Formation and Learning from it 1 0.9 0.8 0.7 0.6 X23X23 - Wa_O,b_O Wa_O,b_O X24X24 - Wb_O,c_O Wb_O,c_O X25X25 - Wc_O,d_O Wc_O,d_O X26X26 - WX22,X16 WWa_O,b_O,Wa_A,b_A X27X27 - WX23,X17 WWb_O,c_O,Wb_A,c_A X28X28 - WX24,X18 WWc_O,d_O,Wc_A,d_A X29X29 - WX22,X19 WWa_O,b_O,Wa_B,b_B X30X30 - WX23,X20 WWb_O,c_O,Wb_B,c_B X31X31 - WX24,X21 WWc_O,d_O,Wc_B,d_B

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Fig. 6.11 The connection weight self-model states for the shared mental model and the weights by which individuals receive instructional learning of the shared mental model

connections Wb_B,c_B and Wc_B,d_B follow a similar pattern but since the persistence factor of B is smaller than of A, they decrease more in the second phase: it can be observed that B is a more forgetful person. State X19 (Wc_A,d_A ) is the W-state for the connection from c_A to d_A within A’s mental model. Because A does not have a nonzero X4 state in the beginning, learning can happen only (by instructional learning in Phase 3) after a unified shared mental model has been formed (in Phase 2). Thus, X19 increases in Phase 3 at about time 450. Same is valid for X20 , the W-state for the connection from a_B to b_B within B’s mental model. This addresses the task a that B does not know about in the beginning. By observing in Fig. 6.10 Phase 4 after time 650, it can be seen that all the Wstates of the individuals make an upward jump. The reason for this is the main focus of this chapter, organisational learning. As will be explained in more detail in the following paragraph, the W-states of the organisation’s shared mental model have links back to the W-states of the individuals’ mental models to provide the ability of individuals to learn (by instructional learning) from the shared mental model. As can be seen in Fig. 6.11, all the second-order self-model W-states (X26 to X31 ) for connections from the unified shared mental model’s W-states to the individuals’ W-states become activated in Phase 3 between 450 and 650. This models the instructional learning: the persons are informed about the shared mental model. Because the characteristics involved have the same values in the role matrices, they trace the same curve. The unified shared mental model gains its characteristics in the second phase at around 350 by the help of a form of aggregation of the W-states of the mental models of the employees A and B. As also can be seen in Fig. 6.11, states X23 , X24 and X25 (shared mental model connection weight self-model states Wa_O,b_O , Wb_O,c_O , and Wc_O,d_O ) jump upward in this phase to form the unified

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shared mental model, and during the phase they decrease a little bit because of the forgetting of the employees.

6.6 Mathematical Analysis of Equilibria of the Network Model In general, a dynamical system is in equilibrium at time t if dY(t)/dt = 0 for all of its state variables Y. The same can be applied to self-modeling network models. However, given the standard Eq. (6.1) in terms of the network characteristics, for network models the condition dY(t)/dt = 0 can be formulated as the following criterion μY = 0 or cY (ω X 1 ,Y X 1 (t), . . . , ω X k ,Y X k (t)) = Y (t)

(6.2)

This can be used to verify if the implemented model is correct with respect to the design of the model. As an example, consider the adaptation of the weights according to the combination function max-hebb defined in Table 6.1. ) ( max − hebbμ (V1 , . . . , Vk ) = max hebbμ (V1 , V2 , V3 ), V4 , . . . , Vk

(6.3)

where hebbμ (V1 , V2 , V3 ) = V1 ∗ V2 (1 − V3 ) + μV3 Therefore, for this case the above criterion for being in an equilibrium state is equivalent to ηY = 0 or max(V1 ∗ V2 (1 − V3 ) + μV3 , V4 , . . . , Vk ) = Y (t)

(6.4)

One of the states to which this combination function is applied (with k = 4) is Wb_A,c_A , which is X18 . It has incoming connections from b_A, c_A (X2 , X3 ) and X18 itself (all three with connection weights 1), and from X24 (with adaptive connection weight represented by self-modeling state WWb_O,c_O , Wb_A,c_A which is X27 ). Moreover, μ = 0.995. From the simulation results it seems that this state is (approximately) stationary at time t = 299 and at time t = 849. The speed factor η of Wb_A,c_A is 0.05 which is nonzero. The values for the relevant states from the simulation at these time points are the following: V1 = X2 (299) = 0.956268089647092

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V2 = X3 (299) = 0.954552603376293 V3 = X18 (299) = 0.994443719684304 V4 = X24 (299) = 0 μ = 0.995 If these values are substituted in (4) we get the following max(V1 ∗ V2 (1 − V3 ) + V3 , V4 , . . . , Vk ) = 0.994543319288979 Y (299) = 0.994443719684304 These two values show a deviation of 0.0000996 which is less than 10–4 . This quite good approximation of the equation in (4) provides evidence that the implemented model is correct with respect to its design. Similarly, for t = 849: V1 = X2 (849) = 0.956269533716948 V2 = X3 (849) = 0.95457581935179 V3 = X18 (849) = 0.994548119402481 V4 = X24 (849) = 0.970297110356546 μ = 0.995 If these values are substituted in (4) we get the following max(V1 ∗ V2 (1 − V3 ) + V3 , V4 , . . . , Vk ) = 0.994552028641134 Y (849) = 0.994548119402481 These two values show a deviation of 0.00000391, which is less than 10–5 . This again quite good approximation of the equation in (4) provides still more evidence that the implemented model is correct with respect to its design.

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6.7 Discussion This chapter is based on material from (Canbalo˘glu et al. 2022). Organisational learning is a complex process that is challenging when computational modeling of it is concerned; computational models of organisational learning are practically absent in the literature. Within mainstream organisational learning literature such as (Kim 1993; Wiewiora et al. 2019), (individual and shared) mental models are considered to be a vehicle for both individual learning and organisational learning. By learning individual mental models, sources for the formation of shared mental models for the level of the organisation as a whole are created. Once these shared organisation mental models have been formed, they are available to be adopted by individuals within the organisation by learning and applying them. This combination of individual mental model learning—shared mental model formation—individual (shared) mental model adoption, and some others indicates a handful of mechanisms of different types that together can be considered to form the basis of organisational learning. The challenges then are (1) to formalize these mechanisms in a computational manner, and (2) to glue them together according to a suitable type of architecture. These mechanisms indeed have been used as a basis for the designed adaptive computational network model. The model was illustrated by a not too complex but realistic case study. Note that for the sake of presentation, in the case study scenario the different types of mechanisms have been structured over time sequentially. This is not inherent in the designed computational network model itself. All these processes can equally well work simultaneously in parallel. The introduced computational model for organisational learning has been designed as a second-order adaptive network model according to the modeling approach based on self-modeling network models described in (Treur 2020b). Here, the three-level cognitive architecture for handling mental models as described in (Van Ments and Treur 2021) was adopted and formalized computationally as a selfmodeling network architecture, where the first-order self-model level models the adaptation of weights of connections within mental models and the second-order selfmodel level models the control over this adaptation. These weights can be adapted in different manners, depending on the context. One context for adapting them is for the focusing on a specific mental model as, for example, is addressed in (Canbalo˘glu and Treur 2021). Another context for adaptation is for Hebbian learning as applied during internal mental simulation in (Canbalo˘glu et al. 2022) and in (Bhalwankar and Treur 2021) during observational learning. These different types of adaptation were also adopted in the adaptive network for organisational learning introduced in the current chapter. Thereby, the context-sensitive control of them was modeling by the second-order self-model level. For this first step in computational formalization of organisational learning by an adaptive network model as presented here, a number of issues have been left out of consideration yet. The model provides a good basis to address these in future work, thereby obtaining extensions or refinements of the model.

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One of these extension possibilities concerns the type of aggregation used for the process of shared mental model formation. In the current model this has been based on the person who has maximal knowledge about a specific mental model connection. But other forms of aggregation can equally well be applied, for example weighted averages. Moreover, the choice of aggregation can be made adaptive in a context-sensitive manner so that for each context a different form of aggregation can be chosen automatically as part of the overall process. Also, aspects of priorities for the importance or reliability of individual mental models compared to each other may be incorporated. Another extension is to make other states used for the control adaptive and contextsensitive, such as the second-order self-model H- and M-states for the individuals, which for the sake of simplicity were kept constant in the current example scenario. A third option to extend the model is by adding states for the actual actions in the world and for observational learning based on such actions observed in the world, such as for example addressed in (Bhalwankar and Treur 2021). Finally, yet another option for an extension is to add an intermediate level of teams in between the individual and organisational level as, for example, discussed in (Wiewiora et al. 2019). In contrast to the current chapter, which used the paper by Kim (1993) as a point of departure and main source of inspiration for this chapter, In Chap. 7 of this volume (Canbalo˘glu et al. 2023), this intermediate level will be addressed in addition.

6.8 Appendix: Full Specification by Role Matrices In this section, the different role matrices are shown that provide a full specification of the network characteristics defining the adaptive network model in a standardised table format. Here in each role matrix, each state has its row where it is listed which are the impacts on it from that role.

6.8.1 Role Matrices for Connectivity Characteristics The connectivity characteristics are specified by role matrices mb and mcw shown in Figs. 6.12, 6.13. Role matrix mb lists the other states (at the same or lower level) from which the state gets its incoming connections, whereas in role matrix mcw the connection weights are listed for these connections. Nonadaptive connection weights are indicated in mcw (in Fig. 6.13) by a number (in a green shaded cell), but adaptive connection weights are indicated by a reference to the (self-model) state representing the adaptive value (in a peach-red shaded cell). This can be seen for states X2 to X4 (with self-model states X17 to X19 ), states X6 to X8 (with self-model states X20 to X22 ), X10 to X12 (with self-model states X23 to X25 ), and X17 to X22 (with self-model states X26 to X31 ).

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mb base connectivity

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Fig. 6.12 Role matrices for the connectivity: mb for base connectivity

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Fig. 6.15 Role matrices for the aggregation characteristics: combination function parameters

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X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17 X18 X19 X20 X21 X22 X23 X24 X25 X26 X27 X28 X29 X30 X31 X32 X33 X34 X35 X36 X37 X38 X39 X40 X41 X42 X43 X44 X45 X46

speed factors

a_A b_A c_A d_A a_B b_B c_B d_B a_O b_O c_O d_O cph1 cph2 cph3 cph4 Wa_A,b_A Wb_A,c_A Wc_A,d_A Wa_B,b_B Wb_B,c_B Wc_B,d_B Wa_O,b_O Wb_O,c_O Wc_O,d_O WWa_O,b_O,Wa_A,b_A WWb_O,c_O,Wb_A,c_A WWc_O,d_O,Wc_A,d_A WWa_O,b_O,Wa_B,b_B WWb_O,c_O,Wb_B,c_B WWc_O,d_O,Wc_B,d_B HWa_A,b_A HWb_A,c_A HWc_A,d_A HWa_B,b_B HWb_B,c_B HWc_B,d_B HWa_O,b_O HWb_O,c_O HWc_O,d_O MWa_A,b_A MWb_A,c_A MWc_A,d_A MWa_B,b_B MWb_B,c_B MWc_B,d_B

1

iv

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X32 X33 X34 X35 X36 X37 X38 X39 X40 0.2 0.2 0.2 0.2 0.2 0.2 0 0 0 0 0 0 0.9 0.9 0.9 0 0 0 0 0 0

X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17 X18 X19 X20 X21 X22 X23 X24 X25 X26 X27 X28 X29 X30 X31 X32 X33 X34 X35 X36 X37 X38 X39 X40 X41 X42 X43 X44 X45 X46

initial values

a_A b_A c_A d_A a_B b_B c_B d_B a_O b_O c_O d_O cph1 cph2 cph3 cph4 Wa_A,b_A Wb_A,c_A Wc_A,d_A Wa_B,b_B Wb_B,c_B Wc_B,d_B Wa_O,b_O Wb_O,c_O Wc_O,d_O WWa_O,b_O,Wa_A,b_A WWb_O,c_O,Wb_A,c_A WWc_O,d_O,Wc_A,d_A WWa_O,b_O,Wa_B,b_B WWb_O,c_O,Wb_B,c_B WWc_O,d_O,Wc_B,d_B HWa_A,b_A HWb_A,c_A HWc_A,d_A HWa_B,b_B HWb_B,c_B HWc_B,d_B HWa_O,b_O HWb_O,c_O HWc_O,d_O MWa_A,b_A MWb_A,c_A MWc_A,d_A MWa_B,b_B MWb_B,c_B MWc_B,d_B

1

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.1 0.1 0 0 0.1 0.1 0 0 0 0 0 0 0 0 0 0.05 0.05 0.05 0.05 0.05 0.05 0 0 0 0.995 0.995 0.995 0.99 0.99 0.99

Fig. 6.16 Role matrices ms for the timing characteristics (speed factors) and initial values iv

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6.8.2 Role Matrices for Aggregation Characteristics The network characteristics for aggregation are defined by the selection of combination functions from the library and values for their parameters. In role matrix mcfw it is specified by weights which state uses which combination function; see Fig. 6.14. In role matrix mcfp (see Fig. 6.15) it is indicated what the parameter values are for the chosen combination functions. Some of them are adaptive, as can be seen in the rows from X17 to X22 (e.g., the persistence factors μ represented by the self-model states X41 to X46 ).

6.8.3 Role Matrices for Timing Characteristics In Fig. 6.16, the role matrix ms for speed factors is shown, which lists all speed factors. Next to it, the list of initial values can be found. Also for ms some entries are adaptive: the speed factors of X17 to X25 are represented by (second-order) self-model states X32 to X40 .

References Argyris Ch., Schön D.A.: Organizational Learning: A Theory of Action Perspective. AddisonWesley, Reading, MA. (1978) Bogenrieder, I.: Social architecture as a prerequisite for organizational learning. Manag. Learn. 33(2), 197–216 (2002) Bazerman, M.H., Giuliano, T., Appelman, A.: Escalation of commitment in individual and group decision making. Organizational Behaviour and Human Performance 33, 141–152 (1984) Bhalwankar, R., Treur, J.: A Second-Order Adaptive Network Model for Learner-Controlled Mental Model Learning Processes. In: Benito R.M., Cherifi C., Cherifi H., Moro E., Rocha L.M., SalesPardo M. (eds), Proc. of the 9th International Conference on Complex Networks and their Applications. Studies in Computational Intelligence, vol 944, pp. 245–259. Springer Nature Switzerland AG. (2021a) Bhalwankar, R., Treur, J.: Modeling Learner-Controlled Mental Model Learning Processes by a Second-Order Adaptive Network Model. PLoS ONE 16(8), e0255503 (2021b) Burthscher, M.J., Kolbe, M., Wacker, J.: Interaction of team mental models and monitoring behaviors predict team performance in simulated anesthesia inductions. J. Exp. Psychol. Appl. 17(3), 257–269 (2011) Canbalo˘glu, G., Treur, J.: Modeling Context-Sensitive Metacognitive Control of Focusing on a Mental Model During a Mental Process. In: Silhavy, R., Silhavy, P., Prokopova, Z. (eds), Data Science and Intelligent Systems. Proc. CoMeSySo 2021. Lecture Notes in Networks and Systems, vol 231, pp 992–1009 Springer Nature (2021) Canbalo˘glu, G., Treur, J., Roelofsma, P.H.M.P.: Computational Modeling of Organisational Learning by Self-Modeling Networks. Cogn. Syst. Res. 73, 51–64 (2022) Canbalo˘glu, G., Treur, J., Wiewiora, A. (eds.), (2023). Computational Modeling of Multilevel Organisational Learning and its Control Using Self-Modeling Network Models (this volume). Springer Nature Craik, K.J.W.: The nature of explanation. University Press, Cambridge, MA (1943)

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Nini, M.: All on the same page: How Team Mental Models (TMM) increase team performance. CQ Net (2019) https://www.ckju.net/en/dossier/team-mental-models-increase-team-performance. (2019) Outland, N.B.: A computational cognitive architecture for exploring team mental models. College of Science and Health Theses and Dissertations. 289. https://via.library.depaul.edu/csh_etd/289 (2019) Ross, L., Greene, D., House, P.: The ‘false consensus effect’: an egocentric bias in social perception and attribution process. J. Exp. Soc. Psychol. 13, 279–301 (1977) Seo, S., Kennedy-Metz, L.R., Zenati, M.A., Shah, J.A., Dias, R.D., Unhelkar, V.V.: Towards an AI coach to infer team mental model allignment in healthcare. Rice University Houston TX, USA, Department of Computer Science (2021) Shih, Y.F., Alessi, S.M.: Mental models and transfer of learning in computer programming. J. Res. Comput. Educ. 26(2), 154–175 (1993) Stelmaszczyk, M.: Relationship between individual and organizational learning: mediating role of team learning. J. Econ. Manag. 26(4), 1732–1947. https://doi.org/10.22367/jem.2016.26.06 (2016) Todd, J.: Audit of compliance with WHO surgical safety checklist and building a shared mental model in the operating theatre. BJM Leader 2(1), 32–135 (2018) Treur, J.: Modeling higher-order adaptivity of a network by multilevel network reification. Network Science 8, S110–S144 (2020a) Treur, J.: Network-oriented modeling for adaptive networks: designing higher-order adaptive biological, mental and social network models. Springer Nature, Cham (2020b) Treur, J., Van Ments, L. (eds.) : Mental Models and their Dynamics, Adaptation, and Control: a Self-Modeling Network Modeling Approach. Springer Nature. (2022) Turi, J.A., Sorooshian, S.: The impact of organizational structure on organizational learning. Middle East J. Management. 6(2), 204–232 (2019) Van Gog, T., Paas, F., Marcus, N., Ayres, P., Sweller, J.: The mirror neuron system and observational learning: Implications for the effectiveness of dynamic visualizations. Educ. Psychol. Rev. 21(1), 21–30 (2009) Van Ments, L., Treur, J.: Reflections on dynamics, adaptation and control: a cognitive architecture for mental models. Cogn. Syst. Res. 70, 1–9 (2021) Van Ments, L., Treur, J., Roelofsma, P.H.M.P.: A Temporal-Causal Network Model for the Relation Between Religion and Human Empathy. Proc. of the 5th International Workshop on Complex Networks and their Applications. Lecture Notes in Computer Science, 693, pp. 55–67. Springer Publications (2016) Van Ments, L., Treur, J., Roelofsma, P.H.M.P.: Modeling the effect of religion on human empathy based on an adaptive temporal-causal network model. Comput. Soc. Netw. 5(1) (2018) Van Ments, L., Treur, J., Klein, J., Roelofsma, P.H.M.P.: A Computational network model for shared mental models in hospital operation rooms. In: Proceedings of the 14th International Conference on Brain Informatics, BI’21. Lecture Notes in AI, 12960, pp. 67–78. Springer Nature. (2021a) Van Ments, L., Treur, J., Klein, J., Roelofsma, P.H.M.P.: A second-order adaptive network model for shared mental models in hospital teamwork. In: Nguyen, N.T., et al. (eds.), Proceedings of the 13th International Conference on Computational Collective Intelligence, ICCCI’21. Lecture Notes in AI, 12876, pp. 126–140. Springer Nature (2021b) Wilson, A.: Creating and applying shared mental models in the operating room. J. Perioper. Nurs. 32(3), 33–36 (2019) Wiewiora, A., Smidt, M., Chang, A.: The ‘How’ of multilevel learning dynamics: a systematic literature review exploring how mechanisms bridge learning between individuals, teams/projects and the organisation. Eur. Manag. Rev. 16, 93–115 (2019) Williams, D.: The mind as a predictive modelling engine: generative models, structural similarity, and mental representation. Ph.D. Thesis, University of Cambridge, UK (2018) Yi, M.Y., Davis, F.D.: Developing and validating an observational learning model of computer software training and skill acquisition. Inf. Syst. Res. 14(2), 146–169 (2003)

Chapter 7

A Controlled Adaptive Self-modeling Network Model of Multilevel Organisational Learning for Individuals, Teams or Projects, and Organisation Gülay Canbalo˘glu, Jan Treur, and Peter H. M. P. Roelofsma Abstract Multilevel organisational learning concerns an interplay of different types of learning at individual, team, and organisational levels. These processes use complex dynamic and adaptive mechanisms. A second-order adaptive network model for this is introduced here and illustrated. Keywords Multilevel organisational learning · Adaptive network model · Self-model

7.1 Introduction Multilevel organisational learning is a complex, dynamic, adaptive, cyclical and nonlinear type of learning involving multiple levels and both dependent on individuals and independent of individuals. It is multilevel because the learning of an organisation involves learning at the level of individuals, at the level of teams (or groups or projects), and at the level of the organisation via feed forward and feedback pathways: Through feed-forward processes, new ideas and actions flow from the individual to the group to the organisation levels. At the same time, what has already been learned feeds back from the organisation to group and individual levels, affecting how people act and think. (Crossan et al. 1999), p. 532. ‘There is growing consensus in the literature that the theory of organisational learning should consider individual, team and organisational levels’ (Wiewiora et al. 2019), p. 94

G. Canbalo˘glu (B) · J. Treur Social AI Group, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands e-mail: [email protected] J. Treur e-mail: [email protected] P. H. M. P. Roelofsma Delft University of Technology, Center for Safety in Healthcare, Delft, The Netherlands e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 G. Canbalo˘glu et al. (eds.), Computational Modeling of Multilevel Organisational Learning and Its Control Using Self-modeling Network Models, Studies in Systems, Decision and Control 468, https://doi.org/10.1007/978-3-031-28735-0_7

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There is a huge amount of literature on multilevel organisational learning such as (Argyris and Schön 1978; Bogenrieder 2002; Crossan et al. 1999; Fischhof and Johnson 1997; Kim 1993; McShane and Glinow 2010; Stelmaszczyk 2016; Wiewiora et al. 2019; Wiewiora et al. 2020). However, until recently systematic approaches to obtain (adaptive) computational models were not easy to find. In the current chapter, a self-modeling network modeling perspective is used to model the different adaptive, interacting processes of multilevel organisational learning. In contrast to the previous Chap. 6 of this volume (Canbalo˘glu et al. 2023b), in the current chapter also the intermediate level of teams or projects is addressed, following (Crossan et al. 1999; Wiewiora et al. 2019) whereas in the previous chapter the paper of Kim (1993) was used as a main source of inspiration, where this intermediate level is not addressed. Computational modeling of multilevel organisational learning provides a more observable formalization of multilevel organisational learning and provides possibilities to perform ‘in silico’ (simulation) experiments with it. To this end, the selfmodeling network modeling approach introduced in (Treur 2020) that is explained in some detail in Sect. 7.3, is used in this current chapter. First, Sect. 7.2 presents how literature provides ideas on mental models at individual, team and organisation level and their role in multilevel organisational learning. Then, Sect. 7.3 explains the characteristics and details of adaptive selfmodeling network models and how they can be used to model the different processes concerning dynamics, adaptation and control of mental models. In Sect. 7.4 the controlled adaptive network model for multilevel organisational learning is introduced. Then in Sect. 7.5, an example simulation scenario is explained in detail. Section 7.6 is a Discussion section.

7.2 Background Literature The quotes in the introduction section illustrate the perspective adopted here. Mental models are considered a vehicle to model the interplay of learning at individual, team and organisational level. Individual mental models learnt are a basis for formation of shared team mental models; these shared team mental models provide input for the shared mental models at the organisation level. Conversely, these shared mental models at organisation and team level are used to improve shared team mental models and individual mental models, respectively. The picture of the different pathways shown in Fig. 7.1 is based on Fig. 4 of Wiewiora et al. (2019) and Fig. 3 of Wiewiora et al. (2020). Inspired by this, as a basis for the analysis made here, the considered overall multilevel organisational learning process consists of the following main pathways and interactions; see also Crossan et al. (1999) and Wiewiora et al. (2019):

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Fig. 7.1 Multilevel organisational learning: multiple levels and nested cycles (with depth 3) of interactions; see also Wiewiora et al. (2019) and Wiewiora et al. (2020)

(a) Individual level (1) (2) (3) (4)

Creating and maintaining individual mental models Choosing for a specific context a suitable individual mental model as focus Applying a chosen individual mental model for internal simulation Improving individual mental models

(b) From individual level to team level (feed forward learning) (1) Deciding about creation of shared team mental models (2) Creating shared team mental models based on developed individual mental models (c) From team level to organisation level (feed forward learning) (1) Deciding about creation of shared mental models (2) Creating shared mental models based on developed individual mental models (d) From organisation level to team level (feedback learning) (1) Deciding about teams to adopt shared organisation mental models (2) Teams adopting shared mental models (e) From team level to individual level (feedback learning) (1) Deciding about individuals to adopt shared team mental models (2) Individuals adopting shared team mental models by learning them (f) Individual level (1) Creating and maintaining individual mental models (2) Choosing for a specific context a suitable individual mental model as focus

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(3) Applying a chosen individual mental model for internal simulation (4) Improving individual mental models This overview provided useful input to the design of the computational network model for multilevel organisational learning that will be introduced in Sect. 7.4.

7.3 The Self-modeling Network Modeling Approach In this section, the self-modeling network modeling approach (Treur 2020) used is explained in some detail. A network model is defined by (where X and Y are nodes or states of the network): • Connectivity characteristics Connections from one state X to a state Y with their weights ωX,Y • Aggregation characteristics For any state Y, a combination function cY (..) is used to specify the aggregation that is applied to the impacts ωX,Y X(t) on Y from the incoming connections from states X to Y • Timing characteristics For each state Y a speed factor ηY defines how fast it changes for given causal impact. Each state or node Y has time t dependent activation values Y(t). The following difference equations are used for simulation; they are based on the network characteristics ωX,Y , cY (..), ηY in a canonical manner: Y (t + /\t) = Y (t) + ηY [cY (ω X 1 ,Y X 1 (t), . . . , ω X k ,Y X k (t)) − Y (t)]/\t

(7.1)

for each state Y, where X 1 to X k are the states from which Y receives incoming connections. The dedicated software environment (Treur 2020, Chap. 9), includes a library with currently around 70 basic combination functions. The examples of basic combination functions that are applied in the model introduced here can be found in Table 7.1. By using a self-modeling principle (also called a reification principle), a networkoriented conceptualisation can also be applied to adaptive networks; see (Treur 2020). Here new states are added to the network (called self-model states) representing network characteristics. These self-model states are depicted at a next level (called self-model level or reification level); the original network is at the base level. This is often applied to the weight ωX,Y of a connection from state X to state Y; this is represented by a self-model state WX,Y . Similarly, any other network characteristic from ωX,Y , cY (..), ηY can be self-modeled by including self-model states. For example, the speed factor ηY of a state Y can be represented by a self-model state HY . This self-modeling network construction can be applied iteratively to obtain multiple orders of self-models at multiple (first-order, second-order, …) self-model

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Table 7.1 The combination functions applied in the introduced network model Notation

Formula

Parameters 1

Advanced alogisticσ,τ (V 1 , …,V k ) logistic sum

1 ] (1 + [ − 1+e στ 1+e−σ(V1 +···+Vk −τ) −στ e )

Steepness σ > 0 Excitability threshold τ

Steponce

steponceα,β (..)

1 if time t is between α and β, else 0

Start time α End time β

Hebbian learning

hebbμ (V 1 , V 2 , V 3 )

V1 ∗ V2 (1 − V3 ) + μV3

V 1 ,V 2 activation levels of states X and Y; V 3 activation level of the self-model state WX,Y Persistence factor μ

Maximum max-hebbμ (V 1 , …, V k ) max(hebbμ (V1 , V2 , V3 ), V4 , . . . , V k ) composed with Hebbian learning Scaled smaxλ (V 1 , …, V k ) maximum

max(V 1 , …, V k )/λ

Scaling factor λ

levels. For example, a second-order self-model may include a second-order selfmodel state HW X,Y representing the speed factor ηW X,Y for the (learning) dynamics of first-order self-model state WX,Y which in turn represents an adaptative connection weight ωX,Y . Similarly, a persistence factor μW X,Y of such a first-order self-model state WX,Y used for adaptation (e.g., based on Hebbian learning) can be represented by a second-order self-model state MW X,Y . In the current chapter, the self-modeling network perspective is applied to design a second-order adaptive mental network architecture addressing the mental and social processes underlying organisational learning by proper handling of individual mental models and shared mental models. In this self-modeling network architecture, the base level addresses the use of a mental model by internal simulation, the first-order self-model the adaptation of the mental model, and the second-order self-model level models the control over this; see Fig. 7.2. In this way the three-level cognitive architecture described in (Van Ments et al. 2021; Treur and Van Ments 2022) is formalized computationally in the form of a self-modeling network architecture. In Bhalwankar and Treur (2021) it is shown how specific forms of learning and their control can be modeled based on this self-modeling network architecture, in particular learning by observation and learning by instruction and combinations thereof (Yi and Davis 2003; Van Gog et al. 2009). Some of these forms of learning will also be applied in the model for multilevel organisational learning introduced here in Sect. 7.4.

7.4 The Network Model for Multilevel Organisational Learning In the considered case study concerning tasks a, b, c, and d, initially the individual mental models of 4 people are different and based on some strong and some weak

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Control of adaptation of a mental model

Second-order self-model of a mental model

Adaptation of a mental model

First-order self-model of a mental model

Internal simulation by a mental model Three-level cognitive architecture

Base level with a mental model as subnetwork

Self-modeling network architecture

Fig. 7.2 Computational formalization of the three-level cognitive architecture for mental model handling from (Treur and Van Ments 2022) by a self-modeling network architecture

connections; they don’t use a stronger shared mental model as that does not exist yet. The multilevel organisational learning addressed to improve the situation covers: 1. Individual (Hebbian) learning by persons of their mental models through internal simulation which results in stronger but still incomplete and different mental models. Person A and C’s mental models have no connection from task c to task d and person B and D’s mental models have no connection from a to b. 2. Formation of two shared team mental models for teams T1 (consisting of persons A and B) and T2 (consisting of persons C and D) based on the different individual mental models. A process of unification by aggregation takes place (feed forward learning). 3. Formation of a shared organisation mental model based on the two team mental models. Again, a process of unification by aggregation takes place (feed forward learning). 4. Flow of information and knowledge from organisation mental model to team mental models, e.g., a form of instructional learning (feedback learning). 5. Learning of individual mental models from the shared team mental models, e.g., also a form of instructional learning (feedback learning). 6. Improvements on these individual mental models by individual learning through internal simulation which results in stronger and now complete mental models (by Hebbian learning). Now person A and C’s mental models have a connection from task c to task d, and person B and D’s mental models have a connection from a to b. The connectivity of the introduced network model is shown in Fig. 7.3 to Fig. 7.6; for an overview of the states, see Figs. 7.7, 7.8, 7.9, 7.10 and 7.11, and for more details about the connections and how they relate to (a)–(f) from Sect. 7.2, see Fig. 7.12. The undermost base level of this model has mental model states for individuals, teams and organisation, and also context states for activation of six different phases (like the (a)–(f) in Sect. 7.2) at different times. The mental states of persons are

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Fig. 7.3 The connectivity of the base level of the adaptive network model: (1) in the ovals the individual mental models of the team members (A and B for Team T1 and C and D for team T2), (2) in the rectangles the shared team mental models for team T1 (blue-grey) and team T2 (pink-purple) and the shared mental model of the whole organisation O (green)

Fig. 7.4 The connectivity between the base level and first-order self-model level for the adaptation of the mental models by Hebbian learning

Fig. 7.5 The connectivity within the first-order self-model level for the adaptation of the mental models by formation of shared team and organisation mental models (links from left to right: feedforward learning) and by instruction learning of individual mental models and shared team mental models from these shared mental models (links from right to left: feedback learning)

connected to each other according to the order of the tasks, and the first ones have a connection from first context state to be able to start to perform internal simulation and learn. As can be seen in Fig. 7.3, some connections between task states of persons are dashed, which means initially there is no connection (initial lack of knowledge).

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Fig. 7.6 The connectivity of the second-order adaptive network model for the second-order selfmodel of the mental models: the interactions between the first-order self-model level and the secondorder self-model level: the second-order Hebbian learning for the second-order W-states (the WW states)

Therefore, states where these dashed connections are, are the ‘hollow’ non-known mental state connections of persons. These states have connections that change over time to enable to observe the improvement of the individual’s knowledge with the impact of organisation and team mental models in the fifth phase. The base level mental states relate to the basic tasks and can be considered as the basic ingredients of the mental models representing knowledge on relations between tasks. To make the mental models adaptive, first-order self-model states are added in the intermediary (first-order self-model) level (blue plane). These are W-states representing adaptive weights for each developed connection between individual, team and organisation mental model states in the base level; see Fig. 7.4. The (blue) upward and (pink) downward connections between the two levels are used to model individual (Hebbian) learning. Within the first-order self-model level (blue plane), there are also intralevel W-toW connections between first-order W-states here to enable feed forward learning (in Phase 2 and Phase 3) and feedback learning (in Phase 4 and Phase 5) (Crossan et al. 1999). These W-to-W connections correspond to the arrows for feed forward and feedback learning shown in Fig. 7.1 (upper part, resp. lower part). Thus, formation of shared team and organisation mental models is performed by this feed forward learning mechanism, and the learning from the shared organisation mental model and the shared team mental model by individuals occurs by the feedback learning mechanism. To control the adaptivity modeled by the first-order adaptation level, second-order self-model states are added in the uppermost level (purple plane). In first place, there

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are WW -states (higher-order W-states) for (intralevel) connections between firstorder adaptivity level W-states, in other words adaptive weight representations of the horizontal connections between adaptive weight representation states in the level below. These control processes (for whether and when to activate feed forward and feedback learning) are not explicitly depicted in Fig. 7.1 based on (Wiewiora et al. 2019) and (Crossan et al. 1999) but still are crucial for the processes to function well. Additionally, HW -states for adaptation speeds of connection weight representations in the first-order adaptation level, and MW -states for persistence of adaptation are placed on the second-order self-model level. This provides the speed and persistence control of the adaptation. For a full specification of the network model, see the Appendix section (Sect. 7.7). In Fig. 7.12 an overview is given of the different types of connections.

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Fig. 7.8 First-order self-model states of the introduced adaptive network model

In summary, first- and second-order self-model states are used to bring multi-order adaptivity to the network model. The first-order adaptation level provides adaptivity of the base level and the second-order one controls this adaptivity. In the first-order self-model level, W-states for all the weights of the connections between the base level states are placed. In the first place, these are the adaptive weights of the base level individual mental state connections of persons. In addition, there are W-states of the developed shared organisation mental model states. At this first-order adaptation level there are (intralevel) connections from all the W-states (two for this case) that specify the weight of a connection between the same tasks for all people (two for this case) to

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State Explanation WWa_T1,b_T1,Wa_A,b_A Second-order self-model state for the weight of the connection from shared team mental model connection weight self-model state Wa_T1,b_T1 to individual mental model connection weight self-model state Wa_A,b_A for instructional (feedback) learning from the shared mental model of team T1 WWb_T1,c_T1,Wb_A,c_A Second-order self-model state for the weight of the connection from shared team mental model connection weight self-model state Wb_T1,c_T1 to individual mental model connection weight self-model state Wb_A,c_A for instructional (feedback) learning from the shared mental model of team T1 WWc_T1,d_T1,Wc_A,d_A Second-order self-model state for the weight of the connection from shared team mental model connection weight self-model state Wc_T1,d_T1 to individual mental model connection weight self-model state Wc_A,d_A for instructional (feedback) learning from the shared mental model of team T1 WWa_T1,b_T1,Wa_B,b_B Second-order self-model state for the weight of the connection from shared team mental model connection weight self-model state Wa_T1,b_T1 to individual mental model connection weight self-model state Wa_B,b_B for instructional (feedback) learning from the shared mental model of team T1 WWb_T1,c_T1,Wb_B,c_B Second-order self-model state for the weight of the connection from shared team mental model connection weight self-model state Wb_T1,c_T1 to individual mental model connection weight self-model state Wb_B,c_B for instructional (feedback) learning from the shared mental model of team T1 WWc_T1,d_T1,Wc_B,d_B Second-order self-model state for the weight of the connection from shared team mental model connection weight self-model state Wc_T1,d_T1 to individual mental model connection weight self-model state Wc_B,d_B for instructional (feedback) learning from the shared mental model of team T1 WWa_T2,b_T2,Wa_C,b_C Second-order self-model state for the weight of the connection from shared team mental model connection weight self-model state Wa_T2,b_T2 to individual mental model connection weight self-model state Wa_C,b_C for instructional (feedback) learning from the shared mental model of team T2 WWb_T2,c_T2,Wb_C,c_C Second-order self-model state for the weight of the connection from shared team mental model connection weight self-model state Wb_T2,c_T2 to individual mental model connection weight self-model state Wb_C,c_C for instructional (feedback) learning of the shared mental model of team T2 WWc_T2,d_T2,Wc_C,d_C Second-order self-model state for the weight of the connection from shared team mental model connection weight self-model state Wc_T2,d_T2 to individual mental model connection weight self-model state Wc_C,d_C for instructional (feedback) learning from the shared mental model of team T2 WWa_T2,b_T2,Wa_D,b_D Second-order self-model state for the weight of the connection from shared team mental model connection weight self-model state Wa_T2,b_T2 to individual mental model connection weight self-model state Wa_D,b_D for instructional (feedback) learning from the shared mental model of team T2 WWb_T2,c_T2,Wb_D,c_D Second-order self-model state for the weight of the connection from shared team mental model connection weight self-model state Wb_T2,c_T2 to individual mental model connection weight self-model state Wb_D,c_D for instructional (feedback) learning from the shared mental model of team T2 WWc_T2,d_T2,Wc_D,d_D Second-order self-model state for the weight of the connection from shared team mental model connection weight self-model state Wc_T2,d_T2 to individual mental model connection weight self-model state Wc_D,d_D for instructional (feedback) learning from the shared mental model of team T2

Fig. 7.9 Second-order self-model states of the introduced adaptive network model: the higherorder W-states for feedback learning from shared team mental model to individual mental models

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G. Canbalo˘glu et al. State Explanation WWa_O,b_O,Wa_T1,b_T1 Second-order self-model state for the weight of the connection from shared organisation mental model connection weight self-model state Wa_O,b_O to shared team mental model connection weight self-model state Wa_T1,b_T1 for instructional (feedback) learning from the shared organisation mental model WWb_O,c_O,Wb_T1,c_T1 Second-order self-model state for the weight of the connection from shared organisation mental model connection weight self-model state Wb_O,c_O to shared team mental model connection weight self-model state Wb_T1,c_T1 for instructional (feedback) learning from the shared organisation mental model WWc_O,d_O,Wc_T1,d_T1 Second-order self-model state for the weight of the connection from shared organisation mental model connection weight self-model state Wc_O,d_O to shared team mental model connection weight self-model state Wc_T1,d_T1 for instructional (feedback) learning from the shared organisation mental model WWa_O,b_O,Wa_T2,b_T2 Second-order self-model state for the weight of the connection from shared organisation mental model connection weight self-model state Wa_O,b_O to shared team mental model connection weight self-model state Wa_T2,b_T2 for instructional (feedback) learning from the shared organisation mental model WWb_O,c_O,Wb_T2,c_T2 Second-order self-model state for the weight of the connection from shared organisation mental model connection weight self-model state Wb_O,c_O to shared team mental model connection weight self-model state Wb_T2,c_T2 for instructional (feedback) learning from the shared organisation mental model WWc_O,d_O,Wc_T2,d_T2 Second-order self-model state for the weight of the connection from shared organisation mental model connection weight self-model state Wc_O,d_O to shared team mental model connection weight self-model state Wc_T2,d_T2 for instructional (feedback) learning from the shared organisation mental model

Fig. 7.10 Second-order self-model states of the introduced adaptive network model: the higherorder W-states for feedback learning from shared organisation mental model to shared team mental models

the W-states representing the weights of the connections of the shared organisation model (for the formation of the shared organisation mental model) and vice versa (for the learning of the shared organisation mental model by the individuals). At the second-order self-model level, there are WW -states specifying the weights of the intralevel connections between the W-states to the individual ones (to initiate and control the learning of the shared organisation mental model by the individuals), HW states for adaptation speeds of connection weights in the first-order adaptation level, and MW -states for persistence of adaptation. This provides the speed and persistence control of the adaptation.

7.5 Example Simulation Scenario In this scenario, for reasons of presentation a multi-phase approach is applied to get a clear picture of the progress of multilevel organisational learning via teams. In general, the model can also process all phases simultaneously. It is possible to see the feed forward flow of the development of shared team mental models from individual mental models first, formation of the shared organisation mental model originating from teams’ mental models then, and finally by the feedback flow the impact of these shared mental models on teams and individuals. In practice, and also in the model,

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Explanation Second-order self-model state for the adaptation speed of all individual mental model connection weight self-model states Wx_A,y_A for formation or revision of the individual mental model of person A Second-order self-model state for the adaptation speed of all individual mental model connection weight self-model states Wx_B,y_B for formation or revision of the individual mental model of person B Second-order self-model state for the adaptation speed of all individual mental model connection weight self-model states Wx_C,y_C for formation or revision of the individual mental model of person C Second-order self-model state for the adaptation speed of all individual mental model connection weight self-model states Wx_D,y_D for formation or revision of the individual mental model of person D Second-order self-model state for the adaptation speed of shared mental model connection weight self-model state Wx_T1,y_T1 for formation or revision of the shared mental model of team T1 Second-order self-model state for the adaptation speed of all shared mental model connection weight self-model states Wx_T2,y_T2 for formation or revision of the shared mental model of team T2 Second-order self-model state for the adaptation speed of all shared organisation mental model connection weight self-model states Wx_O,y_O for formation or revision of the shared organisation mental model Second-order self-model state for persistence of adaptation of individual mental model connection weight self-model state Wa_A,b_A of person A Second-order self-model state for persistence of adaptation of individual mental model connection weight self-model state Wb_A,c_A of person A Second-order self-model state for persistence of adaptation of individual mental model connection weight self-model state Wc_A,d_A of person A Second-order self-model state for persistence of adaptation of individual mental model connection weight self-model state Wa_B,b_B of person B Second-order self-model state for persistence of adaptation of individual mental model connection weight self-model state Wb_B,c_B of person B Second-order self-model state for persistence of adaptation of individual mental model connection weight self-model state Wc_B,d_B of person B Second-order self-model state for persistence of adaptation of individual mental model connection weight self-model state Wa_C,b_C of person C Second-order self-model state for persistence of adaptation of individual mental model connection weight self-model state Wb_C,c_C of person C Second-order self-model state for persistence of adaptation of individual mental model connection weight self-model state Wc_C,d_C of person C Second-order self-model state for persistence of adaptation of individual mental model connection weight self-model state Wa_D,b_D of person D Second-order self-model state for persistence of adaptation of individual mental model connection weight self-model state Wb_D,c_D of person D Second-order self-model state for persistence of adaptation of individual mental model connection weight self-model state Wc_D,d_D of person D

Fig. 7.11 Second-order self-model states of the introduced adaptive network model: the HW -states for adaptive learning speed and MW -states for adaptive persistence of the learning

these phases also can overlap or take place entirely simultaneously. The considered six phases are as follows; see Figs. 7.13, 7.14 and 7.15: • Phase 1: Individual mental model usage and learning This relates to (a) in Sect. 7.2. Different individual mental models by four different persons are constructed and strengthened here. The knowledge of people for the tasks, initially, is not same. Thus, the learning levels are different as can be seen in

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Fig. 7.12 Types of connections in the adaptive network model and how they relate to (a)–(f) identified in Sect. 7.2. For the example scenario, x and y are states from {a, b, c, d}, T is a team from {T1, T2} and Z is a person from {A, B, C, D}

the first phase between time 25 and 200 in the simulation graph in Fig. 7.11 (overall) and Fig. 7.12 (the W-states). For example, activation levels of first three base states for tasks a to c of person A from Team 1 and person C from Team 2 (a_A to c_A and a_C to c_C) increase while the activation levels of states for task d (d_A and d_C) remain at zero indicating that they do not have knowledge on this task. A similar lack of knowledge is observed for the other persons B from Team 1 and D from Team 2, for task a this time. Therefore, the activation levels of their states a_B and a_D remain at zero in this phase, while others get increased (b_B to d_B and

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Fig. 7.12 (continued)

b_D to d_D). After this first individual learning phase, forgetting takes place for all persons because they do not have perfect persistence factors self-model M-state values (values 0, excitability threshold τ

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modeling a form of plasticity. This can be modeled by a second-order self-model state HW X,Y (also called an HW -state). Such second-order self-model states create second-order adaptivity, which can be used to model metaplasticity (Abraham and Bear 1996; Treur 2019). Another form of second-order adaptivity can be modeled by a second-order WW -state (also called a higher-order W-state) controlling the weight of a connection connecting two W-states. In (Treur 2021) it is shown by Theorem 2 that the format defined by (3) together with the concept of self-modeling is able to model any adaptive dynamical system, see also Chap. 16 of this volume (Canbalo˘glu et al. 2023c). To model mental models, their adaptation, and the control of this adaptation, the three-level cognitive architecture, as shown in Fig. 8.1, can be used (Treur and Van Ments 2022; Van Ments and Treur 2021a, 2021b): • The base level models the internal simulations of the mental models. • The middle level describes the adaptation of the mental models, this concerns learning and forgetting of a mental model. • The highest level models the control over these processes.

Fig. 8.1 Cognitive architecture for mental models; adopted from (Treur and Van Ments 2022; Van Ments and Treur 2021a, 2021b)

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8.4 The Introduced Adaptive Network Model The adaptive mental and social processes of the team of match officials are modeled by the second-order adaptive network model introduced in this section. A picture of the connectivity of the model is shown later in this section; it takes the threelevel network structure shown in Fig. 8.1 as point of departure. An overview of all states with their explanation can be found in Sect. 8.8. The full specification by role matrices is defined in the Appendix (see Linked Data at https://www.researchgate. net/publication/357622527). An example simulation for the scenario as described in the case description in Sect. 8.2 is shown in Sect. 8.5. In the base plane, the mental model states of referee and assistants and the shared mental model are modeled (see Fig. 8.2). The shared mental model is represented in the dark-colored rectangle, while the three individual mental models are covered in the oval forms. The officials are represented by the letters R, A1, and A2 for the Referee, Assistant 1, and Assistant 2, respectively. These mental models represent knowledge of the individual referee and assistants and of the shared mental model. Within each mental model, the tasks are represented by nodes; they represent the states of the mental model. For an explanation of these states, see Table 8.2. The mental states of every person are connected by using links. These links represent the fact that the persons know the temporal order of the multiple tasks. The first mental model state for every person, is activated by external activation states (not shown in Fig. 8.2).

Fig. 8.2 Base level of model. The thickened lines are the connections which are initially part of the mental model of the corresponding official (R/A1/A2)

Table 8.2 Description of the base mental model states in the scenario Description

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To model multi-order adaptivity in the network model, a few first- and secondorder self-model states were created for the mental models; see Fig. 8.3. The firstorder adaptivity is modeled in the middle plane, and addresses the adaptivity of the mental models. The middle plane solely consists of such W-states; they represent all the weights of the connections between the base level mental model states. Some arrows are omitted due to clarity. A full overview of the connections can be found in the mcw matrix in the Appendix. Next to the influence on the base-level states, there are intralevel (coloured black) connections from all W-states of individual mental models to their equivalent W-states of the shared mental model and back. These connections represent parts where the individual team members contribute to the formation of the shared organisation mental model (feed forward learning) and vice versa (feedback learning). To be able to control the first-order adaptation processes in a context-dependent manner a third level was created. In this upper plane five types of states are shown (see Fig. 8.3): • Second-order self-model WW -states The self-model WW -states represent the connection weights between the middle level W-states; they are states of the form WW A ,W B for A, B ∈{R, A1, A2, O} (sometimes shortened to WW A,B ). They represent the learning power of the individuals by controlling the exchange via feed forward and feedback organisational learning. • Second-order self-model MW -states Persistence factors μ are used as weights for connections of W-states to themselves. They represent their extent of persistence with 1 as value for fully persistent (perfect recall); less persistence means more extinction or forgetting. Each persistence factor μ is made adaptive (depending on circumstances) by adding a corresponding MW -state to the upper plane: a control state representing the persistence factor, affecting the memory of the individuals. The MW -states are affected by the stress state. Note that, as the persistence factors are modeled in the middle plane as weights of connections from W-states to themselves, MW -states can be considered a special case of WW -states: higher order W-states of the form WW A ,W A for A ∈{R, A1, A2, O}. • Second-order self-model HW -states The self-model HW -states represent the adaptive speed factors ηW for W-states (their learning rate); these HW -states regulate the timing of the W-states when receiving an impact. • Stress state The stress state influences other second-order self-model states, in particular the MW -states. By doing so, they influence the memory of the individuals. If the stress level is 0, perfect recall takes place (μ = 1), if the stress level is >0, then some extinction or forgetting takes place, depending on how high the stress level is.

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Fig. 8.3 The connectivity of the full model depicted in a base-level, adaptation of mental models and control of adaptation of mental model. The black arrows represent intralevel influences, the red lines represent interlevel influences and the blue lines represent the influence from the phases

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• Activation-states The activation states are responsible for the start of the different phases as explained in the case description in Sect. 8.2.

8.5 Simulation of the Scenario Case The case scenario from Sect. 8.2 was simulated with a multi-phase approach, such that the different occurring phases can be observed. Note that in practice, these processes can, and often do, take place simultaneously; the model can also do that but for reasons of presentation the different phases were used. First, the individual models can be observed, some of the officials hold information about certain parts of the processes, while others do not. Therefore, the formation and the effects of the shared mental model for the team are shown. Both the feedforward learning from the different individuals to the shared organisational network and the feedback learning of individuals from the shared mental model, occur. In short, the following phases are shown. Phase 1: Initialization of individual mental models The three distinct individual mental models are of the three Football match officials. Since these persons have different characteristics and knowledge (for example, an Assistant deals with different aspects of the game than the referee), the officials have both common and role-specific knowledge. For this specific scenario, the referee has specific knowledge about the start of the game, and about giving free kicks in case of fouls, while the experienced Assistant has knowledge about the offside decisions, and how they communicate this offside in the team. The inexperienced Junior Assistant does not have any team-specific knowledge, which he first has to learn. Therefore, in this phase, A2 does not have knowledge about this specific part of the job. Moreover, since the three officials have different roles and since they react differently to their environment, they also have different characteristics that govern their learning. For example, the persistence of the learning is different for the two assistants. Phase 2: Formation of the shared mental model (feed forward learning) The match officials are aware that they lack common knowledge in their new team, so they have scheduled a meeting. Here, the formation of a unified shared mental model takes place. The individual mental models are merged, using the aggregation function, through the process of learning to form a shared mental model. Within this shared mental model, each connection strengthens. Phase 3: Learning from the shared model (feedback learning) Since the connections from the weight states stemming from the shared mental model are activated, knowledge is extracted from the shared mental model, the so-called instructional learning from the meeting. In this scenario, the officials learn from the organisation’s shared mental model.

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Phase 4: Using (and forgetting) the learned individual mental models In the last phase of the case simulation, the match officials officiate the game to which they were assigned. The highly stressful environment, make the officials more prone to forget certain rules and/or to make mistakes. This additional stress component makes the connections in their own mental models weaker. During this stage, the effect of the previous learning, the organisation’s shared mental model, and the individual mental models along with the added stress factor all have their influences on the decisions made by the match officials. Figure 8.4 shows the results of the simulation for the entire model. In the subsequent subsections, the behavior of the different match officials is shown in more detail. During the first stage of the simulation, the individual mental models are formed. The WW -states of the match officials towards the organisation (WW R ,W O , WW A1 ,W O , WW A2 ,W O or, shorter, WW R,O , WW A1 ,O , WW A2 ,O ) are active during this stage, as can be seen in Fig. 8.4, allowing for the transfer (feed forward learning), of the individual mental models towards the organisation’s shared mental model. During this stage, only the W-states for the connections which the respective match official has knowledge about are active, while the others are not. During the second stage of the organisational learning, feedback learning takes place in which the individual mental models can learn from the constructed organisation’s shared mental model. For more detailed graphs for the different phases, see Figs. 8.5, 8.6. During this learning stage A, the WW -states representing the feedback learning (WW O,R , WW O, A1 , WW O,A2 ) are active while also the speed factors associated with the W-states for the weights of the connections of the three officials (HW R , HW A1 , and HW A2 ) allow the learning to take place during this stage. It can clearly be seen that the weights of the previous unlearned connections are starting to become active as time progresses, in other words, the match officials are learning from the organisation’s

Fig. 8.4 Result of the full simulation: feed forward learning 20–200, feedback learning 250–500, usage and forgetting during match 590–1100

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Fig. 8.5 Part A: The organisational learning. During this part the shared mental models are formed

Fig. 8.6 Part B: The case. During this phase the mental models are brought into practice

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shared mental model. Note that a distinction is made in terms of weight activation processes for previously unlearned states and between the three different match officials. Roles of the officials which were previously not known, do not have as strong a connection as states which were already known before the organisation’s mental model was constructed, which models a less perfect learner. Moreover, the Referee and Assistant 1 reach slightly higher values for their newly formed connections, since they have experience in officiating a match together. In other words, newly learned roles and behavior are not as strong as ones that were already known, which accurately depicts learning in real life. The results of some of the second-order selfmodel states (WW -states and HW -states) are shown in Fig. 8.7a, b and for some of the first-order self-model states (W-states) in Fig. 8.7c, d. In this figure it can be seen that the W-states of the referee are subject to learning. Initially, the referee is proficient only in possibly detecting offside, whistling for a foul, and letting the game continue after interruptions. Therefore, the W-states for these connections (W Ra ,Rd , W Rd ,Re , W Rd ,R f , W Re ,R f ) have value 1 at the start of the briefing at time 20. During this stage, the Referee transfers his knowledge to the organisation’s shared mental model. However, the other W-states of the Referee (W Ra ,Rb , W Rb ,Rc ) which deal with the communication between the assistant and the referee concerning an offside position are initially of value 0 and thus must be learned by the referee from the organisation’s shared mental model in the next (feedback) stage of the organisational learning. This follows intuitively since this is the first time the three officials officiate a match together. These W-states are increasing once the second stage of the model takes place, during this stage the organisational learning takes place. Assistant 1 initially is proficient in detecting the offside, and communicating this with the referee, W-states W A1a , A1b and W A1b ,A1c therefore have value 1 from the start. The Assistant will transfer this knowledge to the organisational mental model during the feed forward learning stage of the organisation’s shared mental model. The other stages, which are not fully developed yet, have to be learned by the assistant. These other weight states W A1a , A1d , W A1d ,A1e , W A1d , A1 f , W A1e , A1 f have an initial value of 0 and should thus be learned from the organisational model. One can see that this does indeed happen during the second stage of the organisational learning, once the weight states of the connections from the organisation’s shared mental model towards those of the match officials become active. As opposed to the Referee and Assistant 1, the newly joined Assistant A2 does not have any knowledge within this team. Therefore, the Assistant is not yet proficient in any of the tasks. Consecutively, all W-states for A2 (W A2a , A2b , W A2b , A2c , W A2a ,A2d , W A2d ,A2e , W A2d , A2 f , W A2e , A2 f ) are having a value of 0 at the start and have to be learned first during the second stage (feedback learning) of the organisational learning. The weights corresponding to A2’s learning from the organisation’s mental model start to increase in that phase. During this stage, the assistant learns, although the obtained weights are not as strong as those of the Referee and the Assistant because they are more experienced. During the match two instances of offside take place. It can be seen in Fig. 8.8 that when the match (a derby) starts (time 590), via the M-states the induced stress causes the W-states representing the weights of the match officials to decline, with different

8 Organisational Learning and Usage of Mental Models for a Team … Fig. 8.7 The results of the simulation for some firstand second-order self-model states: (a) WW -states, (b) HW -states, (c) W-states Referee, (d) W-states Assistant 1

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Fig. 8.8 Result of the simulation

intensities based on their experience and role. During the first possible offside offense, all three match officials are aware of the offside position of the striker and handle the situation appropriately. The chronological nature of the infringement and the match official’s subsequent behavior is clearly visible. First, the striker moves into the offside position, which is then registered and communicated by the match officials, after which a free kick is given, and the game continues. Later in the game, the striker moves into an offside position again. This time, the inexperienced assistant, who is overloaded with stress and induced forgetting via the M-states, has much lower Wstates and therefore fails to communicate the offside position correctly with the other match officials. Thankfully, because the referee and the other assistant validated the offside position themselves, the appropriate measures could be taken by the match officials and the game could continue. Simulation Result: Referee The result of the states of the referee (R) and the weights of the connections of the referee during the case example simulation are shown in Fig. 8.9. It can be seen that the states of the referee are activated in chronological order of the offside infringements. Firstly, the striker puts himself in an offside position, after which the referee notices the possible offside, for which he receives feedback from both assistants during the first offside infringement, and from only the experienced assistant at the second offside infringement. As can be seen, the referee takes notice of the possible offside at the same time as the assistants, but evaluates the play before making a decision, which allows the communication and the decisions of the assistants to activate before making the final decision to whistle for a foul. Furthermore, as can be seen, the stress states cause the Weight states to decline slightly, but

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Fig. 8.9 The results of the simulation states part 2; referee

not enough to let the referee forget the connections which were formed during the organisational learning phase. Simulation Result: Assistant 1 The result of the states of the experienced Assistant (A1) and the weights of the connections of the assistant during the case example simulation are shown in the figures of the simulation in Fig. 8.10. It can be seen that the states of the experienced assistant are behaving similarly as the ones from the referee. Just like the referee, the activation of the states occurs in chronological order of the offside infringements. Like the referee, the experienced assistant also incurs some stress-related forgetting, which is represented by the decline in the activation of the W-states. However, this forgetting by stress effect is not strong enough to let the assistant forget the connections which were formed during the organisational learning phase.

(a) base states Fig. 8.10 The results of the simulation states part 2; assistant 1

(b) W state

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Simulation Result: Assistant 2 The result of the states of the inexperienced assistant (A2) and the weights of the connections of the assistant during the case example simulation are shown in Fig. 8.11. It can be seen that for the first offside infringement, the states of the assistant are activated in chronological order of the infringement. Firstly, the striker puts himself in an offside position, after which the assistant notices the possible offside, which he communicates with the referee. The referee reacts accordingly and whistles for a foul after which the game continues and the assistants return to their original positions. However, because of the inexperience of the assistant with officiating such a tense derby, the stress levels of the assistant are affecting the performance of the assistant. The W-states of the assistant are negatively affected by the build-up of stress, that is, the stress causes the assistant to forget the learned connections from the organisational model. This causes the assistant to forget important steps during the second offside infringement. As can be seen in the graph, the assistant does detect that the striker is in a possible offside position but is not sure whether an actual offside infringement took place, after which he stalls and fails to communicate his thought process to the referee and the other assistant, which causes the assistant to be unaware of the further steps to take. Therefore, all these states of the assistant do not activate. Thankfully, the referee and the experienced assistant do notice the offside infringement and handle it appropriately.

(a) base states Fig. 8.11 The results of the simulation states part 2; assistant 2

(b) W-state

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8.6 Mathematical Analysis of the Network Model Any given network node can find itself in one of three states. It is either at a stationary point and if not, its level is increasing or decreasing. The following definition is given for these three states: • Y is stationary point at t if dY(t)/dt = 0 • Y is increasing at t if dY(t)/dt > 0 • Y is decreasing at t if dY(t)/dt < 0 The model is in equilibrium at t if and only if every state Y of the model is a stationary point. To test whether the implemented model described in this chapter satisfies these equations and therefore is implemented correctly with respect to its design, some states will be analyzed. This will be done for stationary points of these states. For a more general description of such verification approaches, see Chaps. 16 and 17 of this volume (Canbalo˘glu et al. 2023c). For a network node Y, by (1) and (2) from Sect. 8.3 it is found that having a stationary point is expressed in terms of network characteristics by the following criterion: ηY = 0 or cY (ω X 1 ,Y X (t), . . . ., ω X k ,Y X (t)) = Y (t)

(8.4)

The W-states in the middle-level make use of the advanced logistic sum function given in Table 8.1. It can be observed that for example WRc,Rd has a stationary point at t = 450. This is a consequence of the (adaptive) speed factor being zero: HWR = 0 due to activation state 2. The model follows in this Eq. (8.4). Secondly, the stationary point of X 21 at t = 740 is investigated. At t = 740, Fig. 8.3 shows that X 21 reaches a maximum. The speed factor is fixed and is 0.2, which is non-zero. The advanced logistic sum parameters are given and are respectively 20 and 0.5 for σ and τ. The state at t = 740 can be calculated using only X 20 with connection weight X 47 , being: X 21 = 0.998828X 47 = 0.654299 If these values are substituted in advanced logistic sum function, we get: alogistic20,0.5 (0.654299 ∗ 0.998828) = 0.95566

(8.5)

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According to the simulation X 21 at t = 740 is 0.955735, which compared to the value from (5) only deviates 0.000075, which is < 10−4 . This is a good approximation of the actual simulated value, meaning the model was implemented correctly. A second stationary point for X 20 can be found at t = 1028. At this t, the same calculation can be performed for X 20 , which solely depends on X 19 and its corresponding connection weight X 46 . Substituting this leads to the following aggregated impact: alogistic20,0.3 (0.306668 ∗ 0.997255) = 0.527931

(8.6)

According to the simulation, the value of X 19 at t = 1028 is 0.530266. The deviation is therefore just 0.0023, which is in the order of 10−3 , which is again a good approximation. Similarly, a third verification was done for X 23 at t = 450; this provided a deviation of 0.000194. which is < 10−3 . A last calculation was performed for X 34 at t = 495. Here a deviation of 0.000460 is found, which is also < 10−3 . These verification instances all provide evidence that the implemented model is correct with respect to its design.

8.7 Discussion The material of this chapter is based on (Kuilboer et al. 2022). Computational analysis of organisational learning can offer quite an interesting insight in addition to the mainstream literature within the organisational learning field. By using individual mental models, a shared mental model on the organisational level is formed: feed forward learning. Once formed, the shared mental model can be used to teach the individuals who do not have knowledge of certain parts. To be able to analyse this in a computational manner the underlying conceptual and computational mechanisms have to be identified (Canbalo˘glu et al. 2023b; Wiewiora et al. 2019). The computational model introduced here is a second-order adaptive network model integrating parts described separately in (Canbalo˘glu et al. 2022) for organisational learning and (Treur and Van Ments 2022) for usage of mental models. These sources themselves did not yet address in a detailed manner the integration of formation (by organisational learning) and usage (where also world states and their dynamics play a role) of the (shared) mental models. This research follows a team which comes together to line-up their thoughts and bring them into reality in a match in the world within one model. In addition, a totally unaware teammate is introduced, and he is able to learn from the shared mental model. To demonstrate such, the second junior assistant was introduced, which was unaware of all his tasks. The organisation’s shared mental model was learned using the knowledge of both the referee and the first assistant, and subsequently used to teach the second assistant.

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The model provides a strong basis for computational analysis. However, many improvements and extensions can still be made. For example, currently, it is explicitly stated that the Referee and Assistant 1 both have half of the knowledge, meaning they want to learn from each other. However, one can think of situations where two individuals have different, conflicting looks on a situation. The model has not been designed or tested to cope with this kind of situation. Another possible extension is to further optimize the M-states. Currently, the states follow a likewise trajectory. By implementing differences for states that are more likely to react on certain stress-full situations an even more realistic model can be created. Further extensions could be considered taking into account context-sensitive aggregation of mental models by controlling the type of aggregation (Canbalo˘glu and Treur 2022a, 2022b) and also a distincition may be added between shared mental models at the team level and at a higher organisation level covering more teams, e.g., as addressed in (Canbalo˘glu et al. 2023a).

8.8 Appendix: Overview of the States and Role Matrices

Base states State X1 X2

Name Oa Ob

X3

Oc

X4 X5

Od Oe

X6

Of

X7 X8

Ra Rb

X9

Rc

X10 X11 X12 X13 X14

Rd Re Rf A1a A1b

X15

A1c

X16 X17 X18 X19 X20 X21

A1d A1e A1f A2a A2b

X22 X23 X24

A2d A2e A2f

A2c

Meaning Organisational base state; Striker moves into a potential offside position Organisational base state: Assistant is aware of the possible offside Organisational base state: Assistant raises flag and communicates offside infringement with the match officials Organisational base state: The referee is aware of the possible offside Organisational base state: The referee gives a free kick Organisational base state: The game continues (after handling the possible offside infringement) Referee base state; Striker moves into a potential offside position Referee base state: Assistant is aware of the possible offside Referee base state: Assistant raises flag and communicates offside infringement with the match officials Referee base state: The referee is aware of the possible offside Referee base state: The referee gives a free kick Referee base state: The game continues (after handling the possible offside infringement) Assistant 1 base state; Striker moves into a potential offside position Assistant 1 base state: Assistant is aware of the possible offside Assistant 1 base state: Assistant raises flag and communicates offside infringement with the match officials Assistant 1 base state: The referee is aware of the possible offside Assistant 1 base state: The referee gives a free kick Assistant 1 base state: The game continues (after handling the possible offside infringement) Assistant 2 base state; Striker moves into a potential offside position Assistant 2 base state: Assistant is aware of the possible offside Assistant 2 base state: Assistant raises flag and communicates offside infringement with the match officials Assistant 2 base state: The referee is aware of the possible offside Assistant 2 base state: The referee gives a free kick Assistant 2 base state: The game continues (after handling the possible offside infringement)

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State X25 X26 X27 X28 X29 X30 X31 X32 X33 X34 X35 X36 X37 X38 X39 X40 X41 X42 X43 X44 X45 X46 X47 X48 X49 X50 X51 X52

Name WOa,Ob WOb,Oc WOa,Od WOc,Od WOd,Oe WOd,Of WOe,Of WRa,Rb WRb,Rc WRa,Rd WRc,Rd WRd,Re WRd,Rf WRe,Rf WA1a,A1b WA1b,A1c WA1a,A1d WA1c,A1d WA1d,A1e WA1d,A1f WA1e,A1f WA2a,A2b WA2b,A2c WA2a,A2d WA2c,A2d WA2d,A2e WA2d,A2f WA2e,A2f

State

Name

X53

WWO,R

X54

WWO,A1

X55

WWO,A2

X56

WWR,O

X57

WWA1,O

X58

WWA2,O

Meaning Weights for the organisational base state connections: Oa-Ob Weights for the organisational base state connections: Ob-Oc Weights for the organisational base state connections: Oa-Od Weights for the organisational base state connections: Oc-Od Weights for the organisational base state connections: Od-Oe Weights for the organisational base state connections: Od-Of Weights for the organisational base state connections: Oe-Of Weights for the referee base state connections: Ra-Rb Weights for the referee base state connections: Rb-Rc Weights for the referee base state connections: Ra-Rd Weights for the referee base state connections: Rc-Rd Weights for the referee base state connections: Rd-Re Weights for the referee base state connections: Rd-Rf Weights for the referee base state connections: Re-Rf Weights for the Assistant 1 base state connections: A1a-A1b Weights for the Assistant 1 base state connections: A1b-A1c Weights for the Assistant 1 base state connections: A1a-A1d Weights for the Assistant 1 base state connections: A1c-A1d Weights for the Assistant 1 base state connections: A1d-A1e Weights for the Assistant 1 base state connections: A1d-A1f Weights for the Assistant 1 base state connections: A1e-A1f Weights for the Assistant 2 base state connections: A2a-A2b Weights for the Assistant 2 base state connections: A2b-A2c Weights for the Assistant 2 base state connections: A2a-A2d Weights for the Assistant 2 base state connections: A2c-A2d Weights for the Assistant 2 base state connections: A2d-A2e Weights for the Assistant 2 base state connections: A2d-A2f Weights for the Assistant 2 base state connections: A2e-A2f

Meaning Weights of the Weights of the connections from the Organisational mental model to the Referee mental model. Governing when learning from the organisational model takes place Weights of the Weights of the connections from the Organisational mental model to the Assistant 1 mental model. Governing when learning from the organisational model takes place Weights of the Weights of the connections from the Organisational mental model to the Assistant 2 mental model. Governing when learning from the organisational model takes place Weights of the Weights of the connections from the Referee mental model to the organisational mental model. Governing when learning by the organisational model takes place Weights of the Weights of the connections from the Assistant 1 mental model to the organisational mental model. Governing when learning by the organisational model takes place Weights of the Weights of the connections from the Assistant 2 mental model to the organisational mental model. Governing when learning by the organisational model takes place

8 Organisational Learning and Usage of Mental Models for a Team … X59

HWR

X60

HWA1

X61

HWA2

X62

MWRa,Rb

X63

MWRb,Rc

X64

MWRa,Rd

X65

MWRc,Rd

X66

MWRd,Re

X67

MWRd,Rf

X68

MWRe,Rf

X69

MWA1a,A1b

X70

MWA1b,A1c

X71

MWA1a,A1d

X72

MWA1c,A1d

X73

MWA1d,A1e

X74

MWA1d,A1f

X75

MWA1e,A1f

X76

MWA2a,A2b

X77

MWA2b,A2c

X78

MWA2a,A2d

X79

MWA2c,A2d

X80

MWA2d,A2e

X81

MWA2d,A2f

X82

MWA2e,A2f

X83

Act State 1

X84

Act State 2

X85

Act State 3

X86

HWO

X87

stress State

X88

Act State 4

175

The speed factor of the Weight states of the Referee. Governing the adaptivity of the weight state. The speed factor of the Weight states of the Assistant 1. Governing the adaptivity of the weight state. The speed factor of the Weight states of the Assistant 2. Governing the adaptivity of the weight state. The weight of the self reference of the Weight state of the connection between Ra and Rb. Governing the effect of forgetting with time. The weight of the self reference of the Weight state of the connection between Rb and Rc. Governing the effect of forgetting with time. The weight of the self reference of the Weight state of the connection between Ra and Rd. Governing the effect of forgetting with time. The weight of the self reference of the Weight state of the connection between Rc and Rd. Governing the effect of forgetting with time. The weight of the self reference of the Weight state of the connection between Rd and Re. Governing the effect of forgetting with time. The weight of the self reference of the Weight state of the connection between Rd and Rf. Governing the effect of forgetting with time. The weight of the self reference of the Weight state of the connection between Re and Rf. Governing the effect of forgetting with time. The weight of the self reference of the Weight state of the connection between A1a and A1b. Governing the effect of forgetting with time. The weight of the self reference of the Weight state of the connection between A1b and A1c. Governing the effect of forgetting with time. The weight of the self reference of the Weight state of the connection between A1a and A1d. Governing the effect of forgetting with time. The weight of the self reference of the Weight state of the connection between A1c and A1d. Governing the effect of forgetting with time. The weight of the self reference of the Weight state of the connection between A1d and A1e. Governing the effect of forgetting with time. The weight of the self reference of the Weight state of the connection between A1d and A1f. Governing the effect of forgetting with time. The weight of the self reference of the Weight state of the connection between A1e and A1f. Governing the effect of forgetting with time. The weight of the self reference of the Weight state of the connection between A2a and A2b. Governing the effect of forgetting with time. The weight of the self reference of the Weight state of the connection between A2b and A2c. Governing the effect of forgetting with time. The weight of the self reference of the Weight state of the connection between A2a and A2d. Governing the effect of forgetting with time. The weight of the self reference of the Weight state of the connection between A2c and A2d. Governing the effect of forgetting with time. The weight of the self reference of the Weight state of the connection between A2d and A2e. Governing the effect of forgetting with time. The weight of the self reference of the Weight state of the connection between A2d and A2f. Governing the effect of forgetting with time. The weight of the self reference of the Weight state of the connection between A2e and A2f. Governing the effect of forgetting with time. The activation state, governing when the first stage of the model becomes active. The learning of the organisational model from the initial individual models. The activation state, governing when the second stage of the model becomes active. The learning of the individual models from the organisational model. The activation state, governing when the third stage of the model becomes active. The first occurrence of the possible offside infringement from the case example. The speed factor of the Weight states of the organisational model. Governing the adaptivity of the weight state. The stress state, which regulates the amount of stress the match officials have to endure. This state represents the start and end time of the football match. The activation state, governing when the fourth stage of the model becomes active. The second occurrence of the possible offside infringement from the case example.

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Fig. 8.13 Role matrix mcw table for connection weights The states in green are adaptive

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Fig. 8.14 Role matrix mcfw for combination function weights

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Fig. 8.15 Speedfactor table ms. The states in green are adaptive

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states part 2; assistant Fig. 8.16 Role matrix mcfp table for combination function parameters

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References Abraham, W.C., Bear, M.F.: Metaplasticity: the plasticity of synaptic plasticity. Trends Neurosci. 19(4), 126–130 (1996) Boyko, R.H., Boyko, A.R., Boyko, M.G.: Referee bias contributes to home advantage in English Premiership football. J. Sports Sci. 25(11), 1185–1194 (2007) Canbalo˘glu, G., Treur, J.: Context-sensitive mental model aggregation in a second-order adaptive network model for organisational learning. In: Proceedings of the 10th International Conference on Complex Networks and their Applications. Studies in Computational Intelligence, vol. 1015, pp. 411–423. Springer Nature (2022a) Canbalo˘glu, G., Treur, J.: Using Boolean Functions of Context Factors for Adaptive Mental Model Aggregation in Organisational Learning. Proc. of the 12th International Conference on BrainInspired Cognitive Architectures, BICA’21. Studies in Computational Intelligence, vol. 1032, pp 54–68 Springer Nature, Cham (2022b). Canbalo˘glu, G., Treur, J., Roelofsma, P.H.M.P.: Computational modeling of organisational learning by self-modeling networks. Cogn. Syst. Res. 73, 51–64 (2022) Canbalo˘glu, G., Treur, J., Roelofsma, P.H.M.P.: An adaptive self-modeling network model for multilevel organisational learning. In: Proceedings of the 7th International Congress on Information and Communication Technology, ICICT’22, vol. 2. Lecture Notes in Networks and Systems, vol. 448, pp. 179–191. Springer Nature (2023a) Canbalo˘glu, G., Treur, J., Wiewiora, A.: Computational modeling of multilevel organisational learning: from conceptual to computational mechanisms. In: Shukla, A., Murthy, B.K., Hasteer, N., Van Belle, JP. (eds), Computational Intelligence, Proceedings of InCITe’22. Lecture Notes in Electrical Engineering, vol. 968, pp. 1–17. Springer Nature (2023b) Canbalo˘glu, G., Treur, J., Wiewiora, A. (eds.).: Computational Modeling of Multilevel Organisational Learning and its Control Using Self-Modeling Network Models. Springer Nature (2023c) (this volume) Craik, K.J.W.: The nature of explanation. CUP Arch. 445 (1952) Crossan, M.M., Lane, H.W., White, R.E.: An organisational learning framework: from intuition to institution. Acad. Manag. Rev. 24, 522–537 (1999) Gomez-Carmona, C., Ortega, J.P.: Kinematic and physiological analysis of the performance of the referee football and its relationship with decision making. J. Hum. Sport. Exerc. 11(4), 397–414 (2016) Heil, J.: Philosophy of Mind. Routledge (1998) Hendrikse, S.C.F., Treur, J., Koole, S.L.: Modeling Emerging Interpersonal Synchrony and its Related Adaptive Short-Term Affiliation and Long-Term Bonding: A Second-Order MultiAdaptive Neural Agent Model. International Journal of Neural Systems (2023) Katz-Navon, T.Y., Erez, M.: When collective-and self-efficacy affect team performance: the role of task interdependence. Small Group Res. 36(4), 437–465 (2005) Kim, D.H. (1993). The Link Between Individual and Organisational Learning. Sloan Management Review, Fall 1993, pp. 37–50. Also in: Klein, D.A. (ed.), The Strategic Management of Intellectual Capital. Routledge-Butterworth-Heinemann, Oxford. Kim, D.H.: The link between individual and organisational learning. In: The strategic management of intellectual capital 41, 62 (1998) Kuilboer, S., Sieraad, W., Canbalo˘glu, G., Van Ments, L., Treur, J.: A second-order adaptive network model for organisational learning and usage of mental models for a team of match officials. In: Nguyen, N.T., Manolopoulos, Y., Chbeir, R., Kozierkiewicz, A., Trawi´nski, B. (eds) Computational Collective Intelligence, Proceedings of the 14th International Conference on Computational Collective Intelligence, ICCCI’22. Lecture Notes in AI, vol 13501, pp. 701–716. Springer Nature, Cham (2022) Mathieu, J.E., et al.: The influence of shared mental models on team process and performance. J. Appl. Psychol. 85(2), 273 (2000)

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Part IV

Approaches to Aggregation in the Formation of Shared Mental Models in Organisational Learning

A context within which the learning takes place can influence learning outcomes. The context of learning needs to be considered in computational modeling to better reflect reality. In this part the models are refined in order to address context-sensitive control of aggregation. Building further on the models described in Part III, first a heuristic-based aggregation process is addressed, which may depend on a number of contextual factors. It is shown how a second-order adaptive self-modeling network model for organisation learning can be used to model this process of aggregation of individual mental models in a heuristic context-dependent manner. Next, it is explored how Boolean functions of these context factors can be used to model a nonheuristic, logical form of aggregation.

Chapter 9

Heuristic Context-Sensitive Control of Mental Model Aggregation for Multilevel Organisational Learning Gülay Canbalo˘glu and Jan Treur

Abstract Within organisational learning, aggregation of developed individual mental models to obtain shared mental models for the organisation is a crucial process. This aggregation process usually does not only depend on the mental models used as input for it, but also on several context factors that may vary over circumstances and time. This means that for computational modeling of organisational learning by adaptive networks, where the formation of a shared mental model is a form of network adaptation, the underlying aggregation process better can be controlled by a second-order adaptive dynamical process to obtain a context-sensitive way of aggregation. In this chapter it is explored how context factors can be used to model this form of second-order network adaptation. Indeed, using self-modeling networks, mental model adaptation by learning, formation or aggregation can be modeled in an appropriate manner at a first-order adaptive self-model level, whereas the control over such processes can be modeled at a second-order adaptive self-model level. In this chapter it is shown how by a second-order self-model in such a network, contextrich knowledge can be specified that is used to control the aggregation with the first-order self-model in a context-sensitive manner. This is illustrated for heuristic knowledge. Based on this control knowledge such an adaptive network model can exert context-sensitive control over the mental model aggregation process. Thus, a computational network modeling approach of organisational learning is presented in which the process of aggregation of individual mental models to form shared mental models is controlled in an adaptive context-dependent manner based on heuristic knowledge. Keywords Adaptive network model · Aggregation process · Mental models · Organisational learning G. Canbalo˘glu · J. Treur (B) Social AI Group, Department of Computer Science, Vrije Universiteit Amsterdam, Amsterdam, Netherlands e-mail: [email protected] G. Canbalo˘glu e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 G. Canbalo˘glu et al. (eds.), Computational Modeling of Multilevel Organisational Learning and Its Control Using Self-modeling Network Models, Studies in Systems, Decision and Control 468, https://doi.org/10.1007/978-3-031-28735-0_9

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9.1 Introduction Organisational learning (Argyris 1978; Bogenrieder 2002; Crossan et al. 1999; Fischhof 1997; Kim 1993; McShane 2010; Stelmaszczyk 2016; Wiewiora et al. 2019) is a challenging complex adaptive phenomenon within an organisation, especially when it comes to computational modeling of it. Within organisational learning different types of adaptation processes work together in a dynamical manner via an interplay of individual learning, collaborative learning and a number of feedforward and feedback cycles; e.g., (Crossan et al. 1999; Kim 1993; Wiewiora et al. 2019). Specific adaptation process involved are, for example, individual learning and development of mental models, learning by cooperation between individuals, formation of shared mental models for teams or for the organisation as a whole, and improving individual mental models or team mental models based on a shared mental model of the organisation; e.g., (Crossan et al. 1999; Kim 1993; Wiewiora et al. 2019). For example, Kim (1993) puts forward that. Organisational learning is dependent on individuals improving their mental models; making those mental models explicit is crucial to developing new shared mental models. (Kim 1993), p. 44

Formation of shared mental models usually takes place by a process of aggregation of individual mental models. Concerning this, an interesting challenge addressed in the current chapter is how specific context factors play their role in formation of a shared mental model by aggregating a number of individual mental models in an adaptive, context-sensitive manner. Concerning mental models, in (Treur and Van Ments, 2022) it has been explored how self-modeling networks (Treur 2020a, b) provide an adequate modeling approach to obtain (second-order adaptive) computational models addressing how they are (1) used for internal simulation, (2) adapted by learning, revision or forgetting, and (3) controlled. A basis for this is formed by the three-level cognitive architecture for mental models described in (Van Ments and Treur 2021). As a next step, in (Canbalo˘glu et al. 2022), it has also been shown how based on self-modeling networks computational models of (multilevel) organisational learning can be designed. Here, although the feed forward and feedback organisational learning processes were controlled, the aggregation of individual mental models to form a shared organisation mental model was still addressed in a fixed, nonadaptive manner without explicit context-sensitive control. Flexibility with respect to contextsensitivity of the control of learning is often a main challenge for computational models for learning processes in general. The multi-order adaptive network-based approach introduced in the current chapter provides extended capabilities for adaptive network models in particular that allow to obtain much more realism of such network models by taking into account context factors in a detailed manner in the control of the aggregation used in feed forward organisational learning. In (Canbalo˘glu and Treur 2022) a first contribution was made to model context-sensitive control over the aggregation process. This was done by a heuristic approach. In the current chapter, this is illustrated, but in addition to this, in (Canbalo˘glu et al. 2023), Chap. 10 of this

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volume it is shown how the context-sensitive control of the aggregation process can also be done in a more precise, exact manner by modeling it based on control knowledge expressed by propositions described as (Boolean) functions of the considered context factors. In this chapter, in Sect. 9.2 some background knowledge is discussed. Section 9.3 describes the self-modeling networks modeling approach used. In Sect. 9.4, the computational self-modeling network model for organisational learning based on a heuristic approach to context-dependent aggregation will be introduced with more details in Sect. 9.5. This model is illustrated by an example simulation scenario in Sect. 9.6. Finally, Sect. 9.7 is a discussion and Sect. 9.8 an Appendix with full specifications.

9.2 Background Literature In this section, some of the multidisciplinary literature about the concepts and processes that need to be addressed are briefly discussed. This provides a basis for the self-modeling network model that will be presented in Sect. 9.4 and for the scientific justification of the model. For the history of the mental model area, often Kenneth Craik is mentioned as a central person. In his book Craik (1943) describes a mental model as a small-scale model that is carried by an organism within its head and based on that the organism. ‘is able to try out various alternatives, conclude which is the best of them, react to future situations before they arise, utilize the knowledge of past events in dealing with the present and future, and in every way to react in a much fuller, safer, and more competent manner to the emergencies which face it.’ (Craik 1943, p. 61).

Shih and Alessi (1993) explain that. By a mental model we mean a person’s understanding of the environment. It can represent different states of the problem and the causal relationships among states. (Shih and Alessi 1993), p. 157

In (Van Ments and Treur 2021), an analysis of various types of mental models and the types of mental processes processing involved are reviewed. Based on this analysis a three-level cognitive architecture has been introduced where the base level models internal simulation of a mental model, the middle level models the adaptation of the mental model (formation, learning, revising, and forgetting a mental model, for example), and the upper-level models the (metacognitive) control over these processes (see Fig. 9.1). Mental models also play an important role when people work together in teams. When every team member has a different individual mental model of the task that is performed, then this will stand in the way of good teamwork. Therefore, ideally these mental models should be aligned to such an extent that it becomes one shared mental model for all team members. Examples of computational models of a shared

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Fig. 9.1 Cognitive architecture for mental model handling with three levels of mental processing for mental models

Control of adaptation of mental models

Adaptation of mental models

Use of mental models

mental model and how imperfections in it work out can be found in (Van Ments et al. 2021a, b). Organisational learning is an area which has received much attention over time; see, for example, (Argyris 1978; Bogenrieder 2002; Crossan 1999; Fischhof 1997; Kim 1993; McShane 2010; Stelmaszczyk 2016; Wiewiora et al. 2019). However, contributions to computational formalization of organisational learning are very rare. By Kim (1993), mental models are considered a vehicle for both individual learning and organisational learning. By learning and developing individual mental models, a basis for formation of shared mental models for the level of the organisation is created, which provides a mechanism for organisational learning. As shown in Fig. 9.2, the overall organisational learning process consists of the following cyclical processes and interactions (see also (Kim 1993), Fig. 9.8): (a) Individual level (1) Creating and maintaining individual mental models (2) Choosing for a specific context a suitable individual mental model as focus

Feed forward learning

INDIVIDUALS

Learning within and between individuals

ORGANIZATION

Feedback learning

Fig. 9.2 Different processes within organisational learning. Feed forward learning involves formation of a shared mental model by aggregation of individual mental models. Feedback learning addresses how individuals improve their mental models by learning from a shared mental model

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(3) Applying a chosen individual mental model for internal simulation (4) Improving individual mental models (individual mental model learning) (b) From individual level to organisation level (feed forward learning) (1) Deciding about creation of shared mental models (2) Creating shared mental models based on developed individual mental models (c) Organisation level (1) Creating and maintaining shared mental models (2) Associating to a specific context a suitable shared mental model as focus (3) Improving shared mental models (shared mental model refinement or revision) (d) From organisation level to individual level (feedback learning) (1) Deciding about individuals to adopt shared mental models (2) Individuals adopting shared mental models by learning them (e) From individual level to organisation level (1) Deciding about improvement of shared mental models (2) Improving shared mental models based on further developed individual mental models The computational network models for organisational learning and in particular for the context-sensitive control over the aggregation in them that will be presented in this chapter in a sense combine the two pictures shown in Figs. 9.1, 9.2 in the form of three-level (second-order adaptive) network models.

9.3 The Self-Modeling Network Modeling Approach Used In this section, the network-oriented modeling approach used is briefly introduced. A temporal-causal network model is characterised by; here X and Y denote nodes of the network, also called states (Treur 2020b): • Connectivity characteristics Connections from a state X to a state Y and their weights ωX,Y • Aggregation characteristics For any state Y, some combination function cY (..) defines the aggregation that is applied to the impacts ωX,Y X(t) on Y from its incoming connections from states X • Timing characteristics Each state Y has a speed factor ηY defining how fast it changes for given causal impact.

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Fig. 9.3 The combination functions used in the introduced self-modeling network model

The following canonical difference (or related differential) equations are used for simulation purposes; they incorporate these network characteristics ωX,Y , cY (..), ηY in a standard numerical format: Y (t + /\t) = Y (t) + ηY [cY (ω X 1 ,Y X 1 (t), . . . , ω X k ,Y X k (t)) − Y (t)]/\t

(9.1)

for any state Y and where X 1 to X k are the states from which Y gets its incoming connections. The available dedicated software environment described in (Treur 2020b, Ch. 9), includes a combination function library with currently around 65 useful basic combination functions; see also (Treur and Van Ments 2022, Ch. 17). The above concepts enable to design network models and their dynamics in a declarative manner, based on mathematically defined functions and relations. The examples of combination functions that are applied in the model introduced here can be found in Fig. 9.3. Combination functions as shown in Fig. 9.3 and available in the combination function library are called basic combination functions. For any network model some number m of them can be selected; they are represented in a standard format as bcf1 (..), bcf2 (..), …, bcfm (..). In principle, they use parameters π1,i,Y , π2,i,Y such as the λ, σ, and τ in Fig. 9.3. Including these parameters, the standard format used for basic combination functions is (with V 1 , …, V k the single causal impacts): bcf i (π1,i,Y , π2,i,Y , V1 , . . . , Vk ). For each state Y just one basic combination function can be selected, but also a number of them can be selected, what happens in the current chapter; this will be interpreted as a weighted average of them according to the following format:

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cY (π1,1,Y , π2,1,Y , . . . , π1,m,Y , π2,m,Y , V1 , . . . , Vk ) = γ1,Y bcf1 (π1,1,Y , π2,1,Y , V1 , . . . , Vk ) + . . . + γm,Y bcfm (π1,m,Y , π2,m,Y, V1 , . . . , Vk ) γ1,Y + . . . + γm,Y (9.2) with combination function weights γi,Y . Selecting only one of them for state Y, for example, bcf i (..), is done by putting weight γi,Y = 1 and the other weights 0. This is a convenient way to indicate combination functions for a specific network model. The function cY (..) can just be indicated by the weight factors γi,Y and the parameters πi,j,Y . Realistic network models are usually adaptive: Often not only their states but also some of their network characteristics change over time. By using a self-modeling network (also called a reified network), a network-oriented conceptualization can also be applied to adaptive networks to obtain a declarative description using mathematically defined functions and relations for them as well; see (Treur 2020a, 2020b). This works through the addition of new states to the network (called self-model states) which represent (adaptive) network characteristics. In the graphical 3D-format as shown in Sect. 9.4, such additional states are depicted at a next level (called self-model level or reification level), where the original network is at the base level. As an example, the weight ωX,Y of a connection from state X to state Y can be represented (at a next self-model level) by a self-model state named WX,Y . Similarly, all other network characteristics from ωX,Y , cY (..), ηY can be made adaptive by including self-model states for them. For example, an adaptive speed factor ηY can be represented by a self-model state named HY , an adaptive combination function weight γi,Y can be represented by a self-model state Ci,Y . As the outcome of such a process of network reification is also a temporal-causal network model itself, as has been shown in detail in (Treur 2020b, Ch 10), this selfmodeling network construction can easily be applied iteratively to obtain multiple orders of self-models at multiple (first-order, second-order, …) self-model levels. For example, a second-order self-model may include a second-order self-model state HW X,Y representing the speed factor ηW X,Y for the dynamics of first-order self-model state WX,Y which in turn represents the adaptation of connection weight ωX,Y . Similarly, a persistence factor μW X,Y of such a first-order self-model state WX,Y used for adaptation, e.g., based on Hebbian learning (Hebb 1949) can be represented by a second-order self-model state MW X,Y . By using the notion of self-modeling network described in this section, recently the cognitive architecture for mental models shown in Fig. 9.1 has been formalized computationally and used in computer simulations for various applications of mental models; for an overview of this approach and its applications, see (Treur and Van Ments 2022). In terms of a self-modeling network model used to formalise the threelevel cognitive architecture for mental models (see also Fig. 9.4):

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Control of adaptation of a mental model

Second-order self-model of a mental model

Adaptation of a mental model

First-order self-model of a mental model

Internal simulation by a mental model Three-level cognitive architecture

Base level with a mental model as subnetwork

Self-modeling network architecture

Fig. 9.4 Computational formalization of the three-level cognitive architecture for mental model handling from Fig. 9.1 by a self-modeling network architecture

(1) Using a mental model for internal mental simulation relates to the base level (the pink, lower plane in Fig. 9.1), (2) Learning, developing, improving, forgetting a mental model (the blue, middle plane in Fig. 9.1) relates to the first-order self-model level, and (3) The control of adaptation of a mental model (the purple, upper plane in Fig. 9.1) relates to the second-order self-modeling level. This type of computational formalisation for mental models will also be a point of departure for developing the computational models for organisational learning processes in the subsequent sections. In particular, for the aggregation process for the formation of a shared mental which is a main focus of the current chapter, secondorder self-model states Ci,W X,Y will be used that represent the ith combination function weight γi,W X,Y of the combination functions selected for a shared mental model connection weight WX,Y , where the latter is a first-order self-model state used to model adaptation of a mental model. Such self-model states are sometimes called C-states or Ci,W -states.

9.4 Adaptive Network Modeling for Organisational Learning with Controlled Mental Model Aggregation The case study addressed to illustrate the introduced model was adopted from the more extensive case study in an intubation process from (Van Ments et al. 2021a, b); see also Fig. 9.5. Here only the part of the mental models is used that addresses four mental states; see Table 9.1. In the case study addressed here, initially the mental models of the nurse (person A) and doctor (person B) are different and based on weak connections; they don’t use a stronger shared mental model as that does not exist yet. The organisational learning addressed to improve the situation covers:

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Fig. 9.5 The example mental model from (Van Ments et al. 2021a, 2021b) with indicated the part used in the current chapter

Table 9.1 The mental model used for the simple case study States for mental Short notation models of persons A, B and organisation O

Explanation

a_A

a_B

a_O

Prep_eq_N

Preparation of the intubation equipment by the nurse

b_A

b_B

b_O

Prep_d_N

Nurse prepares drugs for the patient

c_A

c_B

c_O

Pre_oy_D

Doctor executes pre oxygenation

d_A

d_B

d_O

Prep_team_D

Doctor prepares the team for intubation

1. Individual learning by A and B of their mental models through internal simulation which results in stronger but still incomplete and different mental models (by Hebbian learning). Person A’s mental model has no connection from c_A to d_A and person B’s mental model has no connection from a_B to b_B. 2. Formation of a shared organisation mental model based on the two individual mental models. A process of unification takes place. 3. Learning individual mental models from the shared mental model, e.g., a form of instructional learning. 4. Strengthening these individual mental models by individual learning through internal simulation which results in stronger and now complete mental models (by Hebbian learning). Now person A’s mental model has a connection from c_A to d_A and person B’s mental model has a connection from a_B to b_B. In this case study, person A and person B have knowledge on different tasks, and there is no shared mental model at first. Development of the organisational learning covers: 1. Individual learning processes of A and B for their separate mental models through internal simulation. By Hebbian learning (Hebb 1949), mental models become

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stronger but they are still incomplete. A has no knowledge for state d_A, and B has no knowledge for state a_B: they do not have connections to these states. Shared mental model formation by aggregation of the different individual mental models. Individuals’ adoption of shared mental model, e.g., a form of instructional learning. Strengthening of individual mental models by individual learning through internal simulation, strengthening knowledge for less known states of persons A and B (by Hebbian Learning). Then, persons have stronger and now (more) complete mental models. Improvements on the shared mental model by aggregation of the effects of the strengthened individual mental individuals.

A crucial element for the shared mental model formation is the aggregation process. Not all individual mental models will be considered to have equal value. Person A may be more knowledgeable than person B, for example. And when they are equally knowledgeable, can they be considered independent sources, or have they just learnt it from the same source? In the former case, aggregation of their knowledge leads to a stronger outcome than in the latter case. Based on such considerations, a number of context factors have been included that affect the type of aggregation that is applied: They are used to control the process of aggregation leading to a shared mental model in such a way that it becomes context sensitive. As in the network model, aggregation is specified by combination functions (see Sect. 9.3) of the first-order self-model states WX,Y for the weights of the connections X → Y of the shared mental model, this means that these combination functions become adaptive (in a heuristic manner) in relation to the specified context factors. The influences of the context factors on the aggregation as indicated in Table 9.2 have been used to specify this context-sensitive control for the choice of combination function. For example, if A and B have similar knowledgeability, a form of average is supported (a Euclidean or geometric mean combination function), unless they are independent in which case some form of amplification is supported (a logistic combination function). If they differ in knowledgeability, the maximal knowledge is chosen (a maximum combination function). These are meant as examples of heuristics to illustrate the idea and can easily be replaced by other heuristics. To model context-sensitive adaptive control of aggregation of mental models in the current chapter, the self-modeling network model for organisational learning with fixed, nonadaptive aggregation introduced in (Canbalo˘glu et al. 2022) was used as a point of departure. The connectivity of the designed network model is depicted in Fig. 9.6. Recall Figs. 9.1, 9.2, 9.4 in Sects. 9.2, 9.3 that formed inspiration for this design. The base level of this model includes all the individual mental states, shared mental model states, and the context states that are used to initiate different phases. Base level states can be considered as the basis of the model.

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Table 9.2 Examples of heuristics for context-sensitive control of mental model aggregation applied in the example scenario Context: knowledgeable

Context: dependency

A and B both not knowledgeable A and B both knowledgeable

A and B dependent

Context: preference for type of quantity

Combination function type

Additive

Euclidean

Multiplicative

Geometric mean

Additive

Euclidean

Multiplicative

Geometric mean

A and B independent

Logistic

A knowledgeable B not knowledgeable

Maximum

B knowledgeable A not knowledgeable

Maximum

Fig. 9.6 The connectivity of the second-order adaptive network model

The first-order self-model level includes context states that play a role in the aggregation such as context states for knowledgeability level, dependence level and preference for additive or multiplicative aggregation. Derived context states (e.g., representing that none of A and B is knowledgeable) are also placed here to make combinations of context states clearer by specifying in a precise way what it is that affects aggregation. Following the model from (Canbalo˘glu et al. 2022), this level lastly includes W-states representing the weights of the base level connections of the mental models to make them adaptive. At this first-order adaptation level there are a number of (intralevel) connections that connect W-states from individual mental

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models (also called WA -states and WB -states) to shared mental models (also called WO -states), and conversely. The first type of such connections (from left to right) are used for the formation of the shared mental model: They provide the flow of information from the W-states of the individual mental models for A and B (WA and WB -states) to the W-states of the shared mental model (WO -states). This starts the aggregation process by which the shared mental model is formed, feed forward learning (Crossan et al. 1999); see also Fig. 9.2 in Sect. 9.2. The second type of intralevel connections (from right to left) model the influence that a shared mental model has on the individual mental models: From WO -states to WA - and WB -states. This models, for example, instruction of the shared mental model to employees in order to get their individual mental models better, feedback learning (Crossan et al. 1999); see also Fig. 9.2 in Sect. 9.2. The second-order self-model level includes WW -, MW - and HW -states to control the adaptation of the W-states for the mental models at the first-order self-model level. The WW -states (also called higher-order W-states) represent the weights of the connections between W-states of the organisation (the WO -states) and individual mental models (the WA - and WB -states) to initiate the learning from the shared mental model by the individuals (by making these weights within the first-order selfmodel level nonzero), once a shared mental model is available. Note that these WW states are becoming nonzero if (in Phase 3) a control decision is made to indeed let individuals learn from the formed shared mental model, but they also have a learning mechanism so that they are maintained after that as well: Persons will keep relating (and updating) their individual mental model to the shared mental model. This type of learning for WW -states can be considered a form of higher-order Hebbian learning. The HW -states are used for controlling adaptation speeds of connection weights and MW -states for controlling persistence of adaptation. To obtain context-sensitive control of the aggregation of individual mental models for the formation of the shared mental model, second-order Ci,W -states were added to this second-order self-model level. This is the main extension made here to the self-modeling network model for organisational learning with fixed, nonadaptive aggregation from (Canbalo˘glu et al. 2021). This increases the number of states in the network model introduced in (Canbalo˘glu et al. 2022) from 46 to 79 states. Four different types of Ci,W -states were added to represent four different types of combination functions (see Fig. 9.3): • C1,W for the logistic sum combination function alogistic (for logistic amplification) • C2,W for the scaled maximum combination function smax (for maximizing) • C3,W for the Euclidean combination function eucl (for additive averaging) • C4,W for the scaled geometric combination function sgeometric (for multiplicative averaging) So, there are four Ci,W -states (for i = 1, …, 4) for each of the three shared mental model connection weight self-model states Wx_O,y_O for (x, y) ∈ {(a, b), (b, c), (c, d)}. Thus, the model has 12 Ci,W -states at the second-order self-model level to model control over the aggregation process for the shared mental model formation. These

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second-order self-model states and the functions they represent are used depending on the context (due to the connections from the context states to the Ci,W -states), and the weighted average is taken if more than one i has a nonzero Ci,W for a given state Wx_O,y_O . The addition of such second-order self-model Ci,W -states to a network model for organisational learning opens many interesting possibilities to incorporate extended second-order adaptation capabilities for the feed forward organisational learning in the network model. As flexibility with respect to context-sensitivity is often a main challenge for computational models for learning processes in general, these extended capabilities for adaptive network models in particular allow to obtain much more realism of such network models by enabling to take into account context factors in a detailed manner. Note that C1, Wx_O,y_O to C4, Wx_O,y_O in general lead to different values for the firstorder self-model states Wx_O,y_O representing connection weights (for the connection from x_O to y_O) of the obtained aggregated shared mental model. Here, roughly spoken (also depending on settings of the parameters of the combination functions) it can be expected that: • using C1, Wx_O,y_O , the obtained values for Wx_O,y_O are higher than the maximum of the values for Wx_A,y_A and Wx_B,y_B for the individual mental models of A and B (amplification effect). • using C2, Wx_O,y_O , the obtained values for Wx_O,y_O are equal to the maximum of the values for Wx_A,y_A and Wx_B,y_B for the individual mental models of A and B (maximizing effect). • using C3, Wx_O,y_O or C4, Wx_O,y_O , the obtained values for Wx_O,y_O are between the maximum and minimum of the values for Wx_A,y_A and Wx_B,y_B for the individual mental models of A and B (additive or multiplicative averaging effect). The influences of the context factors on the aggregation as pointed out in Table 9.2 have been used to specify in a heuristic manner the context-sensitive control for the choice of combination function via these Ci,Wx_O,y_O -states. For example, if A and B have a similar category of knowledgeability, in principle a form of average is supported (via the states C3, Wx_O,y_O or C4, Wx_O,y_O for a Euclidean or geometric combination function), but if they are independent, some form of amplification is supported (via the state C1, Wx_O,y_O for a logistic combination function). If they differ in knowledgeability, the maximal knowledge is chosen (via the state C2, Wx_O,y_O for a maximum combination function). This setup is meant as an example to illustrate the idea and can easily be replaced by other context factors and other knowledge relating these to the control of the aggregation via the Ci,W -states. A full specification of the model can be found in the Appendix Sect. 9.8.

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9.5 Details of the Adaptive Network for Heuristic Control of Aggregation All states of the model for the different levels of the first adaptive network model (with heuristic control of aggregation) considered here are explained in more detail. After this, the different types of connections are explained in more detail as well. First, in Fig. 9.7, a complete overview is shown of all 16 base states: 12 base states for the three mental models (with 4 base states each) and 4 base states for the context states relating to four different phases of organisational learning that are considered, respectively individual learning, feed forward learning, feedback learning, individual learning. As discussed in Sect. 9.4, first-and second-order self-model states are used to bring multi-order adaptivity to the network model. The first-order adaptation level (the blue plane in Fig. 9.6) provides adaptivity of the base level and the second-order one controls this adaptivity. In the first-order self-model level, W-states for all the weights of the connections between the base level states of the mental models for individuals A and B and the shared mental model for organisation O are placed; see the rows for the 9 states X38 to X46 in Fig. 9.8. In the first place, these are WA states X38 to X40 and WB -states X41 to X43 for the adaptive weights of the base level individual mental state connections of the mental models of persons A and B. In addition, there are WO -states X44 to X46 of the developed shared organisation mental model states. Besides these 9 W-states there are also 21 context states X17 to X37 in relation to the elements considered in Table 9.2. Here context states X17 to X25 represent basic context factors and context states X26 to X37 represent derived context factors used in the heuristic approach applied for context-sensitive control of mental model aggregation during feed forward learning. At this first-order self-model level there are (intralevel) connections from all the W-states (two types for this case: WA -states and WB -states) that specify the weight of a connection between the same tasks for all persons (two for this case) to the WO -states representing the weights of the connections of the shared organisation Nr X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16

State a_A b_A c_A d_A a_B b_B c_B d_B a_O b_O c_O d_O conph1 conph2 conph3 conph4

Explanation Individual mental model state of person A for task a Individual mental model state of person A for task b Individual mental model state of person A for task c Individual mental model state of person A for task d Individual mental model state of person B for task a Individual mental model state of person B for task b Individual mental model state of person B for task c Individual mental model state of person B for task d Shared mental model state of organisation O for task a Shared mental model state of organisation O for task b Shared mental model state of organisation O for task c Shared mental model state of organisation O for task d Context state for Phase 1: individual mental model simulation and learning Context state for Phase 2: creation of a shared mental model for organisation O Context state for Phase 3: learning individual mental models from the shared mental model for organisation O Context state for Phase 4: individual mental model simulation and learning

Fig. 9.7 Base level states of the first adaptive network model

9 Heuristic Context-Sensitive Control of Mental Model Aggregation … Nr X17 X18 X19 X20 X21 X22 X23 X24 X25 X26

State conknow,Wa_A,b_A conknow,Wb_A,c_A conknow,Wc_A,d_A conknow,Wa_B,b_B conknow,Wb_B,c_B conknow,Wc_B,d_B condependencyA,B conadditive conmultiplicative conAnotB,a-b

X27

conBnotA,a-b

X28 X29

conAB,a-b connotAnotB,a-b

X30

conAnotB,b-c

X31

conBnotA,b-c

X32 X33

conAB,b-c connotAnotB,b-c

X34

conAnotB,c-d

X35

conBnotA,c-d

X36

conAB,c-d

X37

connotAnotB,c-d

X38

Wa_A,b_A

X39

Wb_A,c_A

X40

Wc_A,d_A

X41

Wa_B,b_B

X42

Wb_B,c_B

X43

Wc_B,d_B

X44

Wa_O,b_O

X45

Wb_O,c_O

X46

Wc_O,d_O

199

Explanation Context state for how knowledgeable A is concerning the mental model connection from a_A to b_A Context state for how knowledgeable A is concerning the mental model connection from b_A to c_A Context state for how knowledgeable A is concerning the mental model connection from c_A to d_A Context state for how knowledgeable B is concerning the mental model connection from a_B to b_B Context state for how knowledgeable B is concerning the mental model connection from b_B to c_B Context state for how knowledgeable B is concerning the mental model connection from c_B to d_B Context state for how dependent A and B are Context state for preference for additive aggregation Context state for preference for multiplicative aggregation Derived context state for A knowledgeable and B not knowledgeable for their mental model connection from a to b Derived context state for B knowledgeable and A not knowledgeable for their mental model connection from a to b Derived context state for both A and B knowledgeable for their mental model connection from a to b Derived context state for both A and B not knowledgeable for their mental model connection from a to b Derived context state for A knowledgeable and B not knowledgeable for their mental model connection from b to c Derived context state for A not knowledgeable and B knowledgeable for their mental model connection from b to c Derived context state for both A and B knowledgeable for their mental model connection from b to c Derived context state for both A and B not knowledgeable for their mental model connection from b to c Derived context state for A knowledgeable and B not knowledgeable for their mental model connection from c to d Derived context state for A not knowledgeable and B knowledgeable for their mental model connection from c to d Derived context state for both A and B t knowledgeable for their mental model connection from c to d Derived context state for both A and B not knowledgeable for their mental model connection from c to d First-order self-model state for the weight of the connection from a to b within the individual mental model of person A First-order self-model state for the weight of the connection from b to c within the individual mental model of person A First-order self-model state for the weight of the connection from c to d within the individual mental model of person A First-order self-model state for the weight of the connection from a to b within the individual mental model of person B First-order self-model state for the weight of the connection from b to c within the individual mental model of person B First-order self-model state for the weight of the connection from c to d within the individual mental model of person B First-order self-model state for the weight of the connection from a to b within the shared mental model of the organisation O First-order self-model state for the weight of the connection from b to c within the shared mental model of the organisation O First-order self-model state for the weight of the connection from c to d within the shared mental model of the organisation O

Fig. 9.8 First-order self-model states of the introduced adaptive network model

model (for the formation of the shared organisation mental model) and vice versa (for the learning from the shared organisation mental model by the individuals). For these intralevel connections, see the horizontal arrows in the blue plane in Fig. 9.6. At the second-order self-model level (the purple plane in Fig. 9.6), there are (see Figs 9.9, 9.10): • 6 WW -states X47 to X52 specifying the weights of the connections from the Wstates of the organisation’s mental model to the individual ones for A and B (to initiate and control the feedback learning from the shared organisation mental model by the individuals),

200 Nr X47 X48 X49 X50 X51 X52 X53 X54 X55 X56 X57 X58 X59 X60 X61 X62 X63 X64 X65 X66 X67

G. Canbalo˘glu and J. Treur State Explanation WWa_O,b_O,Wa_A,b_A Second-order self-model state for the weight of the connection from shared mental model connection weight self-model state Wa_O,b_O to individual mental model connection weight selfmodel state Wa_A,b_A for instructional learning of the shared mental model WWb_O,c_O,Wb_A,c_A Second-order self-model state for the weight of the connection from shared mental model connection weight self-model state Wb_O,c_O to individual mental model connection weight selfmodel state Wb_A,c_A for instructional learning of the shared mental model WWc_O,d_O,Wc_A,d_A Second-order self-model state for the weight of the connection from shared mental model connection weight self-model state Wc_O,d_O to individual mental model connection weight selfmodel state Wc_A,d_A for instructional learning of the shared mental model WWa_O,b_O,Wa_B,b_B Second-order self-model state for the weight of the connection from shared mental model connection weight self-model state Wa_O,b_O to individual mental model connection weight selfmodel state Wa_B,b_B for instructional learning of the shared mental model WWb_O,c_O,Wb_B,c_B Second-order self-model state for the weight of the connection from shared mental model connection weight self-model state Wb_O,c_O to individual mental model connection weight selfmodel state Wb_B,c_B for instructional learning of the shared mental model WWc_O,d_O,Wc_B,d_B Second-order self-model state for the weight of the connection from shared mental model connection weight self-model state Wc_O,d_O to individual mental model connection weight selfmodel state Wc_B,d_B for instructional learning of the shared mental model HWa_A,b_A Second-order self-model state for the adaptation speed of individual mental model connection weight self-model state Wa_A,b_A HWb_A,c_A Second-order self-model state for the adaptation speed of individual mental model connection weight self-model state Wb_A,c_A HWc_A,d_A Second-order self-model state for the adaptation speed of individual mental model connection weight self-model state Wc_A,d_A HWa_B,b_B Second-order self-model state for the adaptation speed of individual mental model connection weight self-model state Wa_B,b_B HWb_B,c_B Second-order self-model state for the adaptation speed of individual mental model connection weight self-model state Wb_B,c_B HWc_B,d_B Second-order self-model state for the adaptation speed of individual mental model connection weight self-model state Wc_B,d_B HWa_O,b_O Second-order self-model state for the adaptation speed of shared mental model connection weight self-model state Wa_O,b_O for formation or revision of the shared mental model HWb_O,c_O Second-order self-model state for the adaptation speed of shared mental model connection weight self-model state Wb_O,c_O for formation or revision of the shared mental model HWc_O,d_O Second-order self-model state for the adaptation speed of shared mental model connection weight self-model state Wc_O,d_O for formation or revision of the shared mental model MWa_A,b_A Second-order self-model state for persistence of adaptation of individual mental model connection weight self-model state Wa_A,b_A MWb_A,c_A Second-order self-model state for persistence of adaptation of individual mental model connection weight self-model state Wb_A,c_A MWc_A,d_A Second-order self-model state for persistence of adaptation of individual mental model connection weight self-model state Wc_A,d_A MWa_B,b_B Second-order self-model state for persistence of adaptation of individual mental model connection weight self-model state Wa_B,b_B MWb_B,c_B Second-order self-model state for persistence of adaptation of individual mental model connection weight self-model state Wb_B,c_B MWc_B,d_B Second-order self-model state for persistence of adaptation of individual mental model connection weight self-model state Wc_B,d_B

Fig. 9.9 Second-order self-model states of the introduced adaptive network model: the secondorder WW -states, HW -states and MW -states

• 9 HW -states X53 to X61 for adaptation speeds of connection weights in the firstorder adaptation level. This provides the speed control of the adaptation. • 6 MW -states X62 to X67 for persistence of adaptation. This provides the persistence (and forgetting) control of the adaptation. • 12 CWO -states X68 to X79 (see Fig. 9.10) are used to control the type of aggregation applied in the shared mental model formation process during feed forward organisational learning.

9 Heuristic Context-Sensitive Control of Mental Model Aggregation … Nr X68

State C1,Wa_O, b_O

X69

C2,Wa_O, b_O

X70

C3,Wa_O, b_O

X71

C4,Wa_O, b_O

X72

C1,Wb_O, c_O

X73

C2,Wb_O, c_O

X74

C3,Wb_O, c_O

X75

C4,Wb_O, c_O

X76

C1,Wc_O, d_O

X77

C2,Wc_O, d_O

X78

C3,Wc_O, d_O

X79

C4,Wc_O, d_O

201

Explanation Second-order self-model state for the weight for the combination function alogistic for the aggregation for shared mental model connection weight representation Wa O,b O Second-order self-model state for the weight for the combination function smax for the aggregation for shared mental model connection weight representation Wa O,b O Second-order self-model state for the weight for the combination function eucl for the aggregation for shared mental model connection weight representation Wa O,b O Second-order self-model state for the weight for the combination function sgeometric for the aggregation for shared mental model connection weight representation Wa O,b O Second-order self-model state for the weight for the combination function alogistic for the aggregation for shared mental model connection weight representation Wb O,c O Second-order self-model state for the weight for the combination function smax for the aggregation for shared mental model connection weight representation Wb O,c O Second-order self-model state for the weight for the combination function eucl for the aggregation for shared mental model connection weight representation Wb O,c O Second-order self-model state for the weight for the combination function sgeometric for the aggregation for shared mental model connection weight representation Wb O,c O Second-order self-model state for the weight for the combination function alogistic for the aggregation for shared mental model connection weight representation Wc O,d O Second-order self-model state for the weight for the combination function smax for the aggregation for shared mental model connection weight representation Wc O,d O Second-order self-model state for the weight for the combination function eucl for the aggregation for shared mental model connection weight representation Wc O,d O Second-order self-model state for the weight for the combination function sgeometric for the aggregation for shared mental model connection weight representation Wc O,d O

Fig. 9.10 Second-order self-model states of the introduced adaptive network model: the secondorder CW -states for aggregation for the shared mental model connections

9.6 Example Simulation for Heuristic Context-Sensitive Control of Aggregation Recall once more from Sect. 9.3 that aggregation characteristics within a network model are specified by combination functions. In particular, this applies to the aggregation of individual mental models in order to get shared mental models out of them. In this scenario, different combination functions are used to observe different types of aggregation while an organisational learning progresses by the unification of separate individual mental models. With a multi-phase approach, two individual mental models that are distinct in the beginning create the shared mental model of their organisation by time, and there are effects of individuals and the organisation on each other in different time intervals. Thus, it is possible to explore how aggregation occurs during an organisational learning progress. The values used for the basic context factors in this scenario are shown in Fig. 9.12. To see the flow of these processes clearly, the scenario is structured in phases. In practice and also in the model, these processes also can overlap or take place entirely simultaneously. The five phases were designed as follows: • Phase 1: Individual mental model usage and learning (time 20 to 300) This relates to (a) in Sect. 9.2. Two different mental models for person A and B belonging to an organisation are constructed and become stronger here in this phase. Hebbian learning takes place to improve their individual mental models by using them for internal simulations. Person A mainly has knowledge on the first part of the job, and person B has knowledge on the last part, thus A is the person who started the job and B is the one who finished it.

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Fig. 9.11 Types of connections in the adaptive network model and how they relate to (a) to (d) identified in Sect. 9.2. For the example scenario, x and y are states from {a, b, c, d} and Z is a person from {A, B} Context factor Value Explanation X17 conknow,Wa_A,b_A 1 A is fully knowledgeable for a-b X18 conknow,Wb_A,c_A 0.7 A is 0.7 knowledgeable for b-c X19 conknow,Wc_A,d_A 0 A is not at all knowledgeable for c-d X20 conknow,Wa_B,b_B 0 B is not at all knowledgeable for a-b X21 conknow,Wb_B,c_B 0.8 B is 0.8 knowledgeable for b-c X22 conknow,Wc_B,d_B 1 B is fully knowledgeable for c-d X23 condependencyA,B 0.1 A and B have almost no dependency X24 conadditive 0.1 Almost no preference for additive aggregation X25 conmultiplicative 0.1 Almost no preference for multiplicative aggregation

Fig. 9.12 Values for the basic context factors used in the example scenario

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• Phase 2: Shared mental model formation: feed forward learning (time 350 to 400) This relates to (b) and (c) in Sect. 9.2. Unification and aggregation of individual mental models occur here. During this formation of shared mental model, different combination functions are used for different cases in terms of knowledgeability, dependence and preference of additivity or multiplicativity. Organisational learning takes place with the determination of the values of the WO -states for the organisation’s general (non-personal) states for the job a_O to d_O. An incomplete and non-perfect shared mental model is formed and maintained by the organisation. • Phase 3: Learning from the shared mental model by the individuals: feedback learning (time 450 to 600) This relates to (c) and (d) in Sect. 9.2. Learning from the organisation’s shared mental model, which can be considered as learning from each other in an indirect manner, begins in this phase by the activation of the connections from the organisation’s general WO -states to the individual WA -states and WB -states. Persons receive the knowledge from the shared mental model as a form of instructional learning. There is no need for many mutual one-to-one connections between persons since there is a single shared mental model. • Phase 4: Individual mental model usage and learning (time 650 to 850) This relates to (d) in Sect. 9.2. Further improvements on individual mental models of persons are observed by the help of Hebbian learning during usage of the mental model for internal simulation in this phase. Person A starts to learn about task d (state d_A) by using the knowledge from the shared mental model (obtained from person B) and similarly B learns about task a (state a_B) that they did not know in the beginning. Therefore, these ‘hollow’ states become meaningful for the individuals. The individuals take advantage of the organisational learning. • Phase 5: Strengthening shared mental model with gained knowledge (time 900 to 950) This relates to (e) in Sect. 9.2. People of the organisation start to affect the shared mental model as they gain improved individual knowledge by time. The activation of organisation’s general states causes improvements on shared mental model, and it becomes closer to the perfect complete shared mental model. This phase was added in a later stage (using an additional context state X80 ) of the development of the model to illustrate multiple phases of feed forward learning that can occur and these can make the shared mental model gradually better over time.

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1.3 1.2 1.1 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

0

50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000 X1 - a_A X2 - b_A X3 - c_A X4 - d_A X5 - a_B X6 - b_B X7 - c_B X8 - d_B X9 - a_O X10 - b_O X11 - c_O X12 - d_O X13 - con_ph1 X14 - con_ph2 X15 - con_ph3 X16 - con_ph4 X17 - conknow,Wa_A,b_A X18 - conknow,Wb_A,c_A X19 - conknow,Wc_A,d_A X20 - conknow,Wa_B,b_B X21 - conknow,Wb_B,c_B X22 - conknow,Wc_B,d_B X23 - condependencyA,B X24 - conadditive X25 - conmultiplicative X26 - conAnotBa->b X27 - conBnotAa->b X28 - conABa->b X29 - connotAnotBa->b X30 - conAnotBb->c X31 - conBnotAb->c X32 - conABb->c X33 - connotAnotBb->c X34 - conAnotBc->d X35 - conBnotAc->d X36 - conABc->d X37 - connotAnotBc->d X38 - Wa_A,b_A X39 - Wb_A,c_A X40 - Wc_A,d_A X41 - Wa_B,b_B X42 - Wb_B,c_B

Fig. 9.13 Overview of the simulated scenario

Figures 9.13, 9.14, 9.15, 9.16 show different views on one example simulation. Figure 9.13 shows an overall overview of all states of the simulation. In Fig. 9.7 it is shown how the shared mental model of the organisation initially is formed in Phase 3 but is still improved in Phase 5. Figure 9.15 focuses on the individuals A and B and their internal simulation and learning, whereas Fig. 9.16 focuses on the C-states to control the aggregation within feed forward learning in a context-sensitive manner. In Fig. 9.13, individual learning by using mental models for internal simulation (Hebbian learning) takes place in the first phase happening between time 10 and 300. Only X4 (d_A) and X5 (a_B) remain at 0 because of the absence of knowledge. These ‘hollow’ states will increase in Phase 4 after learning during Phase 3 from the unified shared mental model developed in Phase 2. The WA -states and WB -states of the individuals A and B representing their knowledge and learning slightly decrease starting from the end of Phase 1 at about 300 since the persistence factors’ selfmodel M-states do not have the perfect value 1, meaning that persons forget. Since the persistence factor of B is smaller than of A, B’s W-states decrease more in the second phase: It can be deduced that B is a more forgetful person.

9 Heuristic Context-Sensitive Control of Mental Model Aggregation …

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1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2

X44 - Wa_O,b_O X45 - Wb_O,c_O X46 - Wc_O,d_O

0.1 0 0

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550

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650

700

750

800

850

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1000

Fig. 9.14 Shared mental model formation

1 0.9 0.8

X1 - a_A X2 - b_A X3 - c_A X4 - d_A X5 - a_B X6 - b_B X7 - c_B X8 - d_B X38 - Wa_A,b_A X39 - Wb_A,c_A X40 - Wc_A,d_A X41 - Wa_B,b_B X42 - Wb_B,c_B X43 - Wc_B,d_B

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0

50

100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000

Fig. 9.15 Learning and internal simulation by individuals A and B

Context states for different combination functions determine the aggregation pattern of the shared mental model in Phase 2. For 4 different combination functions, there are 12 Ci,W -states in total, differentiated for the organisation’s three connection weight self-model states (Wa_O,b_O , Wb_O,c_O , and Wc_O,d_O ), with different activation levels. Some of them are even above 1 but this does not cause a problem because the weighted average of them will be taken (according to formula (9.2) in Sect. 9.3). The shared mental model is formed in this phase based on the context-sensitive control of the aggregation used.

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1.3 1.2 1.1 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0

5 X68 - C1,Wa_O, b_O

10 X69 - C2,Wa_O, b_O

X70 - C3,Wa_O, b_O

15 X71 - C4,Wa_O, b_O

X72 - C1,Wb_O, c_O

X73 - C2,Wb_O, c_O

X74 - C3,Wb_O, c_O

X75 - C4,Wb_O, c_O

X76 - C1,Wc_O, d_O

X77 - C2,Wc_O, d_O

X78 - C3,Wc_O, d_O

X79 - C4,Wc_O, d_O

Fig. 9.16 The C-states for context-sensitive control of aggregation during the initial period from 0 to 15

The WO -states of the organisation’s shared mental model have links back to the WA -states and WB -states of the individuals’ mental models to make individual learning (by instructional learning) from the shared mental model possible. In Phase 3, all the higher-order self-model W-states (X47 to X52 , also called WW -states) for these connections from the shared mental model’s to the individuals’ first-order Wstates become activated. This models the instructional learning: The persons are informed about the shared mental model. Forgetting also takes place for the connections from the W-states of the organisation’s shared mental model to those of the individuals’ mental models. It means that a fast-starting learning process becomes stagnant over time. By observing Phase 4, it can be seen that after time 650, all the W-states of the individuals make an upward jump because of further individual learning. In Phase 5, like in Phase 2, the W-states of the organisation’s shared mental model increase (due to the individual mental models that were improved in Phase 4) and get closer to a perfect complete shared mental model. This improved shared mental model in principle also has effect on individual mental models, as also the higher-order W-states are still activated here.

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Finally, Fig. 9.16 shows how in the initial time period from time 0 to time 15, in a heuristic manner based on the values of the basic context states as shown in Fig. 9.12, the values of the C-states to control the aggregation of the mental models to obtain a shared mental model during feed forward learning are determined. This is done by using the sum function (which is the Euclidean combination function of order n = 1 and with scaling factor λ = 1). By this sum function the criteria derived from Table 9.2 are considered as indications in favour of one of the options for combination functions for the aggregation and simply added to each other to obtain an overall heuristic indicator. Note that in contrast to this, the second model introduced later in Sect. 9.7 addresses a different approach with exact logical knowledge modeled by propositional functions.

9.7 Discussion This chapter is based on material from (Canbalo˘glu and Treur, 2022a). Organisational learning usually exploits developed individual mental models in order to form shared mental models for the organisation; e.g., (Kim 1993; Wiewiora et al. 2019). This happens by some form of aggregation. The current chapter focuses on this aggregation process, which often depends on contextual factors. It was shown how a secondorder adaptive self-modeling network model for organisational learning (Canbalo˘glu et al. 2022) based on self-modeling network models described in (Treur 2020b) can model this process of aggregation of individual mental models in a context-dependent manner. Compared to (Canbalo˘glu et al. 2022) the type of aggregation used for the process of shared mental model formation was explicitly addressed and made context sensitive. Different forms of aggregation have been incorporated, for example, Euclidean and geometric mean weighted averages, maximum functions and logistic forms. The choice of aggregation was made adaptive in a context-sensitive manner so that for each context a different form of aggregation can be chosen automatically as part of the overall process. The presented approach is quite general, as easily more types of aggregation can be added and more or different context factors. In Chap. 10 of this volume (Canbalo˘glu et al. 2023), an alternative approach for context-sensitive control of aggregation is addressed, based on Boolean propositions in contrast to the heuristic approach in the current chapter.

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9.8 Appendix Full Specifications by Role Matrices In this section full specifications by role matrices are provided. Role Matrices for Connectivity Characteristics In this section the different role matrices are shown that provide a full specification of the network characteristics defining the adaptive network model in a standardised table format. Here in each role matrix, each state has its row where it is listed which are the impacts on it from that role. The connectivity characteristics are specified by role matrices mb and mcw shown in Fig. 9.17 and 9.18. Role matrix mb lists the other states (at the same or lower level) from which the state gets its incoming connections, whereas in role matrix mcw the connection weights are listed for these connections.

mb base connectivity

X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17 X18 X19 X20 X21 X22 X23 X24 X25 X26 X27 X28 X29 X30 X31 X32 X33 X34 X35 X36 X37 X38 X39 X40 X41 X42 X43 X44 X45 X46

a_A b_A c_A d_A a_B b_B c_B d_B a_O b_O c_O d_O conph1 conph2 conph3 conph4 conknow,Wa_A,b_A conknow,Wb_A,c_A conknow,Wc_A,d_A conknow,Wa_B,b_B conknow,Wb_B,c_B conknow,Wc_B,d_B condependencyA,B conadditive conmultiplicative conAnotB,a b conBnotA,a b conAB,a b connotAnotB,a b conAnotB,b c conBnotA,b c conAB,b c connotAnotB,b c conAnotB,c d conBnotA,c d conAB,c d connotAnotB,c d Wa_A,b_A Wb_A,c_A Wc_A,d_A Wa_B,b_B Wb_B,c_B Wc_B,d_B Wa_O,b_O Wb_O,c_O Wc_O,d_O

1

2

3

4

X13 X16 X1 X2 X3 X16 X5 X13 X6 X7 X9 X10 X11 X13 X14 X15 X16 X17 X18 X19 X20 X21 X22 X23 X24 X25 X17 X17 X17 X17 X18 X18 X18 X18 X19 X19 X19 X19 X1 X2 X3 X5 X6 X7 X38 X39 X40

X20 X20 X20 X20 X21 X21 X21 X21 X22 X22 X22 X22 X2 X3 X4 X6 X7 X8 X41 X42 X43

5

6

7

mb base connectivity

X47 X48 X49 X50 X51 X52 X53 X54 X55 X56 X57 X58 X59 X60 X61 X62 X63 X64 X65 X66 X67 X68 X69 X70 X71 X72 X73 X74 X75 X76 X77 X78 X79 X38 X39 X40 X41 X42 X43

WWa_O,b_O,Wa_A,b_A WWb_O,c_O,Wb_A,c_A WWc_O,d_O,Wc_A,d_A WWa_O,b_O,Wa_B,b_B WWb_O,c_O,Wb_B,c_B WWc_O,d_O,Wc_B,d_B HWa_A,b_A HWb_A,c_A HWc_A,d_A HWa_B,b_B HWb_B,c_B HWc_B,d_B HWa_O,b_O HWb_O,c_O HWc_O,d_O MWa_A,b_A MWb_A,c_A MWc_A,d_A MWa_B,b_B MWb_B,c_B MWc_B,d_B C1,Wa_O, b_O C2,Wa_O, b_O C3,Wa_O, b_O C4,Wa_O, b_O C1,Wb_O, c_O C2,Wb_O, c_O C3,Wb_O, c_O C4,Wb_O, c_O C1,Wc_O, d_O C2,Wc_O, d_O C3,Wc_O, d_O C4,Wc_O, d_O

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X44 X45 X46 X44 X45 X46 X1 X2 X3 X5 X6 X7 X14 X14 X14 X1 X2 X3 X5 X6 X7 X14 X14 X14 X14 X14 X14 X14 X14 X14 X14 X14 X14

X38 X39 X40 X41 X42 X43 X2 X3 X4 X6 X7 X8

X13 X13 X13 X13 X13 X13 X38 X39 X40 X41 X42 X43

X14 X14 X14 X14 X14 X14 X53 X54 X55 X56 X57 X58

X15 X15 X15 X15 X15 X15

X2 X3 X4 X6 X7 X8 X28 X26 X28 X28 X32 X30 X32 X32 X36 X34 X36 X36

X38 X39 X40 X41 X42 X43 X23 X27 X29 X29 X23 X31 X33 X33 X23 X35 X37 X37

X62 X63 X64 X65 X66 X67

X13 X13 X13 X13 X13 X13

X23 X23

X24 X25

X23 X23

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X23 X23

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X44 X45 X46 X44 X45 X46

Fig. 9.17 Role matrices for the connectivity: mb for base connectivity

6

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X14 X14 X14 X14 X14 X14

X15 X15 X15 X15 X15 X15

9 Heuristic Context-Sensitive Control of Mental Model Aggregation … mcw

X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17 X18 X19 X20 X21 X22 X23 X24 X25 X26 X27 X28 X29 X30 X31 X32 X33 X34 X35 X36 X37 X38 X39 X40 X41 X42 X43 X44 X45 X46

connection weights

a_A b_A c_A d_A a_B b_B c_B d_B a_O b_O c_O d_O conph1 conph2 conph3 conph4 conknow,Wa_A,b_A conknow,Wb_A,c_A conknow,Wc_A,d_A conknow,Wa_B,b_B conknow,Wb_B,c_B conknow,Wc_B,d_B condependencyA,B conadditive conmultiplicative conAnotB,a b conBnotA,a b conAB,a b connotAnotB,a b conAnotB,b c conBnotA,b c conAB,b c connotAnotB,b c conAnotB,c d conBnotA,c d conAB,c d connotAnotB,c d Wa_A,b_A Wb_A,c_A Wc_A,d_A Wa_B,b_B Wb_B,c_B Wc_B,d_B Wa_O,b_O Wb_O,c_O Wc_O,d_O

1

2

1 X38 X39 X40 1 X41 X42 X43

1

X44 X45 X46 1 1 1 1 1 1 1 1 1 1 1 1 1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 1 1 1 1 1 1 1 1

3

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mcw

-1 1 1 -1 -1 1 1 -1 -1 1 1 -1 1 1 1 1 1 1 1 1 1

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X47 X48 X49 X50 X51 X52 X53 X54 X55 X56 X57 X58 X59 X60 X61 X62 X63 X64 X65 X66 X67 X68 X69 X70 X71 X72 X73 X74 X75 X76 X77 X78 X79

connection weights

WWa_O,b_O,Wa_A,b_A WWb_O,c_O,Wb_A,c_A WWc_O,d_O,Wc_A,d_A WWa_O,b_O,Wa_B,b_B WWb_O,c_O,Wb_B,c_B WWc_O,d_O,Wc_B,d_B HWa_A,b_A HWb_A,c_A HWc_A,d_A HWa_B,b_B HWb_B,c_B HWc_B,d_B HWa_O,b_O HWb_O,c_O HWc_O,d_O MWa_A,b_A MWb_A,c_A MWc_A,d_A MWa_B,b_B MWb_B,c_B MWc_B,d_B C1,Wa_O, b_O C2,Wa_O, b_O C3,Wa_O, b_O C4,Wa_O, b_O C1,Wb_O, c_O C2,Wb_O, c_O C3,Wb_O, c_O C4,Wb_O, c_O C1,Wc_O, d_O C2,Wc_O, d_O C3,Wc_O, d_O C4,Wc_O, d_O

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1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0

1 1 1 1 1 1 1 1 1 1 1 1

0 0 0 0 0 0 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1

0 0 0 0 0 0 1 1 1 1 1 1

1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 -1 1 1 1 -1 1 1 1 -1 1 1 1

1 1 1 1 1 1

-1 -1 -1 -1 -1 -1

1 1

1 1

1 1

1 1

1 1

1 1

6

7

-1 -1 -1 -1 -1 -1

-1 -1 -1 -1 -1 -1

Fig. 9.18 Role matrices for the connectivity: mcw for connection weights

Nonadaptive connection weights are indicated in mcw (in Fig. 9.18) by a number (in a green shaded cell), but adaptive connection weights are indicated by a reference to the (self-model) state representing the adaptive value (in a peach-red shaded cell). This can be seen for states X2 to X4 (with self-model states X38 to X40 ), states X6 to X8 (with self-model states X41 to X43 ), X10 to X12 (with self-model states X44 to X46 ), and X38 to X43 (with self-model states X47 to X52 ).

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X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17 X18 X19 X20 X21 X22 X23 X24 X25 X26 X27 X28 X29 X30 X31 X32 X33 X34 X35 X36 X37 X38 X39 X40 X41 X42 X43 X44 X45 X46

a_A b_A c_A d_A a_B b_B c_B d_B a_O b_O c_O d_O conph1 conph2 conph3 conph4 conknow,Wa_A,b_A conknow,Wb_A,c_A conknow,Wc_A,d_A conknow,Wa_B,b_B conknow,Wb_B,c_B conknow,Wc_B,d_B condependencyA,B conadditive conmultiplicative conAnotB,a b conBnotA,a b conAB,a  b connotAnotB,a  b conAnotB,b  c conBnotA,b  c conAB,b  c connotAnotB,b  c conAnotB,c d conBnotA,c  d conAB,c  d connotAnotB,c  d Wa_A,b_A Wb_A,c_A Wc_A,d_A Wa_B,b_B Wb_B,c_B Wc_B,d_B Wa_O,b_O Wb_O,c_O Wc_O,d_O

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X68 X72 X76

X69 X73 X77

X70 X74 X78

X71 X75 X79

Fig. 9.19 Role matrices for the aggregation characteristics: combination function weights

Role Matrices for Aggregation Characteristics The network characteristics for aggregation are defined by the selection of combination functions from the library and values for their parameters. In role matrix mcfw it is specified by weights which state uses which combination function; see Fig. 9.19.

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mcfw 1 2 3 4 5 6 combination alogistic steponce maxhebb smax eucl sgeomean function weights

X47 X48 X49 X50 X51 X52 X53 X54 X55 X56 X57 X58 X59 X60 X61 X62 X63 X64 X65 X66 X67 X68 X69 X70 X71 X72 X73 X74 X75 X76 X77 X78 X79

WWa_O,b_O,Wa_A,b_A WWb_O,c_O,Wb_A,c_A WWc_O,d_O,Wc_A,d_A WWa_O,b_O,Wa_B,b_B WWb_O,c_O,Wb_B,c_B WWc_O,d_O,Wc_B,d_B HWa_A,b_A HWb_A,c_A HWc_A,d_A HWa_B,b_B HWb_B,c_B HWc_B,d_B HWa_O,b_O HWb_O,c_O HWc_O,d_O MWa_A,b_A MWb_A,c_A MWc_A,d_A MWa_B,b_B MWb_B,c_B MWc_B,d_B C1,Wa_O, b_O C2,Wa_O, b_O C3,Wa_O, b_O C4,Wa_O, b_O C1,Wb_O, c_O C2,Wb_O, c_O C3,Wb_O, c_O C4,Wb_O, c_O C1,Wc_O, d_O C2,Wc_O, d_O C3,Wc_O, d_O C4,Wc_O, d_O

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Fig. 9.19 (continued)

Here many combination function weights are adaptive (represented by secondorder self-model Ci,W -states X68 to X79 ) for states X44 to X46 (the W-states of the shared mental model) to model the context-sensitive control of the aggregation in shared mental model formation.

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Fig. 9.20 Role matrices for the aggregation characteristics: combination function parameters

In role matrix mcfp (see Fig. 9.20) it is indicated what the parameter values are for the chosen combination functions. Some of them are adaptive, as can be seen in the rows from X38 to X43 (e.g., the persistence factors μ represented by the self-model states X62 to X67 ).

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Fig. 9.20 (continued)

Role Matrices for Timing Characteristics In Fig. 9.21, the role matrix ms for speed factors is shown, which lists all speed factors. Next to it, the list of initial values can be found. Also, for ms some entries are adaptive: The speed factors of X38 to X46 are represented by (second-order) self-model states X53 to X61 .

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Fig. 9.21 Role matrices ms for the timing characteristics (speed factors) and initial values iv

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Fig. 9.21 (continued)

References Argyris Ch., Schön D.A.: Organisational learning: a theory of action perspective. addison-wesley, reading, MA (1978) Bogenrieder, I.: Social architecture as a prerequisite for organisational learning. Manag. Learn. 33(2), 197–216 (2002) Canbalo˘glu, G., Treur, J.: Context-Sensitive Mental Model Aggregation in a Second-Order Adaptive Network Model for Organisational Learning. In: Benito R.M., Cherifi C., Cherifi H., Moro E., Rocha L.M., Sales-Pardo M. (eds) Complex Networks & Their Applications X. COMPLEX NETWORKS 2021. Studies in Computational Intelligence, vol. 1015, pp. 411-423. Springer Nature, Cham. https://doi.org/10.1007/978-3-030-93409-5_35 (2022) Canbalo˘glu, G., Treur, J., Roelofsma, P.H.M.P.: Computational modeling of organisational learning by self-modeling networks. Cognitive Systems Research 73, 51-64 https://doi.org/10.1016/j.cog sys.2021.12.003 (2022) Canbalo˘glu, G., Treur, J., Wiewiora, A. (eds.): Computational Modeling of Multilevel Organisational Learning and its Control Using Self-Modeling Network Models. Springer Nature (this volume) (2023) Craik, K.J.W.: The nature of explanation. University Press, Cambridge, MA (1943) Crossan, M.M., Lane, H.W., White, R.E.: An organisational learning framework: From intuition to institution. Acad. Manag. Rev. 24, 522–537 (1999)

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Fischhof, B., Johnson, S.: Organisational decision making. Cambridge University Press, Cambridge (1997) Hebb, D.O.: The organisation of behavior: A neuropsychological theory. John Wiley and Sons, New York (1949) Kim, D.H.: The Link Between Individual and Organisational Learning. Sloan Management Review, Fall 1993, pp. 37–50. Also in: Klein, D.A. (ed.), The Strategic Management of Intellectual Capital. Routledge-Butterworth-Heinemann, Oxford (1993) McShane, S.L., von Glinow, M.A.: Organisational Behavior. McGraw-Hill, Boston (2010) Shih, Y.F., Alessi, S.M.: Mental models and transfer of learning in computer programming. J. Res. Comput. Educ. 26(2), 154–175 (1993) Stelmaszczyk, M.: Relationship between individual and organisational learning: mediating role of team learning. J. Econ. Manag. 26(4), 1732–1947. https://doi.org/10.22367/jem.2016.26.06 (2016) Treur, J.: Modeling higher-order adaptivity of a network by multilevel network reification. Netw. Sci. 8, S110–S144 (2020a) Treur, J.: Network-Oriented modeling for adaptive networks: Designing higher-order adaptive biological, mental and social network models. Springer Nature, Cham (2020b) Treur, J., Van Ments, L. (eds.): Mental models and their dynamics, adaptation, and control: a self-modeling network modeling approach. Springer Nature (2022) Van Ments, L., Treur, J.: Reflections on dynamics, adaptation and control: a cognitive architecture for mental models. Cogn. Syst. Res. 70, 1–9 (2021) Van Ments, L., Treur, J., Klein, J., Roelofsma, P.H.M.P.: A computational network model for shared mental models in hospital operation rooms. In: Proceedings of the 14th International Conference on Brain Informatics, BI’21. Lecture Notes in Computer Science, vol. 12960, pp. 67–78. Springer Nature (2021a) Van Ments, L., Treur, J., Klein, J., Roelofsma, P.H.M.P.: A Second-Order adaptive network model for shared mental models in hospital teamwork. In: Nguyen, N.T., et al. (eds.), Proc. of the 13th International Conference on Computational Collective Intelligence, ICCCI’21. Lecture Notes in AI, 12876, pp. 126–140. Springer Nature (2021b) Wiewiora, A., Smidt, M., Chang, A.: The ‘How’ of multilevel learning dynamics: a systematic literature review exploring how mechanisms bridge learning between individuals, teams/projects and the organisation. Eur. Manag. Rev. 16, 93–115 (2019)

Chapter 10

Adaptive Mental Model Aggregation in Organisational Learning Using Boolean Propositions of Context Factors Gülay Canbalo˘glu and Jan Treur

Abstract Aggregation of developed individual mental models to obtain shared mental models for the organisation is a crucial process for organisational learning. This aggregation process usually does not only depend on the mental models used as input for it, but also on several context factors that may vary over circumstances and time. This means that for computational modeling of organisational learning the aggregation process better can be modeled as an adaptive dynamical process where adaptation is used to obtain a context-sensitive outcome of the aggregation. In this chapter it is explored how Boolean functions of these context factors can be used to model this form of adaptation. Using self-modeling networks, mental model adaptation by learning, formation or aggregation can be modeled in an appropriate manner at a first-order self-model level, whereas the control over such processes can be modeled at a second-order self-model level. Therefore, for adaptation of aggregation of mental models in particular, a second-order adaptive self-modeling network model for organisational learning can be used. In this chapter it is shown how in such a network model at the second-order self-model level, Boolean functions can be used to express logical combinations of context factors and based on this can exert contextsensitive control over the mental model aggregation process. Thus, a computational network model of organisational learning is presented in which the process of aggregation of individual mental models to form shared mental models takes place in an adaptive context-dependent manner based on any Boolean combinations of context factors. Keywords Adaptive self-modeling network model · Aggregation process · Boolean functions · Mental models

G. Canbalo˘glu · J. Treur (B) Social AI Group, Department of Computer Science, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands e-mail: [email protected] G. Canbalo˘glu e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 G. Canbalo˘glu et al. (eds.), Computational Modeling of Multilevel Organisational Learning and Its Control Using Self-modeling Network Models, Studies in Systems, Decision and Control 468, https://doi.org/10.1007/978-3-031-28735-0_10

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10.1 Introduction Organisational learning (Argyris and Schön 1978; Bogenrieder 2002; Crossan et al. 1999; Fischhof and Johnson 1997; Kim 1993; McShane and Glinow 2010; Stelmaszczyk 2016; Wiewiora et al. 2019) is a challenging complex adaptive phenomenon within an organisation, especially when it comes to computational modeling of it. Within organisational learning different types of adaptation processes work together in a dynamical manner via a number of feedforward and feedback cycles, e.g., (Crossan et al. 1999; Kim 1993; Wiewiora et al. 2019). Specific adaptation process involved are, for example, individual learning and development of mental models, formation of shared mental models for teams or for the organisation as a whole, and improving individual mental models or team mental models based on a shared mental model of the organisation, e.g., (Crossan et al. 1999; Kim 1993; Wiewiora et al. 2019). Kim (1993), p. 44, puts forward that ‘Organisational learning is dependent on individuals improving their mental models; making those mental models explicit is crucial to developing new shared mental models.’. An interesting challenge addressed in the current chapter is how specific context factors play their role in formation of a shared mental model by aggregating a number of individual mental models in an adaptive, context-sensitive manner. Concerning mental models, in (Treur and Van Ments 2022) it has been explored how self-modeling networks (Treur 2020) provide an adequate modeling approach to obtain computational models addressing how they are used for internal simulation, adapted by learning, revision or forgetting, and the control of this. In (Canbalo˘glu et al. 2022), it has also been shown how based on self-modeling networks computational models of organisational learning can be designed; here aggregation of individual mental model was addressed in a fixed, nonadaptive manner. In (Canbalo˘glu and Treur 2021b) a first attempt was made to model context-sensitive adaptation of the aggregation process, in that case by some heuristic approach, see also (Canbalo˘glu et al. 2023), Chap. 9 (this volume) or (Canbalo˘glu and Treur 2022a). In contrast to this, the current chapter addresses the adaptation of the aggregation process in a more precise manner by modeling it based on more exact knowledge expressed by Boolean propositions or functions of the considered context factors. In this chapter, in Sect. 10.2 some background knowledge is discussed. Section 10.3 describes the self-modeling networks modeling approach. In Sect. 10.4 and 10.5 a computational self-modeling network model for organisational learning with context-dependent aggregation based on Boolean functions will be introduced. Section 10.6 illustrates the model by an example simulation scenario. Finally, Sect. 10.7 is a discussion and Sect. 10.8 an Appendix with full specifications.

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10.2 Mental Models and Organisational Learning In this section, some of the multidisciplinary literature about the concepts and processes that need to be addressed are briefly discussed. This provides a basis for the self-modeling network model that will be presented in Sect. 10.4 and for the scientific justification of the model. For the history of the mental model area, often Kenneth Craik is mentioned as a central person. In his book Craik (1943) describes a mental model as a smallscale model that is carried by an organism within its head and based on that the organism ‘is able to try out various alternatives, conclude which is the best of them, react to future situations before they arise, utilize the knowledge of past events in dealing with the present and future, and in every way to react in a much fuller, safer, and more competent manner to the emergencies which face it.’ (Craik 1943, p. 61). Shih and Alessi (1993, p. 157) explain that ‘By a mental model we mean a person’s understanding of the environment. It can represent different states of the problem and the causal relationships among states.’ In (Van Ments and Treur 2021), an analysis of various types of mental models and the types of mental processes processing them are reviewed. Based on this analysis a three-level cognitive architecture has been introduced, where: • the base level models internal simulation of a mental model • the middle level models the adaptation of the mental model (formation, learning, revising, and forgetting a mental model, for example) • the upper-level models the (metacognitive) control over these processes By using the notion of self-modeling network (or reified network) from (Treur 2020), recently this cognitive architecture has been formalized computationally and used in computer simulations for various applications of mental models. For an overview of this approach and its applications, see (Treur and Van Ments 2022). Mental models also play an important role when people work together in teams. When every team member has a different individual mental model of the task that is performed, then this will stand in the way of good teamwork. Therefore, ideally these mental models should be aligned to such an extent that it becomes one shared mental model for all team members. An example of a computational model of a shared mental model and how imperfections in it work out can be found in (Van Ments et al. 2021). Organisational learning is an area which has received much attention over time; see, for example, (Argyris and Schön 1978; Bogenrieder 2002; Crossan et al. 1999; Fischhof and Johnson 1997; Kim 1993; McShane and Glinow 2010; Stelmaszczyk 2016; Wiewiora et al. 2019). However, contributions to computational formalization of organisational learning are very rare. By Kim (1993), mental models are considered a vehicle for both individual learning and organisational learning. By learning and developing individual mental models, a basis for formation of shared mental models for the level of the organisation is created, which provides a mechanism

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for organisational learning. The overall process consists of the following cyclical processes and interactions (see also Kim 1993, Fig. 8): (a) Individual level (1) (2) (3) (4)

Creating and maintaining individual mental models Choosing for a specific context a suitable individual mental model as focus Applying a chosen individual mental model for internal simulation Improving individual mental models (individual mental model learning)

(b) From individual level to organisation level (1) Deciding about creation of shared mental models (2) Creating shared mental models based on developed individual mental models (c) Organisation level (1) Creating and maintaining shared mental models (2) Associating to a specific context a suitable shared mental model as focus (3) Improving shared mental models (shared mental model refinement or revision) (d) From organisation level to individual level (1) Deciding about individuals to adopt shared mental models (2) Individuals adopting shared mental models by learning them (e) From individual level to organisation level (1) Deciding about improvement of shared mental models (2) Improving shared mental models based on further developed individual mental models In terms of the three-level cognitive architecture described in (Van Ments and Treur 2021), applying a chosen individual mental model for internal mental simulation relates to the base level, learning, developing, improving, forgetting the individual mental model relates to the middle level, and control of adaptation of a mental model relates to the upper level. Moreover, both interactions from individual to organisation level and vice versa involve changing (individual or shared) mental models and therefore relate to the middle level, while the deciding actions as a form of control relate to the upper level. This overview will provide useful input to the design of the computational network model for organisational learning and in particular the aggregation in it that will be introduced in Sect. 10.4.

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10.3 The Self-Modeling Network Modeling Approach Used In this section, the network-oriented modeling approach used is briefly introduced. A temporal-causal network model is characterised by; here X and Y denote nodes of the network, also called states (Treur 2020): • Connectivity characteristics Connections from a state X to a state Y and their weights ωX,Y • Aggregation characteristics For any state Y, some combination function cY (..) defines the aggregation that is applied to the impacts ωX,Y X(t) on Y from its incoming connections from states X • Timing characteristics Each state Y has a speed factor ηY defining how fast it changes for given causal impact. The following canonical difference (or related differential) equations are used for simulation purposes; they incorporate these network characteristics ωX,Y , cY (..), ηY in a standard numerical format: Y (t + /\t) = Y (t) + ηY [cY (ω X 1 ,Y X 1 (t), . . . , ω X k ,Y X k (t)) − Y (t)]/\t

(10.1)

for any state Y and where X 1 to X k are the states from which Y gets its incoming connections. The available dedicated software environment described in (Treur 2020, Ch. 9), includes a combination function library with currently around 50 useful basic combination functions. The above concepts enable to design network models and their dynamics in a declarative manner, based on mathematically defined functions and relations. The examples of combination functions that are applied in the model introduced here can be found in Table 10.1. Combination functions as shown in Table 10.1 and available in the combination function library are called basic combination functions. For any network model some number m of them can be selected; they are represented in a standard format as bcf1 (..), bcf2 (..), …, bcfm (..). In principle, they use parameters π1,i,Y , π2,i,Y such as the λ, σ, and τ in Table 1. Including these parameters, the standard format used for basic combination functions is (with V 1 , …, V k the single causal impacts): bcf i (π1,i,Y , π2,i,Y , V1 , . . . , Vk ) For each state Y just one basic combination function can be selected, but also a number of them can be selected, what happens in the current chapter; this will be interpreted as a weighted average of them according to the following format: cY (π1,1,Y , π2,1,Y , . . . , π1,m,Y , π2,m,Y , V1 , . . . , Vk ) γ1,Y bcf1 (π1,1,Y , π2,1,Y , V1 , . . . Vk ) + γm,Y bcfm (π1,m,Y , π2,m,Y , V1 , . . . , Vk ) = γ1,Y + · · · + γm,Y (10.2)

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Table 10.1 The combination functions used in the introduced self-modeling network model Notation

Formula

Parameters 1

Advanced logistic sum

alogisticσ,τ (V 1 ,…,V k )

[ − 1στ) ] (1 + 1+e 1+e−σ(V1 +···+Vk −τ) e−στ )

Steponce

steponceα,β (..)

1 if time t is between α and β, else 0

Start time α End time β

Hebbian learning

hebbμ (V 1 , V 2 , V 3 )

V1 ∗ V2 (1 − V3 ) + μV3

V 1 ,V 2 activation levels of the connected states; V 3 activation level of the self-model state for the connection weight Persistence factor μ

Maximum composed with Hebbian learning

max-hebbμ (V 1 , …, V k )

max(hebbμ (V1 , V2 , V3 ), V4 , . . . , V k )

V 1 ,V 2 activation levels of the connected states; V 3 activation level of the self-model state for the connection weight Persistence factor μ

Scaled maximum

smaxλ (V 1 , …, V k )

max(V 1 , …, V k )/λ

Scaling factor λ

Euclidean

eucln,λ (V 1 , …, V k )

Scaled geometric mean

sgeomeanλ (V 1 , …, V k )

Steepness σ > 0 Excitability threshold τ

/

n V1 n +···+Vk n

λ

/

k V1 ∗···∗Vk

λ

Order n Scaling factor λ Scaling factor λ

with combination function weights γi,Y . Selecting only one of them for state Y, for example, bcf i (..), is done by putting weight γi,Y = 1 and the other weights 0. This is a convenient way to indicate combination functions for a specific network model. The function cY (..) can then just be indicated by the weight factors γi,Y and the parameters πi,j,Y . Realistic network models are usually adaptive: often not only their states but also some of their network characteristics change over time. By using a self-modeling network (also called a reified network), a similar network-oriented conceptualization can also be applied to adaptive networks to obtain a declarative description using mathematically defined functions and relations for them as well; see (Treur 2020).

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This works through the addition of new states to the network (called self-model states) which represent (adaptive) network characteristics. In the graphical 3D-format as shown in Sect. 10.4, such additional states are depicted at a next level (called self-model level or reification level), where the original network is at the base level. As an example, the weight ωX,Y of a connection from state X to state Y can be represented (at a next self-model level) by a self-model state named WX,Y . Similarly, all other network characteristics from ωX,Y , cY (..), ηY can be made adaptive by including self-model states for them. For example, an adaptive speed factor ηY can be represented by a self-model state named HY , an adaptive combination function weight γi,Y can be represented by a self-model state Ci,Y . As the outcome of such a process of network reification is also a temporal-causal network model itself, as has been shown in (Treur 2020, Ch 10), this self-modeling network construction can easily be applied iteratively to obtain multiple orders of self-models at multiple (first-order, second-order, …) self-model levels. For example, a second-order self-model may include a second-order self-model state HW X,Y representing the speed factor ηW X,Y for the dynamics of first-order self-model state WX,Y which in turn represents the adaptation of connection weight ωX,Y . Similarly, a persistence factor μW X,Y of such a first-order self-model state WX,Y used for adaptation (e.g., based on Hebbian learning) can be represented by a second-order self-model state MW X,Y . In particular, for the aggregation process for the formation of a shared mental which is a main focus of the current chapter, in Sect. 10.4 second-order selfmodel states Ci,W X,Y will be used that represent the ith combination function weight γi,W X,Y of the combination functions selected for a shared mental model connection weight WX,Y (where the latter is a first-order self-model state).

10.4 The Adaptive Network Model for Organisational Learning The self-modeling network model for organisational learning with adaptive aggregation introduced here is illustrated for a scenario using the more extensive case study in an intubation process from (Van Ments et al. 2021). The part of the mental models used addresses four mental states; see Table 10.2, which involve tasks that for the sake of simplicity are indicated by a, b, c, and d. Initially the mental models of the nurse (person A) and doctor (person B) are different and based on weak connections; they cannot use a stronger shared mental model as that does not exist yet. The organisational learning addressed to improve the situation covers: 1. Individual learning by A and B of their mental models through internal simulation which results in stronger but still incomplete and different mental models (by Hebbian learning). Person A’s mental model has no connection from c_A to d_A and person B’s mental model has no connection from a_B to b_B.

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Table 10.2 The mental model used for the simple case study States for mental Short notation models of persons A, B and organisation O

Explanation

a_A

a_B

a_O

Prep_eq_N

Preparation of the intubation equipment by the nurse

b_A

b_B

b_O

Prep_d_N

Nurse prepares drugs for the patient

c_A

c_B

c_O

Pre_oy_D

Doctor executes pre oxygenation

d_A

d_B

d_O

Prep_team_D

Doctor prepares the team for intubation

2. Formation of a shared organisation mental model based on the two individual mental models (feed forward learning). A process of unification takes place. 3. Learning individual mental models from the shared mental model (feedback learning); e.g., a form of instructional learning. 4. Strengthening these individual mental models by individual learning through internal simulation which results in stronger and now complete mental models (by Hebbian learning). Now person A’s mental model has a connection from c_A to d_A and person B’s mental model has a connection from a_B to b_B. 5. Improvement of the shared organisation mental model based on the two improved individual mental models. A process of unification takes place. In this scenario, person A and person B have knowledge on different tasks. Development of the organisational learning covers: 1. Individual learning processes of A and B for their separate mental models through internal simulation. By Hebbian learning, mental models become stronger but they are still incomplete. A has no knowledge for state d_A, and B has no knowledge for state a_B: they do not have connections to these states. 2. Shared mental model formation by aggregation of the different individual mental models (feed forward learning). Here the considered context factors exert control over the aggregation process. 3. Individuals’ adoption of shared mental model (feedback learning), e.g., a form of instructional learning. 4. Strengthening of individual mental models by individual learning through internal simulation, strengthening knowledge for less known states of persons A and B (by Hebbian Learning). Then, persons have stronger and now (more) complete mental models. 5. Improvements on the shared mental model by aggregation of the effects of the strengthened individual mental individuals. Again, the considered context factors (which may have changed in the meantime) exert control over the aggregation process. In the aggregation process for the shared mental model formation, not all individual mental models will be considered to be equally valuable. Due to more experience, Person A may be more knowledgeable than person B who is a beginner, for example. And when they are both experienced, can they be considered independent

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sources, or have they learnt it from the same source? In the former case, aggregation of their knowledge may be assumed to lead to a stronger outcome than in the latter case. Based on such considerations, a number of example context factors have been included that affect the type of aggregation that is applied. They are used to control the process of aggregation in such a way that it becomes context sensitive. Recall that in a network model in general, aggregation is specified by combination functions (see Sect. 10.3) indicated by combination function weights γi,Y (and parameters πi,j,Y of these functions). In the specific case of mental model aggregation considered here, it concerns aggregation for the first-order self-model states WX,Y for the weights of the connections X → Y of the shared mental model. Therefore to make aggregation of mental models adaptive, the (choice of) combination functions for these states WX,Y have to become become adaptive in relation to the considered context factors and specifically here using knowledge expressed by Boolean propositions or functions of the considered context factors. In the example scenario four options for combination functions are considered for these W-states of the shared mental model (see Table 10.1): alogistic, smax, eucl, sgeomean, numbered by i = 1, …, 4 in this order. To make the combination functions of the first-order self-model states WX,Y adaptive, second-order self-model states Ci,W X,Y , i = 1, ..., 4 are introduced that represent the combination function weights γi,W X,Y : • • • •

C1,W X,Y C2,W X,Y C3,W X,Y C4,W X,Y

for the logistic sum combination function alogistic for the scaled maximum combination function smax for the euclidean combination function eucl for the scaled geometric mean combination function sgeometric

So, there are four Ci,W X,Y -states for each shared mental model connection, which is three in total. Thus, the model has 12 Ci,W X,Y -states at the second-order self-model level to model the aggregation process. These second-order self-model states and the functions they represent are used depending on the context (due to the connections from the context states to the Ci,W X,Y -states), and the average is taken (according to (2) in Sect. 10.3) if more than one i has a nonzero Ci,W X,Y for a given WX,Y -state. The influences of the context factors on the aggregation as pointed out in Table 10.3 have been used to specify the context-sensitive control for the choice of combination function via these Ci,W X,Y -states. For example, if A and B have a similar category of knowledgeability, in principle a form of average is supported (via the states C3,W X,Y or C4,W X,Y for a Euclidean or geometric mean combination function), but if they are independent, some form of amplification is supported (via the state Ci,W X,Y for a logistic combination function). If they differ in knowledgeability, the maximal knowledge is chosen (via the state C2,W X,Y for a maximum combination function). This setup is meant as example to illustrate the idea and can easily be replaced by other context factors and other knowledge relating them to the control of the aggregation via the Ci,W X,Y ,-states. The indications from Table 10.3 have been represented by four Boolean functions for the considered combination functions in Table 10.4.

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Table 10.3 Examples of criteria for context-sensitive control of mental model aggregation applied in the example scenario Context: knowledgeable

Context: dependency

A and B both not experienced A and B both experienced

A and B dependent

Context: preference for type of quantity

Combination function type

Additive

Euclidean

Multiplicative

Geometric mean

Additive

Euclidean

Multiplicative

Geometric mean

A and B not dependent

Logistic

A experienced B not experienced

Maximum

B experienced A not experienced

Maximum

Table 10.4 Examples of Boolean functions formalising the indications from Table 10.3 expA

expB

depAB

addpref

alogistic

smax

Euclidean

sgeomean

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In a standard manner, such Boolean functions can also be represented by Boolean propositions (in disjunctive normal form) as shown in the upper part of Box 10.1. Here ∧ means the conjunction (AND), ∨ the disjunction (OR) and ¬ the negation (NOT). As handling negations adds undesirable complexity to the model, the choice has been made to have additional context states for the opposites of the given context states: begX

X is beginner (¬ expX)

10 Adaptive Mental Model Aggregation in Organisational Learning Using …

indepAB multpref

227

A and B are independent (¬ depAB) preference for multiplicative (¬ addpref)

By replacing the negations within the upper part by these opposite states, the lower part in Box 10.1 is obtained. Box 10.1 Boolean propositions specifying the knowledge relating context factors to control states Ci,W X,Y

From this it can easily be derived which connections are needed from the context states to the Ci,W X,Y -states, as shown in Table 10.5. To specify such Boolean propositions in the developed self-modeling network model, not only the connections as shown in Table 10.5 are needed but also the function for the propositional structure. As it is chosen to use the standardised disjunctive normal form (every proposition can be rewritten in that format), that can be done by one function based on a combination of minimum of each of the conjunctions followed by the maximum of the disjunction. For any propositional formula F in Table 10.5 The different connections from the considered context states to the second-order selfmodel states Ci,W X,Y for i = 1,…, 4. Note that two connections from the addpref and multpref are needed (indicated by ++) and all connections should be in the order indicated in Box 10.1 Combination Ci,WX,Y State Context states function expA expB begA begB depAB indepAB addpref multpref Logistic

C1,W X,Y

+

+

+

Maximum

C2,W X,Y

+

+

+

+

Euclidean

C2,W X,Y

+

+

+

+

+

Geometric

C4,W X,Y

+

+

+

+

+

++ ++

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disjunctive normal form F = [a1,1 ∧ . . . ∧ a1,q1 ] ∨ . . . ∨ [a p,1 ∧ . . . ∧ a p,q p ] when (truth) values 0 or 1 are assigned to the ai,j , the value of F can be determined by the following function: maxmin([[a1,1 , . . . , a1,q1 ], . . . , [a p,1 , . . . , a p,q p ]]) = max(min(a1,1 , . . . , a1,q1 ), . . . , min(a p,1 , . . . , a p,q p )) Note that this function is also meaningful if continuous values within the [0, 1] interval are used. This may also enable adaptation based on gradual changes of the context factors. For the current scenario where only one or two conjunctions occur (see Box 10.1), the function maxmin2 was used, defined as maxmin2([[a1,1 , . . . , a1,q1 ], [a2,1 , . . . , a2,q2 ]]) = max(min(a1,1 , . . . , a1,q1 ), min(a2,1 , . . . , a2,q2 )) In MATLAB terms this function was implemented with a parameter p(1) for the length of the first conjunction as maxmin2(p, v) = max([min(v(1 : p(1))), min(v(p(1) + 1 : end)]) and added to the combination function library in the software environment. Given the specification in Box 10.1, the parameter p(1) is 2 for the maximum function, 3 for the logistic function, and 4 for the other two combination functions (Euclidean and geometric mean). The approach to adaptive aggregation of mental models described above was integrated in the self-modeling network model for organisational learning (with fixed, nonadaptive aggregation) introduced in (Canbalo˘glu et al. 2022); see also (Canbalo˘glu et al. 2023), Chap. 6 (this volume). The connectivity of the network model extended in this way is depicted in Fig. 10.1. The added states for the context factors are depicted by the 16 grey ovals in the middle (blue) plane. Moreover, the added Ci,W X,Y -states are depicted by the 12 blue-green ovals in the upper (purple) plane. This increases the number of states in the network model introduced in (Canbalo˘glu et al. 2022) from 46 to 74 states. At the base level (the pink plane), states for the individual and shared mental models are included. Moreover, context states for the different phases were added here. The middle level (the blue plane) represents the first-order self-model level. This is based on W-states representing the weights of the connections between states within the mental models. For the organisational learning, a few (intralevel) connections that connect W-states from individual mental models to shared mental models and conversely are crucial. From left to right, these intralevel connections are used to

10 Adaptive Mental Model Aggregation in Organisational Learning Using …

229

HWc_A,d_A

C4,Wa_O,b_O C4,Wb_O,c_O C4,Wc_O,d_O MWc_A,d_A HWb_O,c_OHWc_O,d_O HWa_O,b_O MWb_A,c_A C3,Wb_O,c_O C3,Wc_O,d_O WWb_O,c_O,Wb_A,c_A MWa_A,b_A Second-order C3,Wa_O,b_O WWc_O,d_O,Wc_A,d_A WWa_O,b_O,Wa_A,b_A C2,Wc_O,d_O self-model level for control of MWc_B,d_B C2,Wa_O,b_O C2,Wb_O,c_O W Wb_O,c_O,Wb_B,c_B MWb_B,c_B network C1,Wc_O,d_O adaptation C WWa_O,b_O,Wa_B,b_B WWc_O,d_O,Wc_B,d_B1,Wa_O,b_O C1,Wb_O,c_O

HWb_A,c_A HWa_A,b_A HWc_B,d_B HWb_B,c_B HWa_B,b_B

MWa_B,b_B

Wb_A,c_A

Wa_A,b_A

Wb_B,c_B

Wc_A,d_A

Wc_B,d_B

conbeg,Wc_B,d_B conbeg,Wc_B,d_B conexp,Wc_A,d_A conexp,Wc_A,d_A conmultpref conbeg,Wb_B,c_B conbeg,Wb_B,c_B Wb_O,c_O con exp,Wb_A,c_A conexp,Wb_A,c_A conaddpref conexp,Wa_A,b_Aconbeg,Wa_B,b_B conbeg,Wa_B,b_B conexp,Wa_A,b_A Wc_O,d_O

Wa_B,b_B

Wa_O,b_O

conph3 aa_A A

conph4

a_B B

b_B b B

bb_A A

cc_B B

conindep_AB condepAB First-order self-model level for network adaptation

conph2

c_A d_A

dd_B B

a_O

b_O

c_O

d_O

Base level

conph1

Fig. 10.1 The connectivity of the second-order adaptive network model

provide input from the W-states to the W-states of the shared mental model for the formation (or improvement) of the shared mental model: feed forward learning in terms of (Crossan et al. 1999). The intralevel connections from right to left model the influence of the shared mental model on the individual mental models, for example, based on instruction of the shared mental model to employees: feedback learning in terms of (Crossan et al. 1999). The middle level also includes context states for the context factors that are used at the second-order self-model level (the purple plane) in the Boolean functions for the control of the aggregation for shared mental model formation. Overall, the second-order self-model level includes WW -, MW and HW -states to control the adaptations of the W-states at the first-order self-model level. The WW -states can be seen as higher-order W-states; they represent the weights of the intralevel connections from W-states of the shared organisation mental model to W-states of the individual mental models used for feedback learning. The WW -states initiate and control this feedback learning by making these weights within the first-order self-model level nonzero when a shared mental model has become available. The WW -states also have a learning mechanism (which can be considered a form of higher-order Hebbian learning), so that they are maintained over time: individuals will keep relating and updating their individual mental model to the shared mental model. Finally, the HW states are used for controlling adaptation speeds of connection weights and MW -states for controlling persistence of adaptation.

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State a_A b_A c_A d_A a_B b_B c_B d_B a_O b_O c_O d_O conph1 conph2

X15

conph3

X16 X17

conph4 conph5

Explanation Individual mental model state for person A for task a Individual mental model state for person A for task b Individual mental model state for person A for task c Individual mental model state for person A for task d Individual mental model state for person B for task a Individual mental model state for person B for task b Individual mental model state for person B for task c Individual mental model state for person B for task d Shared mental model state for organisation O for task a Shared mental model state for organisation O for task b Shared mental model state for organisation O for task c Shared mental model state for organisation O for task d Context state for Phase 1: individual mental model simulation and learning Context state for Phase 2: creation of a shared mental model for organisation O Context state for Phase 3: learning individual mental models from the shared mental model for organisation O Context state for Phase 4: individual mental model simulation and learning Context state for Phase 5: improvement of the shared mental model for organisation O

Fig. 10.2 Base level states of the introduced adaptive network model

10.5 States and Connections Used in the Model In this section some more details of the states and connections are shown. First, an overview is provided of all states of the model with their explanation. Figure 10.2 addresses the states at the base level. In Fig. 10.3, the first-order self-model W-states are listed, together with the context states for the context factors used in the Boolean functions for control of aggregation. In Figs. 10.4 and 10.5 the second-order self-model states are explained. First in Table 3 the self-model WW -states, HW -states and MW -states are addressed. Next, in Fig. 10.5 the second-order self-model states Ci,W X,Y for combination function weights are addressed. They are the ones that play a crucial role for the main focus of this chapter: the control over mental model aggregation by Boolean functions of context factors. Finally, in Fig. 10.6 (intralevel) and 10.7 (interlevel) an overview of the types of connections is given.

10.6 Example Simulation Scenarios In this section some of our simulation results are discussed. A full specification of the model can be found in the Appendix Sect. 10.8. The aggregation characteristics for the aggregation of individual mental models in order to get a shared mental model out of them are specified by weights of combination functions. In this scenario, different options for combination functions are used to observe different types of aggregation while a feed forward organisational learning progresses by the aggregation of separate individual mental models. In the current we explore how during a feed forward

10 Adaptive Mental Model Aggregation in Organisational Learning Using … Nr X18

State conexp,Wa_A,b_A

X19

conexp,Wb_A,c_A

X20

conexp,Wc_A,d_A

X21

conexp,Wa_B,b_B

X22

conexp,Wb_B,c_B

X23

conexp,Wc_B,d_B

X18

conbeg,Wa_A,b_A

X19

conbeg,Wb_A,c_A

X20

conbeg,Wc_A,d_A

X21

conbeg,Wa_B,b_B

X22

conbeg,Wb_B,c_B

X23

conbeg,Wc_B,d_B

X30 X31 X32 X33 X34

condepA,B conindepA,B conaddpref conmultpref Wa_A,b_A

X35

Wa_A,b_A

X36

Wb_A,c_A

X37

Wc_A,d_A

X38

Wa_B,b_B

X39

Wb_B,c_B

X40

Wc_B,d_B

X41

Wa_O,b_O

X42

Wb_O,c_O

X43

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Explanation Context state for how experienced A is concerning the mental model connection from a_A to b_A Context state for how experienced A is concerning the mental model connection from b_A to c_A Context state for how experienced A is concerning the mental model connection from c_A to d_A Context state for how experienced A is concerning the mental model connection from a_A to b_A Context state for how experienced A is concerning the mental model connection from b_A to c_A Context state for how experienced A is concerning the mental model connection from c_A to d_A Context state for how unexperienced A is concerning the mental model connection from a_A to b_A Context state for how unexperienced A is concerning the mental model connection from b_A to c_A Context state for how unexperienced A is concerning the mental model connection from c_A to d_A Context state for how unexperienced A is concerning the mental model connection from a_A to b_A Context state for how unexperienced A is concerning the mental model connection from b_A to c_A Context state for how unexperienced A is concerning the mental model connection from c_A to d_A Context state for how dependent A and B are Context state for how independent A and B are Context state for preference for additive aggregation Context state for preference for multiplicative aggregation First-order self-model state for the weight of the connection from a to b within the individual mental model of person A First-order self-model state for the weight of the connection from a to b within the individual mental model of person A First-order self-model state for the weight of the connection from b to c within the individual mental model of person A First-order self-model state for the weight of the connection from c to d within the individual mental model of person A First-order self-model state for the weight of the connection from a to b within the individual mental model of person B First-order self-model state for the weight of the connection from b to c within the individual mental model of person B First-order self-model state for the weight of the connection from c to d within the individual mental model of person B First-order self-model state for the weight of the connection from a to b within the shared mental model of the organisation O First-order self-model state for the weight of the connection from b to c within the shared mental model of the organisation O First-order self-model state for the weight of the connection from c to d within the shared mental model of the organisation O

Fig. 10.3 First-order self-model and context states of the introduced adaptive network model

organisational learning progress, aggregation occurs in a context-sensitive manner based on Boolean functions. To see the different processes better, the scenario was structured in phases. In reality and also in the model, these processes also can overlap or take place entirely simultaneously. The five phases were designed as follows:

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Nr X44

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X45

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MWc_B,d_B

Explanation Second-order self-model state for the weight of the connection from shared mental model connection weight self-model state Wa_O,b_O to individual mental model connection weight self-model state Wa_A,b_A for instructional learning of the shared mental model Second-order self-model state for the weight of the connection from shared mental model connection weight self-model state Wb_O,c_O to individual mental model connection weight self-model state Wb_A,c_A for instructional learning of the shared mental model Second-order self-model state for the weight of the connection from shared mental model connection weight self-model state Wc_O,d_O to individual mental model connection weight self-model state Wc_A,d_A for instructional learning of the shared mental model Second-order self-model state for the weight of the connection from shared mental model connection weight self-model state Wa_O,b_O to individual mental model connection weight self-model state Wa_B,b_B for instructional learning of the shared mental model Second-order self-model state for the weight of the connection from shared mental model connection weight self-model state Wb_O,c_O to individual mental model connection weight self-model state Wb_B,c_B for instructional learning of the shared mental model Second-order self-model state for the weight of the connection from shared mental model connection weight self-model state Wc_O,d_O to individual mental model connection weight self-model state Wc_B,d_B for instructional learning of the shared mental model Second-order self-model state for the adaptation speed of individual mental model connection weight self-model state Wa_A,b_A Second-order self-model state for the adaptation speed of individual mental model connection weight self-model state Wb_A,c_A Second-order self-model state for the adaptation speed of individual mental model connection weight self-model state Wc_A,d_A Second-order self-model state for the adaptation speed of individual mental model connection weight self-model state Wa_B,b_B Second-order self-model state for the adaptation speed of individual mental model connection weight self-model state Wb_B,c_B Second-order self-model state for the adaptation speed of individual mental model connection weight self-model state Wc_B,d_B Second-order self-model state for the adaptation speed of shared mental model connection weight self-model state Wa_O,b_O for formation or revision of the shared mental model Second-order self-model state for the adaptation speed of shared mental model connection weight self-model state Wb_O,c_O for formation or revision of the shared mental model Second-order self-model state for the adaptation speed of shared mental model connection weight self-model state Wc_O,d_O for formation or revision of the shared mental model Second-order self-model state for persistence of adaptation of individual mental model connection weight self-model state Wa_A,b_A Second-order self-model state for persistence of adaptation of individual mental model connection weight self-model state Wb_A,c_A Second-order self-model state for persistence of adaptation of individual mental model connection weight self-model state Wc_A,d_A Second-order self-model state for persistence of adaptation of individual mental model connection weight self-model state Wa_B,b_B Second-order self-model state for persistence of adaptation of individual mental model connection weight self-model state Wb_B,c_B Second-order self-model state for persistence of adaptation of individual mental model connection weight self-model state Wc_B,d_B

Fig. 10.4 S-order self-model states of the introduced adaptive network model: the second-order WW -states, HW -states and MW -states

• Phase 1: Individual mental model usage and learning Two different mental models for person A and B belonging to an organisation are learnt in this phase by Hebbian learning for internal simulations of the mental models. Person A mainly has knowledge on the first part of the job, and person B has knowledge on the last part.

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State C1,Wa_O, b_O

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Explanation Second-order self-model state for the weight for the combination function alogistic for the aggregation for shared mental model connection weight representation Wa_O,b_O Second-order self-model state for the weight for the combination function smax for the aggregation for shared mental model connection weight representation Wa_O,b_O Second-order self-model state for the weight for the combination function eucl for the aggregation for shared mental model connection weight representation Wa_O,b_O Second-order self-model state for the weight for the combination function sgeometric for the aggregation for shared mental model connection weight representation Wa_O,b_O Second-order self-model state for the weight for the combination function alogistic for the aggregation for shared mental model connection weight representation Wb_O,c_O Second-order self-model state for the weight for the combination function smax for the aggregation for shared mental model connection weight representation Wb_O,c_O Second-order self-model state for the weight for the combination function eucl for the aggregation for shared mental model connection weight representation Wa_O,b_O Second-order self-model state for the weight for the combination function sgeometric for the aggregation for shared mental model connection weight representation Wb_O,c_O Second-order self-model state for the weight for the combination function alogistic for the aggregation for shared mental model connection weight representation Wc_O,d_O Second-order self-model state for the weight for the combination function smax for the aggregation for shared mental model connection weight representation Wc_O,d_O Second-order self-model state for the weight for the combination function eucl for the aggregation for shared mental model connection weight representation Wa_O,b_O Second-order self-model state for the weight for the combination function sgeometric for the aggregation for shared mental model connection weight representation Wc_O,d_O

Fig. 10.5 S-order self-model states of the introduced adaptive network model: the second-order CW -states for aggregation for the shared mental model connections

Fig. 10.6 Types of intralevel connections in the adaptive network model and how they relate to (a) to (d) identified in Sect. 10.2. For the example scenario, x and y are states from {a, b, c, d} and Z is a person from {A, B}

• Phase 2: Feed forward organisational learning: shared mental model formation Aggregation of individual mental models occurs here to for the shared mental model: feed forward organisational learning. During this formation, different combination functions are used for different cases in terms of context factors such as knowledgeability, dependence and preference of additivity or multiplicativity. This feed forward organisational learning takes place by the determination of the values of the W-states for the organisation’s general states for the jobs a_O to d_O.

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Fig. 10.7 Types of interlevel connections in the adaptive network model and how they relate to (a) to (d) identified in Sect. 10.2. For the example scenario, x and y are states from {a, b, c, d} and Z is a person from {A, B}

• Phase 3: Feedback organisational learning: the shared mental model is learnt by the individuals Feedback learning from the organisation’s shared mental model, can be viewed as learning from each other in an indirect manner. It takes place in this phase by the activation of the connections from the organisation’s general W-states to the individual W-states. By that, individuals receive the knowledge from the

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235

Fig. 10.8 Overview of the values for the context factors for the different scenarios

shared mental model, for example, as a form of instructional learning. Since there is a single shared mental model, there is no need for many mutual one-to-one connections between persons to learn from each other. • Phase 4: Individual mental model usage and learning Further improvements on individual mental models of persons take place using Hebbian learning during internal simulation of the mental model in this phase, similar to Phase 1. Four scenarios are discussed to see how the context factors affect the aggregation process. In Fig. 10.8 an overview is shown of the different values for the context factors: binary in Scenario 1 and 3, nonbinary in Scenario 2 and 4, static in Scenario 1 and 2, and changing in Scenario 3 and 4. Scenario 1: All context states 0 or 1 (binary case) For this first scenario, we have binary values for the context states. In Fig. 10.9 the phases are shown: phase 1 (individual mental model learning), phase 2 (feed forward learning for formation of the shared mental model), phase 3 (feedback learning of individual mental models from the shared mental models) and phase 4 (further individual mental model learning) show a classical organisation process. In the beginning of the whole simulation, we have the selection of the combination functions by determining values for the C-states based on the context states. For example, in Fig. 10.10 it can be seen that C2 is selected; it becomes 1 and remains at one during the simulation.

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Fig. 10.9 Overall simulation of Scenario 1

Scenario 2: Context states nonbinary In the second scenario (Figs. 10.11 and 10.12), we use nonbinary values for the context states. For example, one has value 0.9 and one has 0.2. Because of these different values for context states, our selected combination functions become different too, so our feed forward learning and the aggregation used in it becomes different from the previous one scenario. Now the C-states are in different ratios and more than one of them is nonzero. In the simulation a weighted average of them is used with the values of the four C-states as weights. Scenario 3: Changing context states (binary) In the third scenario binary values for the context factors are used, but this time the context changes after time 400 (see Figs. 10.13 and 10.14). As can be seen in Fig. 10.14 the values of the context indeed become different after 400. Therefore, the C-states for our combination functions also change there. Scenario 4: Changing context states (nonbinary) For the last scenario (Figs. 10.15 and 10.16), we use non-binary values, and we also change the context after time 400. Because we use changing nonbinary context

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1.1 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0

5 X17 - con_exp,Wa_A,b_A

10 X18 - con_exp,Wb_A,c_A

15 X19 - con_exp,Wc_A,d_A

20 X20 - con_exp,Wa_B,b_B

X21 - con_exp,Wb_B,c_B

X22 - con_exp,Wc_B,d_B

X23 - con_beg,Wa_A,b_A

X24 - con_beg,Wb_A,c_A

X25 - con_beg,Wc_A,d_A

X26 - con_beg,Wa_B,b_B

X27 - con_beg,Wb_B,c_B

X28 - con_beg,Wc_B,d_B

X29 - con_depAB

X30 - con_indepAB

X31 - con_addpref

X32 - con_multpref

X48 - C1,Wa_O, b_O

X49 - C2,Wa_O, b_O

X50 - C3,Wa_O, b_O

X51 - C4,Wa_O, b_O

X52 - C1,Wb_O, c_O

X53 - C2,Wb_O, c_O

X54 - C3,Wb_O, c_O

X55 - C4,Wb_O, c_O

X56 - C1,Wc_O, d_O

X57 - C2,Wc_O, d_O

X58 - C3,Wc_O, d_O

X59 - C4,Wc_O, d_O

Fig. 10.10 Context factors and initial adaptation of the C-states for Scenario 1 (binary)

state values, after time 400 also the combination functions change in a nonbinary way, as can be seen in Fig. 10.16.

10.7 Discussion This chapter uses material from (Canbalo˘glu and Treur 2022b). An important process with organisational learning is the aggregation of developed individual mental models to obtain shared mental models, e.g., (Kim 1993; Wiewiora et al. 2019). The current chapter focuses on how Boolean functions of context factors can be used in this aggregation process. It was shown how a second-order adaptive self-modeling network model for organisation learning based on self-modeling network models described in (Treur 2020) can model the adaptivity of this process of aggregation of individual mental models based on Boolean combinations of context factors. In previous work (Canbalo˘glu et al. 2022) addressing organisational learning, the type of aggregation used for the process of shared mental model formation was fixed and not addressed in an adaptive manner and not made context sensitive. In (Canbalo˘glu and Treur 2022a) forms of aggregation have been incorporated and addressed in an adaptive heuristic manner, see also (Canbalo˘glu et al. 2023), Chap. 9 (this volume). In contrast, in the current chapter Boolean functions of context factors were used to address the adaptivity of the aggregation, which provides a more precise way to specify knowledge for the context-sensitive adaptive control.

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Fig. 10.11 Overall simulation of Scenario 2 1.1 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0

5 X17 - con_exp,Wa_A,b_A X21 - con_exp,Wb_B,c_B X25 - con_beg,Wc_A,d_A X29 - con_depAB X48 - C1,Wa_O, b_O X52 - C1,Wb_O, c_O X56 - C1,Wc_O, d_O

10 X18 - con_exp,Wb_A,c_A X22 - con_exp,Wc_B,d_B X26 - con_beg,Wa_B,b_B X30 - con_indepAB X49 - C2,Wa_O, b_O X53 - C2,Wb_O, c_O X57 - C2,Wc_O, d_O

15 X19 - con_exp,Wc_A,d_A X23 - con_beg,Wa_A,b_A X27 - con_beg,Wb_B,c_B X31 - con_addpref X50 - C3,Wa_O, b_O X54 - C3,Wb_O, c_O X58 - C3,Wc_O, d_O

20 X20 - con_exp,Wa_B,b_B X24 - con_beg,Wb_A,c_A X28 - con_beg,Wc_B,d_B X32 - con_multpref X51 - C4,Wa_O, b_O X55 - C4,Wb_O, c_O X59 - C4,Wc_O, d_O

Fig. 10.12 Context factors and initial adaptation of the C-states for Scenario 2 (nonbinary)

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Fig. 10.13 Overall simulation of Scenario 3

1.1 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0

50

100

X17 - con_exp,Wa_A,b_A X21 - con_exp,Wb_B,c_B X25 - con_beg,Wc_A,d_A X29 - con_depAB X48 - C1,Wa_O, b_O X52 - C1,Wb_O, c_O X56 - C1,Wc_O, d_O

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X18 - con_exp,Wb_A,c_A X22 - con_exp,Wc_B,d_B X26 - con_beg,Wa_B,b_B X30 - con_indepAB X49 - C2,Wa_O, b_O X53 - C2,Wb_O, c_O X57 - C2,Wc_O, d_O

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X19 - con_exp,Wc_A,d_A X23 - con_beg,Wa_A,b_A X27 - con_beg,Wb_B,c_B X31 - con_addpref X50 - C3,Wa_O, b_O X54 - C3,Wb_O, c_O X58 - C3,Wc_O, d_O

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X20 - con_exp,Wa_B,b_B X24 - con_beg,Wb_A,c_A X28 - con_beg,Wc_B,d_B X32 - con_multpref X51 - C4,Wa_O, b_O X55 - C4,Wb_O, c_O X59 - C4,Wc_O, d_O

Fig. 10.14 Context factors and adaptation of the C-states for Scenario 3 initially and after time 400 (binary)

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Fig. 10.15 Overall simulation of Scenario 4

Fig. 10.16 Context factors and adaptation of the C-states for Scenario 3 initially and after time 400 (nonbinary)

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10.8 Appendix: Role Matrices In this section full specifications by role matrices are provided of the model. Role Matrices for Connectivity Characteristics In Figs. 10.17, 10.18, 10.19, 10.20, 10.21, the different role matrices are shown that provide a full specification of the network characteristics defining the adaptive network model in a standardised table format. Here in each role matrix, each state has its row where it is listed which are the impacts on it from that role. The connectivity characteristics are specified by role matrices mb and mcw shown in Figs. 10.17 and 10.18. Role matrix mb lists the other states (at the same or lower level) from which the state gets its incoming connections, whereas in role matrix mcw the connection weights are listed for these connections.

Fig. 10.17 Role matrices for the connectivity: mb for base connectivity

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Nonadaptive connection weights are indicated in mcw (in Fig. 10.18) by a number (in a green shaded cell), but adaptive connection weights are indicated by a reference to the (self-model) state representing the adaptive value (in a peach-red shaded cell). This can be seen for states X2 to X4 (with self-model states X38 to X40 ), states X6 to X8 (with self-model states X41 to X43 ), X10 to X12 (with self-model states X44 to X46 ), and X38 to X43 (with self-model states X47 to X52 ). Role Matrices for Aggregation Characteristics The network characteristics for aggregation are defined by the selection of combination functions from the library and values for their parameters. In role matrix mcfw it is specified by weights which state uses which combination function; see Fig. 10.19.

Fig. 10.18 Role matrices for the connectivity: mcw for connection weights

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Fig. 10.19 Role matrices for the aggregation characteristics: combination function weights

Here many combination function weights are adaptive (represented by secondorder self-model Ci,W -states X68 to X79 ) for states X44 to X46 (the W-states of the shared mental model) to model the context-sensitive control of the aggregation in shared mental model formation.

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Fig. 10.19 (continued)

In role matrix mcfp (see Fig. 10.20) it is indicated what the parameter values are for the chosen combination functions. Some of them are adaptive, as can be seen in the rows from X38 to X43 (e.g., the persistence factors μ represented by the self-model states X62 to X67 ).

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Fig. 10.20 Role matrices for the aggregation characteristics: combination function parameters

Role Matrices for Timing Characteristics In Fig. 10.21, the role matrix ms for speed factors is shown, which lists all speed factors. Next to it, the list of initial values can be found. Also, for ms some entries are adaptive: the speed factors of X38 to X46 are represented by (second-order) self-model states X53 to X61 .

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Fig. 10.21 Role matrices ms for the timing characteristics (speed factors) and initial values iv. Note that the values listed for the context factors X17 to X32 (yellow shaded) are those for Scenario 1. For all four scenarios they can be found in Table 10.21

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References Argyris, C., Schön, D.A.: Organisational Learning: A Theory of Action Perspective. AddisonWesley, Reading, MA (1978) Bogenrieder, I.: Social architecture as a prerequisite for organisational learning. Manag. Learn. 33(2), 197–216 (2002) Canbalo˘glu, G., Treur, J.: Context-sensitive mental model aggregation in a second-order adaptive network model for organisational learning. In: Benito, R.M., Cherifi, C., Cherifi, H., Moro, E., Rocha, L.M., Sales-Pardo, M. (eds.) Complex Networks & Their Applications X. Proceedings of the 10th International Conference on Complex Networks and their Applications. Studies in Computational Intelligence, vol 1015, pp. 411–423. Springer Nature, Cham Springer Nature (2022a) Canbalo˘glu, G., Treur, J.: Using Boolean functions of context factors for adaptive mental model aggregation in organisational learning. In: Klimov, V.V., Kelley, D.J. (eds.) Biologically Inspired Cognitive Architectures 2021. BICA 2021. Studies in Computational Intelligence, vol 1032, pp. 54–68. Springer Nature, Cham (2022b). https://www.researchgate.net/publication/ 354402996 Canbalo˘glu, G., Treur, J., Roelofsma, P.H.M.P.: Computational modeling of organisational learning by self-modeling networks. Cogn. Syst. Res. 73, 51–64 (2022) Canbalo˘glu, G., Treur, J., Wiewiora, A. (eds.): Computational Modeling of Multilevel Organisational Learning and its Control Using Self-Modeling Network Models. Springer Nature, this volume (2023) Craik, K.J.W.: The Nature of Explanation. University Press, Cambridge, MA (1943) Crossan, M.M., Lane, H.W., White, R.E.: An organisational learning framework: From intuition to institution. Acad. Manage. Rev. 24, 522–537 (1999) Fischhof, B., Johnson, S.: Organisational Decision Making. Cambridge University Press, Cambridge (1997) Kim, D.H.: The Link Between Individual and Organisational Learning. Sloan Management Review, Fall 1993, pp. 37–50. Also in: Klein, D.A. (ed.), The Strategic Management of Intellectual Capital. Routledge-Butterworth-Heinemann, Oxford. (Cited by 4688 in Google Scholar dd. August 10, 2021) (1993) McShane, S.L., von Glinow, M.A.: Organisational Behavior. McGraw-Hill, Boston (2010) Shih, Y.F., Alessi, S.M.: Mental models and transfer of learning in computer programming. J. Res. Comput. Educ. 26(2), 154–175 (1993) Stelmaszczyk, M.: Relationship between individual and organisational learning: mediating role of team learning. J. Econ. Manage. 26(4), 1732–1947 (2016). https://doi.org/10.22367/jem.2016. 26.06 Treur, J.: Network-Oriented Modeling for Adaptive Networks: Designing Higher-Order Adaptive Biological, Mental and Social Network Models. Springer Nature, Cham (2020) Treur, J., Van Ments, L. (eds.): Mental Models and their Dynamics, Adaptation, and Control: A Self-Modeling Network Modeling Approach. Springer Nature (2022). Van Ments, L., Treur, J.: Reflections on dynamics, adaptation and control: a cognitive architecture for mental models. Cogn. Syst. Res. 70, 1–9 (2021) Van Ments, L., Treur, J., Klein, J., Roelofsma, P.H.M.P.: A second-order adaptive network model for shared mental models in hospital teamwork. In: Nguyen, N.T., et al. (eds.) Proceedings of the 13th International Conference on Computational Collective Intelligence, ICCCI’21. Lecture Notes in AI, vol. 12876, pp. 126–140. Springer Nature (2021) Wiewiora, A., Smidt, M., Chang, A.: The ‘How’ of multilevel learning dynamics: a systematic literature review exploring how mechanisms bridge learning between individuals, teams/projects and the organisation. Eur. Manag. Rev. 16, 93–115 (2019)

Part V

Computational Analysis of the Role of Leadership in Real-World Scenarios for Multilevel Organisational Learning

Leaders, with their position of power and influence, are important learning actors who can trigger or restrict learning flows. This part addresses the role of leaders and their leadership styles in influencing learning outcomes. In continuation of Part IV, in this part leadership styles are introduced to the models as a context-sensitive control influencing multilevel learning flows. Realistic case studies with focus on the role of leaders for control of multilevel organisational learning are addressed.

Chapter 11

Computational Analysis of the Role of Leadership Style for Its Context-Sensitive Control over Multilevel Organisational Learning Gülay Canbalo˘glu, Jan Treur, and Anna Wiewiora Abstract This chapter addresses formalisation and computational modeling of context-sensitive control over multilevel organisational learning and in particular the role of the leadership style in influencing feed forward learning flows. It addresses a realistic case study with focus on the role of managers for control of multilevel organisational learning. To this end a second-order adaptive self-modeling network model is introduced and an example simulation for the case study is discussed. Keywords Organisational learning · Leadership style · Context-sensitive control · Computational modeling · Self-modeling networks

11.1 Introduction Organisational learning is a shared knowledge development process involving individuals, groups and the organisation. Organisational learning occurs through formation of shared mental models and common believes developed by organisational members and institutionalised for future use. Intermediary agents such as projects or teams are also involved in the process of learning (Fiol and Lyles 1985; Crossan et al. 1999; Wiewiora et al. 2019, 2020). The team level occurs through discussion and developing of shared understanding at the team level, achieved through collective G. Canbalo˘glu · J. Treur (B) Social AI Group, Department of Computer Science, Vrije Universiteit Amsterdam, Amsterdam, Netherlands e-mail: [email protected] G. Canbalo˘glu e-mail: [email protected] A. Wiewiora School of Management, QUT Business School, Queensland University of Technology, Brisbane, Australia e-mail: [email protected]

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 G. Canbalo˘glu et al. (eds.), Computational Modeling of Multilevel Organisational Learning and Its Control Using Self-modeling Network Models, Studies in Systems, Decision and Control 468, https://doi.org/10.1007/978-3-031-28735-0_11

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actions, dialogue, shared practices and mutual adjustment. Although organisational members are involved in the process of organisational learning, organisational level learning can be people-independent and exists, captured in routines and practices, even if the organisation loses some of its members. The process of organisational learning is non-linear, dynamic and context specific. It can be influenced by contextual factors such as leadership style, organisational culture or structure (Wiewiora et al. 2019). The diversity of the involved individuals and contextual factors brings an abundance of possible learning scenarios. Even in a project run by a single team, there may be multiple learning scenarios and contextual factors affecting decisions related to the organisational learning process. The multilevel and context dependent characteristic of organisational learning makes it hard to observe and analyse. Computational modeling and in particular the self-modeling network modeling approach introduced in Treur (2020) and explained in Sect. 11.3 in this chapter, offers a useful tool to comprehend and represent the complex process of organisational learning, e.g., Canbalo˘glu and Treur (2022a, b), Canbalo˘glu et al. (2022b). A detailed real-world learning scenario, explained in the in Sect. 11.2, is used to observe and analyse the process of organisational learning, with a focus on a context specific control of a leadership style. Using self-modeling networks with different context factors allows to incorporate a variety of management contexts, which enriches the possible learning scenarios, and provide better understanding of the effects of these contexts on the learning outcomes. The designed computational model is described in more detail in Sect. 11.4. Simulation results of the model follow in Sect. 11.5 with added images for a simulation scenario. A discussion part is included in Sect. 11.6 and an Appendix with full specifications in Sect. 11.7.

11.2 Multilevel Organisational Learning and Leadership In this section, it is briefly discussed how multilevel organisation learning works and by an example scenario it is illustrated how leadership style can play an important role in it.

11.2.1 Multilevel Organisational Learning Organisations operate as a system or organism of interconnected parts. Similarly, organisational learning is considered a multilevel phenomenon involving dynamic connections between individuals, teams and organisation (Kim 1993; Fiol and Lyles 1985; Crossan et al. 1999). Due to the complex and changing environment within which organisations operate, the learning constantly evolves and some learning may become obsolete. Organisational learning is a vital means of achieving strategic renewal and continuous improvement, as it allows an organisation to explore new

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possibilities as well as exploit what they have already learned (March 1991). Organisational learning is a dynamic process that occurs in feedback and feed forward directions. Feedback learning helps in exploiting existing and institutionalized knowledge, making it available for teams and individuals to utilise. Feed forward learning assists in exploring new knowledge by individuals and teams and institutionalizing this knowledge at the organisational level (Crossan et al. 1999). As such, organisations may learn from individuals and teams via feed forward learning. Institutionalised on the organisational level can subsequently be accessed and used by the teams and individuals via feedback learning. This dynamic and adaptive process is depicted in Fig. 11.1. There are number of ways by which individuals, teams and organisations learn. For example, individuals can learn by reflecting on their past experiences and observing others. Teams can learn via joint problem solving or sharing their mental models. Organisations can learn from individuals and teams by capturing learning and practices into organisational manuals, policies or templates, which are then made available for teams and individuals to utilise. Recent research has pointed to the role of leaders in influencing learning flows between individuals, teams and organisations, which is discussed in the following section. Fig. 11.1 Multilevel organisational learning: multiple levels and nested cycles (with depth 3) of interactions

ORGANIZATION

TEAMS or PROJECTS

Learning within and between individuals

INDIVIDUALS

Feedback learning

Feed forward learning

Learning within and between teams or projects

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11.2.2 The Influential Role of Leaders in Facilitating Multilevel Learning Management research found that leaders influence organisational learning (Edmondson 2002; Hannah and Lester 2009). Leaders have been described as social architects of organisational learning (Hannah and Lester 2009; Chang et al. 2021) who can either inhibit or facilitate learning flows (Wiewiora et al. 2020). For example, findings from Mazutis and Slawinski (2008) suggest that leaders facilitate feed forward learning by creating an environment for open and transparent communication. Edmondson (2002) demonstrated that those leaders who purposefully obliterate power differences and encourage input and debate promote an environment conducive to learning, whereas leaders who choose to retain their status and power tend to tighten control at the expense of learning. Such leaders provide environment in which individuals are discouraged to share ideas or be open to others. More recently, research identified the role of leaders in facilitating learning linkages between individuals, teams and organisation. A case study on multilevel learning in the context of a global project-based organisation revealed that senior leaders facilitate individual to individual and team to team (same level), as well as individual to team and individual to organisation (feed forward) learning flows (Wiewiora et al. 2020). This is because senior leaders have access to different parts of the organisation, well developed networks and a position of power to influence transfer of learning between the levels. As such, senior leaders can facilitate an environment in which individuals can exchange knowledge, bounce ideas off each other, discuss ideas and engage in joint problem solving. Furthermore, Wiewiora et al.’s (2020) research demonstrated that by using a position of influence, leaders can either restrict or promote individual ideas for organisational improvement, hence affect institutionalisation of learning. Overall, existing research found evidence that leaders and their leadership styles impact the flow of learning within organisations. Systematic literature review of mechanisms facilitating multilevel organisational learning revealed that although research begins to identify the role of leaders in facilitating learning flows, more studies are required to better understand this phenomena and dive deeper into the specific contextual factors and connections that leaders can influence to enable multilevel learning flows (Wiewiora et al. 2019).

11.2.3 The Example Scenario Used as Illustration In this section, we illustrate a real learning scenario that occurred in a projectbased setting. An experienced project manager—Tom (pseudo name) was recently employed in an established large, and highly hierarchical organisation—Alpha (pseudo name). (1) Tom brought with him to the organisation learnings and insights from his previous roles in managing projects.

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(2) During a team meeting, he shared one of his past learnings with other project managers. It was an idea to implement tollgates (approval points before proceeding to the next stage of the project that allows to review readiness and progress of the project). The organisation has not used tollgates or other processes to monitor the progress of the project. (3) The idea was well received by the team, but no call for action to implement the idea was requested by Tom’s immediate boss. This was described by one of Tom’s peers, in the following quote: It seems somehow it’s like a relationship where the woman doesn’t tell the man what to do. I mean after one month the man says why don’t we do that? Yes let’s do that. They [some leaders] are a little bit reluctant to listen, they want to do it themselves in their own way at their own pace. (4) After several months, Tom raised the idea again with a higher-level manager, who liked the idea and discussed it with others in the organisation who supported the idea and requested that tollgates is implemented as a new process to manage projects. Variables identified in this example are learning from past experiences, role of leaders to effectively transfer learning and institutionalise learning, and possibly also a resistance to learn from a novice. This example also demonstrates that leaders have a powerful role in the organisation to promote ideas and institutionalise them. In Table 11.1 further analysis of the scenario can be found in terms of the conceptual mechanisms involved and how they can be related to computational mechanisms.

11.3 The Self-modeling Network Modeling Approach Used In this section, the network-oriented modeling approach used is briefly introduced. A temporal-causal network model is characterised by; here X and Y denote nodes of the network that have activation levels that can change over time, also called states (Treur 2020): • Connectivity characteristics: Connections from a state X to a state Y and their weights ωX,Y • Aggregation characteristics: For any state Y, some combination function cY (..) defines the aggregation that is applied to the single causal impacts ωX,Y X(t) on Y from its incoming connections from states X • Timing characteristics: Each state Y has a speed factor ηY defining how fast it changes for given causal impact. The following canonical difference (or related differential) equations are used for simulation purposes; they incorporate these network characteristics ωX,Y , cY (..), ηY in a standard numerical format: Y (t + ∆t) = Y (t) + ηY [cY (ω X 1 ,Y X 1 (t), . . . , ω X k ,Y X k (t)) − Y (t)]∆t

(11.1)

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Table 11.1 Further analysis of the example scenario Scenario

Conceptual mechanisms

Computational mechanisms

(1) Tom brought with him to the organisation learnings and insights from his previous roles in managing projects

Individual learning His individual mental models based on individual learning from past experiences

Learning by observation within project teams World states with mirroring links to mental states and hebbian learning for the mental model • Team 1 without tollgates → weaker world states • Team 2 with tollgates → stronger world states • Tom decides to learn the mental model from Team 2

(2) During a team meeting, he shared one of his past learnings with other project managers. It was an idea to implement tollgates (approval points before proceeding to the next stage of the project that allows to review readiness and progress of the project). The organisation did not use tollgates or other processes to monitor the progress of the project

Feed forward learning from individual Tom to Team 3 Individual to team learning/sharing mental models based on past experiences

Controlled individual and feed forward learning from individual mental model of Tom to mental models of the other individuals in the team and to team mental model formation • Controlled decision of Tom to communicate his individual mental model to the other individuals in Team 3 • Shared mental model formation within Team 3

(3) The idea was well received by the team, but no call for action to implement the idea was requested by Tom’s immediate boss

No feed forward learning from Team 3 to the organisation Lack of approval for a novice. Organisational learning stops, due to lack of interest from the immediate leader/or reluctance to take on board insights suggested by a novice. Illustrating the influential role of leaders

Controlled feed forward learning from team to organisation • Controlled by a control state for the immediate manager’s approval • Due to the lack of this approval no feed forward learning to the organisation level takes place • This depends on the context factor that Tom is a novice in the new organisation • This also depends on the leadership style of Tom’s immediate boss. That leader chooses to retain their power to tighten control in expense of learning (continued)

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Table 11.1 (continued) Scenario

Conceptual mechanisms

Computational mechanisms

(4) After several months, Tom raised the idea again with a higher level manager, who liked the idea and discussed it with others in the organisation who supported the idea and requested that tollgates is implemented as a new process to manage projects

Feed forward learning from Team 3 to the organisation By approval from higher level manager: institutionalisation of learning illustrating the influential role of leaders

Controlled feedforward learning from team to organisation based on communication with others • Controlled by a control state for the higher maneger’s approval • This control state does not depend on being a novice • Instead it depends on feedback of some others in the organisation • This is obtained by communication channels back and forth to them • This depends on the leadership style of the higher-level manager who displayed openness and welcomed the new idea from the employee

for any state Y and where X 1 to X k are the states from which Y gets its incoming connections. The above concepts enable to design network models and their dynamics in a declarative manner, based on mathematically defined functions and relations. The available dedicated software environment described in Treur (2020, Chap. 9), includes a combination function library with currently around 70 useful basic combination functions. Some examples of combination functions that are applied here can be found in Table 11.2. Table 11.2 Examples of combination functions for aggregation available in the library Notation

Formula

Advanced logistic sum

alogisticσ,τ (V 1 , …, V k ) [

Steponce

steponceα,β (..)

Parameters 1

1+e−σ(V1 +···+Vk −τ) (1 + e−στ )

−

1 1+eστ ]

1 if time t is between α and Start time α; end time β β, else 0

Complement comp-id(V 1 , …, V k ) identity

1 − V1

Hebbian learning

V1 ∗ V2 (1 − V3 ) + μV3

hebbμ (V 1 , V 2 , V 3 )

Steepness σ > 0; excitability threshold τ

V 1 ,V 2 activation levels of the connected states; V 3 activation level of the self-model state for the connection weight; persistence factor μ

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Combination functions as shown in Table 11.2 are called basic combination functions. For any network model some number m of them can be selected; they are represented in a standard format as bcf1 (..), bcf2 (..), …, bcfm (..). In principle, they use parameters π1,i,Y , π2,i,Y such as the λ, σ, and τ in Table 11.2. Including these parameters, the standard format used for basic combination functions is (with V 1 , …, V k the single causal impacts): bcf i (π1,i,Y , π2,i,Y , V1 , . . . , Vk ). For each state Y just one basic combination function can be selected, but also a number of them can be selected; this will be interpreted as a weighted average of them with combination function weights γi,Y as follows: cY (π1,1,Y , π2,1,Y , . . . , π1,m,Y , π2,m,Y , V1 , . . . , Vk ) =

γ1,Y bcf 1 (π1,1,Y , π2,1,Y , V1 , . . . , Vk ) + · · · + γm,Y bcf m (π1,m,Y , π2,m,Y , V1 , . . . , Vk ) γ1,Y + · · · + γm,Y

(11.2)

Selecting only one of them for state Y, for example, bcf i (..), is done by putting weight γi,Y = 1 and the other weights 0. This is a convenient way to indicate combination functions for a specific network model. The function cY (..) can then just be indicated by the weight factors γi,Y and the parameters πi,j,Y , according to (11.2). Realistic network models are usually adaptive: often not only their states but also some of their network characteristics change over time. By using a self-modeling network (also called a reified network), a similar network-oriented conceptualization can also be applied to adaptive networks to obtain a declarative description using mathematically defined functions and relations for them as well; see Treur (2020). This works through the addition of new states to the network (called self-model states) which represent (adaptive) network characteristics. In the graphical 3D-format as shown in Sect. 11.4, such additional states are depicted at a next level (called selfmodel level or reification level), where the original network is at the base level. As an example, the weight ωX,Y of a connection from state X to state Y can be represented (at a next self-model level) by a self-model state named WX,Y . Similarly, all other network characteristics from ωX,Y , γi,Y , πi,j,Y , ηY can be made adaptive by including self-model states for them. For example, an adaptive speed factor ηY can be represented by a self-model state named HY , an adaptive combination function weight γi,Y can be represented by a self-model state Ci,Y . As the outcome of such a process of network reification is also a temporalcausal network model itself, as has been shown in Treur (2020, Chap. 10), this selfmodeling network construction can easily be applied iteratively to obtain multiple orders of self-models at multiple (first-order, second-order, …) self-model levels. For example, a second-order self-model may include a second-order self-model state HW X,Y representing the speed factor ηW X,Y for the dynamics of first-order self-model state WX,Y which in turn represents the adaptation of connection weight ω X,Y . Similarly, the weight ωZ,W X,Y of an incoming connection from some state Z to a first-order self-model state WX,Y can be represented by a second-order self-model state WZ,W X,Y .

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11.4 The Adaptive Computational Network Model Designed In this section the designed computational network model will be explained. Based on the analysis of the learning scenario presented in Sect. 11.2 and Table 11.1 in particular the following computational mechanisms were considered for the different phases in the example scenario. Note that teams T1 and T2 are from Tom’s previous organisation and team T3 is in his current organisation. (1) Team learning by observation for teams T1 and T2 and feedback learning from team T2 to individual A Team mental model learning for teams T1 and T2 is assumed to be based on observation of world states and mirroring them in the mental model combined with Hebbian learning. Here team T1 without tollgates shows weaker world states (lower activation levels), whereas team T2 with tollgates shows stronger world states. Based on this difference in success, A (which is Tom) makes a controlled decision to individually learn the shared team mental model from team T2 (feedback learning). The control is based on the good performance of team T2. (2) Individual and team learning from the individual mental model of A to mental models of the other individuals B and C in team T3 and to (feed forward) mental model formation by team T3 Tom makes a controlled decision to communicate his individual mental model (learnt in the past from team T2) to the other individuals B and C in team T3 (individual learning from other individuals); control is based on providing space and time for team T3 to exchange knowledge. Within this team, this is followed by shared mental model formation which makes the mental model of Tom the shared team mental model of team T3 (feed forward learning). (3) Feed forward learning from team T3 to organisation controlled by A’s immediate manager D Control is modeled by a control state related to the immediate manager D’s approval. Due to the lack of this approval no feed forward learning to the organisation level takes place. D’s non-approval depends on the context factor that Tom is a novice in the new organisation, and D’s leadership style which is based on retaining power at the expense of learning. (4) Feed forward learning from team T3 to organisation controlled by a higher manager E Control is modeled by a control state related to the higher maneger E’s approval. This control state does not depend on being a novice; instead it depends on feedback of some other individuals F and G in the organisation. This feedback is obtained by communication from E (after having received the proposal) to F and G and from F and G back to E’s state for approval. The leadership style of E also played a role. E displayed openness to ideas from others, hence he was

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more receptive welcomed the tollgate idea as a way to improve organisational processes. The introduced model makes use of mental models as a vehicle (Kim 1993; Treur and Van Ments 2022). In previous work (Canbalo˘glu et al. 2022a, 2023a), a few of the involved computational mechanisms already have been described and used, see also Chaps. 6 and 7 of this volume (Canbalo˘glu et al. 2023). In other work (Canbalo˘glu et al. 2022a) (see also Chap. 5 of this volume) some other mechanisms have been pointed out but not used yet. For example, learning by observation is only briefly described for individuals in Canbalo˘glu et al. (2022a), but in the current chapter it is actually applied in (1) at the level of teams T1 and T2. Furthermore, the mechanisms for the control decisions for Tom (a) to decide to adopt the mental model of team T2 in (1), and (b) to decide to share this mental model with the members of team T3 in (2), are new too. Moreover, an important focus of the current chapter is the control of the feed forward learning by managers in (3) and (4) above; this also is new here as that was not addressed in previous work such as Canbalo˘glu et al. (2022b, 2023). The states in the designed network model are described in Figs. 11.2 and 11.3 (base level), Figs. 11.4 and 11.5 (first-order self-model level), and Fig. 11.6 (second-order self-model level). Note that for the sake of simplicity, the model is illustrated for a relatively simple process consisting of sequentially ordered tasks a, b, c, d (without tollgates) or a, b, go_c, nogo_c, c, d (with a tollgate using an added feedback cycle from b via nogo_c to a). Within the overall network model, this example mental model can be replaced by any other example mental model. In Sects. 11.4.1–11.4.3 some more details of the network model are explained. For full specifications, see the Appendix in Sect. 11.7.

11.4.1 Team Learning by Observation for Teams T1 and T2 and Feedback Learning from T2 to Individual A In Fig. 11.7a adopted from (Canbalo˘glu et al. 2022) it is shown how internal simulation of a mental model by any individual B (triggered by context state con1 ) activates subsequently the mental model states a_B to d_B of B and these activations in turn activate Hebbian learning of their mutual connection weights. Here for the Hebbian learning (Hebb 1949), the self-model state WX,Y for the weight of the connection from X to Y, uses the combination function hebbμ (V 1 , V 2 , W ) shown in Table 11.2, last row. More specifically, this function hebbμ (V 1 , V 2 , W ) is applied to the activation values V 1 , V 2 of X and Y and the current value W of WX,Y . To this end upward (blue) connections are included in Fig. 11.7a (also a connection to WX,Y itself is assumed but usually such connections are not depicted). The (pink) downward arrow from WX,Y to Y depicts how the obtained value of WX,Y is actually used in activation of Y. Thus, the mental model is learnt by individual B. If the persistence parameter μ is 1, the learning result persists forever; if μ < 1, then forgetting takes place. For example, when μ = 0.9, per time unit 10% of the learnt result is lost.

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World states for team T1

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A’s individual mental model states based on team T2

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Nr X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17 X18 X19 X20 X21 X22 X23 X24 X25 X26 X27 X28 X29 X30 X31 X32 X33 X34 X35 X36 X37 X38 X39 X40 X41 X42 X43 X44 X45 X46 X47 X48 X49 X50 X51 X52 X53 X54

State a_WS_T1 b_WS_T1 c_WS_T1 d_WS_T1 a_WS_T2 b_WS_T2 go_c_WS_T2 nogo_c_WS_T2 c_WS_T2 d_WS_T2 a_A_T1 b_A_T1 c_A_T1 d_A_T1 a_A_T2 b_A_T2 go_c_A_T2 nogo_c_A_T2 c_A_T2 d_A_T2 a_B b_B go_c_B nogo_c_B c_B d_B a_C b_C go_c_C nogo_c_C c_C d_C a_T1 b_T1 c_T1 d_T1 a_T2 b_T2 go_c_T2 nogo_c_T2 c_T2 d_T2 a_T3 b_T3 go_c_T3 nogo_c_T3 c_T3 d_T3 a_O b_O go_c_O nogo_c_O c_O d_O

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Explanation World state for team T1 for task a World state for team T1 for task b World state for team T1 for task c World state for team T1 for task d World state for team T2 for task a World state for team T2 for task b World state for team T2 for task go_c World state for team T2 for task nogo_c World state for team T2 for task c World state for team T2 for task d Individual mental model state for person A for task a for team T1 Individual mental model state for person A for task b for team T1 Individual mental model state for person A for task c for team T1 Individual mental model state for person A for task d for team T1 Individual mental model state for person A for task a for team T2 Individual mental model state for person A for task b for team T2 Individual mental model state for person A for task go_c for team T2 Individual mental model state for person A for task nogo_c for team T2 Individual mental model state for person A for task c for team T2 Individual mental model state for person A for task d for team T2 Individual mental model state for person B for task a Individual mental model state for person B for task b Individual mental model state for person B for task go_c Individual mental model state for person B for task nogo_c Individual mental model state for person B for task c Individual mental model state for person B for task d Individual mental model state for person C for task a Individual mental model state for person C for task b Individual mental model state for person C for task go_c Individual mental model state for person C for task nogo_c Individual mental model state for person C for task c Individual mental model state for person C for task d Shared mental model state for team T1 for task a Shared mental model state for team T1 for task b Shared mental model state for team T1 for task c Shared mental model state for team T1 for task d Shared mental model state for team T2 for task a Shared mental model state for team T2 for task b Shared mental model state for team T2 for task go_c Shared mental model state for team T2 for task nogo_c Shared mental model state for team T2 for task c Shared mental model state for team T2 for task d Shared mental model state for team T2 for task a Shared mental model state for team T2 for task b Shared mental model state for team T3 for task go_c Shared mental model state for team T3 for task nogo_c Shared mental model state for team T3 for task c Shared mental model state for team T3 for task d Shared mental model state for organisation O for task a Shared mental model state for organisation O for task b Shared mental model state for organisation O for task go_c Shared mental model state for organisation O for task nogo_c Shared mental model state for organisation O for task c Shared mental model state for organisation O for task d

Fig. 11.2 Base states: world states and mental model states

For learning by observation as used as an individual learning mechanism in the current chapter, the above is applied in conjunction with mirroring links to model the observation (Van Gog et al. 2009; Rizzolatti and Sinigaglia 2008), see Fig. 11.7b. Here mirror links are the (black) links from World States a_WS to d_WS to the corresponding mental model states a_B to d_B. When the world states are activated because things are happening in the world, through these mirror links they

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Base states for manager D’s approval Base states for manager E’s approval

Context states for learning of teams T1 and T2 and for A’s control decisions Additional context states (currently not used)

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Explanation Tom is new in the organisation D hears about and considers institutionalisation proposal D approves institutionalisation E hears about and considers institutionalisation proposal F supports institutionalisation G supports institutionalisation E approves institutionalisation Context state for teams T1 and T2 mental model simulation and observational learning Context state for A to decide for individual mental model learning of the formed mental model of team T2 Context state for A to decide for communication from A’s individual mental model to persons B and C in team T3

X65 X66 X67 X68

Fig. 11.3 Base states for manager communication and context

in turn activate B’s related mental model states which in their turn activate Hebbian learning like in the case of pure internal simulation pointed out above. In the network model introduced in the current chapter, the mechanism of learning by observation as described is applied at the team level to teams T1 and T2.

11.4.2 Abstracted Overall View on the Process After the teams T1 and T2 have learned their (shared) mental models, individual A (Tom) decides to adopt the team mental model of team T2 as his own individual mental model: feedback learning. This is shown in Fig. 11.8 which gives an abstracted view of the overall process. This time, the ovals stand for groups of states: in the base plane groups of base states for one mental model and at the first-order self-model level (blue middle plane) for groups of self-model W-states for one mental model. The arrow from the first-order self-model for the shared mental model for team T2 indicated by SMM-W-T2 to the first-order self-model for the individual A’s mental model indicated by IMM-W-A-T2 depicts the adoption by A of the team mental model of team T2 as individual mental model (feedback learning). This happens (via the pink downward link) under control of second-order selfmodel state WSMM-W-T2,IMM-W-A-T2 that gives the weight of this connection from SMM-W-T2 to IMM-W-A-T2 values 0 or 1. This second-order self-model state WSMM-W-T2,IMM-W-A-T2 depends on a sufficiently high activation value (>0.6) of team T2’s world state d_WS_T2, which makes the control of the adoption decision for feedback learning context sensitive.

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Self-model states for team T1’s shared mental model

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Explanation First-order self-model state for the weight of the connection from a to b within the shared mental model of team T1 First-order self-model state for the weight of the connection from b to c within the shared mental model of team T1 First-order self-model state for the weight of the connection from c to d within the shared mental model of team T1 First-order self-model state for the weight of the connection from a to b within the shared mental model of team T2 First-order self-model state for the weight of the connection from b to go_c within the shared mental model of team T2 First-order self-model state for the weight of the connection from b to nogo_c within the shared mental model of team T2 First-order self-model state for the weight of the connection from nog_c to a within the shared mental model of team T2 First-order self-model state for the weight of the connection from go_c to c within shared mental model of team T2 First-order self-model state for the weight of the connection from c to d within the shared mental model of team T2 First-order self-model state for the weight of the connection from a to b within the individual mental model of person A based on team T2 First-order self-model state for the weight of the connection from b to c within the individual mental model of person A based on team T2 First-order self-model state for the weight of the connection from c to d within the individual mental model of person A based on team T2 First-order self-model state for the weight of the connection from a to b within the individual mental model of person A based on team T2 First-order self-model state for the weight of the connection from b to c within the individual mental model of person A based on team T2 First-order self-model state for the weight of the connection from c to d within individual mental model of person A based on team T2 First-order self-model state for the weight of the connection from a to b within the individual mental model of person B First-order self-model state for the weight of the connection from b to c within the individual mental model of person B First-order self-model state for the weight of the connection from c to d within the individual mental model of person B First-order self-model state for the weight of the connection from a to b within the individual mental model of person B First-order self-model state for the weight of the connection from b to c within the individual mental model of person B First-order self-model state for the weight of the connection from c to d within the individual mental model of person B First-order self-model state for the weight of the connection from a to b within the individual mental model of person C First-order self-model state for the weight of the connection from b to c within the individual mental model of person C First-order self-model state for the weight of the connection from c to d within the individual mental model of person C First-order self-model state for the weight of the connection from a to b within the individual mental model of person C First-order self-model state for the weight of the connection from b to c within the individual mental model of person C First-order self-model state for the weight of the connection from c to d within the individual mental model of person C

Fig. 11.4 First-order self-model states for shared mental models for teams T1 and T2 and individual mental models

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Explanation First-order self-model state for the weight of the connection from a to b within the shared mental model of team T3 First-order self-model state for the weight of the connection from b to c within the shared mental model of team T3 First-order self-model state for the weight of the connection from c to d within the shared mental model of team T3 First-order self-model state for the weight of the connection from a to b within the shared mental model of team T3 First-order self-model state for the weight of the connection from b to c within the shared mental model of team T3 First-order self-model state for the weight of the connection from c to d within the shared mental model of team T3 First-order self-model state for the weight of the connection from a to b within the shared mental model of organisation O First-order self-model state for the weight of the connection from b to c within the shared mental model of organisation O First-order self-model state for the weight of the connection from c to d within the shared mental model of organisation O First-order self-model state for the weight of the connection from a to b within the shared mental model of organisation O First-order self-model state for the weight of the connection from b to c within the shared mental model of organisation O First-order self-model state for the weight of the connection from c to d within the shared mental model of organisation O

Fig. 11.5 First-order self-model states for shared mental models for team T3 and organisation O

Second-order self-model states for control

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Explanation Second-order self-model state for the weights of the connections from the first-order self-model states of the shared mental model of team T2 to the first-order self-model states of Tom’s individual mental model based on team T2’s shared mental model Second-order self-model state for the weights of the connections from the first-order self-model states of Tom’s individual mental model based on team T2’s shared mental model to the first-order self-model states of B and C’s individual mental models Second-order self-model state for the speed factors of first-order selfmodel states of the shared mental model of organisation O

Fig. 11.6 Second-order self-model states for control of A’s individual mental model adoption and communication and of organisation O’s shared mental model formation

In the new organisation, Tom decides to communicate this individual mental model to the team members (B and C) in team T3. This is depicted in Fig. 11.8 by the arrows from IMM-W-A-T2 to IMM-W-B and IMM-W-C. This is learning for one individual from another individual. Note that also here control is used for the decision to actually do this: the two pink downward arrows from the control state WIMM-W-A-T2,IMM-W-BC at the second-order self-model level to IMM-W-B and IMMW-C. This control state WIMM-W-A-T2,IMM-W-BC is context-sensitive as it depends on a suitable time within team T3’s meetings. After that, within team T3 this model is chosen as shared mental model, depicted in Fig. 11.8 by the arrows from IMM-W-B and IMM-W-C to SMM-W-T3 (feed forward learning). Note that in the model, for the sake of simplicity no explicit control over this shared mental model formation for T3 was included. As a next step it is shown in Fig. 11.8 how this shared mental model of T3 is institutionalised and becomes shared mental model for the organisation O.

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Fig. 11.7 a Left. Learning by internal simulation: Hebbian learning during internal simulation b Right. Learning by observation: Hebbian learning after mirroring of the world states

However, for this step control is needed by an authorized manager D or E (the pink downward connection from state HSMM-W-O , which is also context-sensitive as it depends on approval by D or E. This form of context-sensitive control is described in more detail in Sect. 11.4.3 and Fig. 11.9.

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WIMM-W-A-T2,IMM-W-BC HSMM-W-O

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Fig. 11.8 Abstracted view on the connectivity of the first- and second-order self-model of the mental models: SMM = Shared Mental Model, IMM = Individual Mental Model, S = States of mental model, W = Connection Weights of mental model, T1 and T2 = teams from previous organisation, T3 = team in current organisation, A = Tom, B and C = team members in T3, O = organisation

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Fig. 11.9 Network for approval of institutionalisation and the context-sensitive control over it

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11.4.3 Context-Sensitive Control of Institutionalisation of the Shared Mental Model by Managers D and E For the control of the process of institutionalisation some context factors are crucial: approval from an authorized manager is required; see Fig. 11.9. In this scenario two of such managers act: D and E. As can be seen in the base plane, manager D makes approval dependent on the fact that Tom is a novice because of his leadership style focused on retaining control and power. This makes that D does not approve. However, manager E whose leadership style was based on distributed power and opennes to ideas lets approval depend on whether some knowledgeable persons F and G from the organisation are in support of approval, and then follows their suggestion; see the four (two incoming and two outgoing) arrows in the base plane related to the states F supports proposal and G supports proposal. The (blue) upward links from base plane to upper plane activate the control for effectuation of the decision for approval, by making the adaptation speed of the related W-states in the middle plane nonzero. It is by these mechanisms that the control of the institutionalisation is addressed in a context-sensitive manner. For more details of the model, see the Appendix Sect. 11.7.

11.5 Simulation Results In this section, the simulation results are discussed for the example scenario described in Sect. 11.2. The included figures show the graphs for all 110 states of the model (Fig. 11.10), the graphs for the 10 world states for teams T1 and T2 in particular (Fig. 11.11), and an overview of the adaptations of the different mental models learnt with the context-sensitive control over these adaptations (Fig. 11.12). In Fig. 11.11 the world states for team T1 (the team not using tollgates) and for team T2 (the team using tollgates) are shown. The monotonically increasing curves show the world states for team T1; here the value for the last task d stays under 0.4 (the thicker red curve). The curves for the world states for team T2 show increasing pattern with initially a slight fluctuation due to the nogo-feedback loop. Although a bit slower than for team T1, in the end the last task d for T2 reaches a value above 0.6 (the thicker green curve). This value satisfies the criterion of Tom for adopting the team mental model of T2 as his own individual mental model (feedback learning). Figure 11.12 shows an overview of the adaptations of the different mental models learnt together with the context-sensitive control over these adaptations. In the different phases the following can be seen:

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d_WS_T1 nogo_c_WS_T2 b_A_T1 b_A_T2 d_A_T2 nogo_c_B b_C d_C d_T1 nogo_c_T2 b_T3 d_T3 nogo_c_O Dconsidersproposal Gsupportsproposal conTomsSharing Wa_T2,b_T2 Wgo_c_T2,c_T2 Wb_A_T2,nogo_c_A_T2 Wa_B,b_B Wgo_c_B,c_B Wb_C,nogo_c_C Wa_T3,b_T3 Wgo_c_ T3,c_ T3 Wb_O,nogo_c_O WW,TomsChoice

Fig. 11.10 Overall simulation outcomes 1.1

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40 c_WS_T1 go_c_WS_T2

Fig. 11.11 Simulation outcomes for the world states for teams T1 and T2

50 X4

d_WS_T1

11 Computational Analysis of the Role of Leadership Style for Its …

271

Adaptations of the Different Mental Models Learnt and the Context-Sensitive Control over the Adaptations 1.1 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3

0.2 0.1 0

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d_WS_T2 Fsupportsproposal conTomsChoice Wc_T1,d_T1 Wnogo_c_T2,a_T2 Wb_A_T2,go_c_A_T2 Wc_A_T2,d_A_T2 Wnogo_c_B,a_B Wb_C,go_c_C Wc_C,d_C Wnogo_c_ T3,a_ T3 Wb_O,go_c_O Wc_O,d_O

250

300 X56 X60 X64 X72 X76 X80 X84 X88 X92 X96 X100 X104 X108

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Dconsidersproposal Gsupportsproposal conTomsSharing Wa_T2,b_T2 Wgo_c_T2,c_T2 Wb_A_T2,nogo_c_A_T2 Wa_B,b_B Wgo_c_B,c_B Wb_C,nogo_c_C Wa_T3,b_T3 Wgo_c_ T3,c_ T3 Wb_O,nogo_c_O WW,TomsChoice

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550 X57 X61 X69 X73 X77 X81 X85 X89 X93 X97 X101 X105 X109

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Dapproves Eapproves Wa_T1,b_T1 Wb_T2,go_c_T2 Wc_T2,d_T2 Wnogo_c_A_T2,a_A_T2 Wb_B,go_c_B Wc_B,d_B Wnogo_c_C,a_C Wb_ T3,go_c_ T3 Wc_ T3,d_ T3 Wnogo_c_O,a_O WW,TomsSharing

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Econsidersproposal conTeamsT1andT2Learn Wb_T1,c_T1 Wb_T2,nogo_c_T2 Wa_A_T2,b_A_T2 Wgo_c_A_T2,c_A_T2 Wb_B,nogo_c_B Wa_C,b_C Wgo_c_C,c_C Wb_ T3,nogo_c_ T3 Wa_O,b_O Wgo_c_O,c_O HW,institutionalisation

Fig. 11.12 Simulation outcomes for the first-order self-model states for adaptation of the various mental models learnt, the second-order self-model states for control over the adaptation, and the context factors making this control context-sensitive

Time 0–150: Within the previous organisation, teams T1 and T2 learn their (shared) mental models (team learning by observation as discussed in Sect. 11.4.1). Time 150–200: Within the previous organisation (because of good results in the world), at this point Tom decides to adopt the shared mental model of team T2 (time 150) and actually adopts it (around time 200). This control decision is based on the good results of the outcomes of team T2 (here state X10 is used as an indicator; see the green line in Figs. 11.11 and 11.12) together with an appropriate timing for, which is a context factor modeled by state X63 (pink curve occurring at time 150); these two together activate second-order self-model state WW,TomsChoice for control of the effectuation of this decision (the orange curve starting at time 150). Time 300–400: In the new organisation, Tom decides to share (time 300) and actually shares (around time 350) his mental model of team T2 with team members B and C in team T3. This control decision is based on another context factor modeled by state X64 (pink curve occurring at time 300). This context factor activates secondorder self-model state WW,TomsSharing for control of the effectuation of this sharing decision (the blue curve starting at time 300), so that the communication actually takes place. After having received it, B and C adopt the communicated individual mental model as shared mental model for team T3 (at time 350).

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Time 400–450: The just formed shared mental model of team T3 is proposed for institutionalisation to manager D (between time 350 and 400); D does not approve it, due to Tom being a novice and due to D’s leadership style of retaining power (yet another context factor, modeled by state X55 ). Time 600–650: Tom happens to meet manager E and uses the occasion to propose the institutionalisation (this is a last context factor, modeled by state X61 ; see the curve occurring at time 600). Manager E communicates this proposal to F and G, and they give supportive feedback. Upon this E approves the proposal (state X61 , the pink curve occurring between times 600 and 625). This activates second-order self-model state HW,institutionalisation (the brown curve starting around time 615) which controls that the institutionalisation is actually realised (around time 650).

11.6 Discussion This chapter uses material from Canbalo˘glu et al. (2023b). As holds for many social processes, multilevel organisational learning suffers from the many context factors that often influence these processes and their outcomes in decisive manners. For example, an important decision for the organisation may depend on unplanned and occasionally meeting a higher manager like in the example case study addressed in this chapter. Due to such context factors, it may seem that sustainable generally valid laws or models will never be found, as any proposal often can easily be falsified by putting forward an appropriate context factor violating it. Given this perspective of highly context-sensitive processes, in particular when addressing a serious challenge like mathematical formalisation and computational modeling of multilevel organisational learning, it makes sense to explicitly address relevant context factors within such formalisations. This already has been done in particular for the specific process of aggregation of mental models in feed forward multilevel organisational learning in Canbalo˘glu and Treur (2022a, b). In the current chapter, this idea of context-sensitivity also has been addressed for other subprocesses in multilevel organisational learning. Analysing a realistic case study, context factors have been identified that play a role in a number of steps within the example multilevel organisation learning process covered by the case study. These context factors have decisive effects on different parts of the process, such as adopting mental models for proven good practices and managers with their specific world view that need to give approval to institutionalisation. In the case study, the context factors had a proper setting so that in the end instituationalisation actually took place. However, if only one of the chains of these context factors would have had a different setting, that outcome would not have been achieved. The developed computational model explicitly addresses these decisive context factors and is able to explore for any setting of them what the outcome will be, thus covering both successful and less successful outcomes.

11 Computational Analysis of the Role of Leadership Style for Its …

273

In previous work (Canbalo˘glu et al. 2022b, 2023a), a number of the computational mechanisms involved in the case study addressed here already have been introduced. However, there are a number of new ones too. For example, learning by observation is briefly pointed out for individuals in Canbalo˘glu et al. (2022a), but here it is actually applied in (1) in Table 11.2 at the level of Team 1 and Team 2 for simulation. Furthermore, the mechanisms for the control decisions for Tom (a) to decide to adopt the mental model of Team 2 in (1) and (b) to decide to share this mental model with the members of Team 3 in (2) in Table 11.2, are new too. Moreover, an important focus of the current chapter is the control of the feed forward learning by managers in (3) and (4) in Table 11.2; this indeed is new here as that was not addressed in previous work such as Canbalo˘glu et al. (2022b, 2023a). The presented findings have important implications for management studies, suggesting that computational modeling is a promising tool to predict changes in learning over time and demonstrate, via modeling, how different leadership styles can facilitate or inhibit organisational learning, hence further expand on findings by Edmondson (2002) and Wiewiora et al. (2020). Using computational tools for modeling learning scenarios has many benefits for practice. Modeling learning is a cost-effective decision making tool that helps predict learning outcomes and select best mechanisms for learning without investing time and money on implementing untested solutions. Using computational modeling enables to forecast different scenarios, which then provide basis for more informed decisions about the best possible mechanisms for implementation in the real world. For example, as demonstrated in our study, computational modeling can help organisations make more informed decisions on the most suitable leadership styles that will promote organisational learning. In doing so, organisations can invest in leadership training to achieve greater learning outcomes.

11.7 Appendix: Role Matrices Specification In this section, the different role matrices are shown that provide a full specification of the network characteristics defining the adaptive network model in a standardised table format. Here in each role matrix, each state has its row where it is listed which are the impacts on it from that role. Role matrices for connectivity characteristics The connectivity characteristics are specified by role matrices mb and mcw shown in Figs. 11.13 and 11.14. Role matrix mb lists the other states (at the same or lower level) from which the state gets its incoming connections, whereas in role matrix mcw the connection weights are listed for these connections.

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G. Canbalo˘glu et al. mb base connectivity: base states World states for team T1 World states for team T2

A’s individual mental model states based on team T1

A’s individual mental model states based on team T2

B’s individual mental model states

C’s individual mental model states

Team T1’s shared mental model states

Team T2’s shared mental model states

Team T3’s shared mental model states

nr

state

X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17 X18 X19 X20 X21 X22 X23 X24 X25 X26 X27 X28 X29 X30 X31 X32 X33 X34 X35 X36 X37 X38 X39 X40 X41 X42 X43 X44 X45 X46 X47 X48

a_WS_T1 b_WS_T1 c_WS_T1 d_WS_T1 a_WS_T2 b_WS_T2 go_c_WS_T2 nogo_c_WS_T2 c_WS_T2 d_WS_T2 a_A_T1 b_A_T1 c_A_T1 d_A_T1 a_A_T2 b_A_T2 go_c_A_T2 nogo_c_A_T2 c_A_T2 d_A_T2 a_B b_B go_c_B nogo_c_B c_B d_B a_C b_C go_c_C nogo_c_C c_C d_C a_T1 b_T1 c_T1 d_T1 a_T2 b_T2 go_c_T2 nogo_c_T2 c_T2 d_T2 a_T3 b_T3 go_c_T3 nogo_c_T3 c_T3 d_T3

1 X62 X1 X2 X3 X62 X5 X6 X7 X7 X9 X62 X11 X12 X13 X62 X15 X16 X17 X17 X19 X21 X21 X22 X23 X23 X25 X27 X27 X28 X29 X29 X31 X62 X33 X34 X35 X62 X37 X38 X38 X39 X41 X43 X43 X44 X45 X45 X47

2

3

X8

X18

X24

X30

X1 X2 X3 X4 X40 X6 X7 X8 X9 X10 X46

X5

Fig. 11.13 Role matrices for the connectivity: mb for base connectivity for the base states

11 Computational Analysis of the Role of Leadership Style for Its …

Organisation O’s shared mental model states

X49 X50 X51 X52 X53 X54

a_O b_O go_c_O nogo_c_O c_O d_O

X49 X49 X50 X51 X51 X53

X55 X56 X57 X58 X59 X60 X61 X62 X63 X64 X65 X66 X67 X68

Anovice Dconsidersproposal Dapproves Econsidersproposal Fsupportsproposal Gsupportsproposal Eapproves conTeamsT1andT2Learn conTomsChoice conTomsSharing

X55 X48 X56 X58 X58 X58 X59

275 X52

X55

X60

X62 X63 X64

Fig. 11.13 (continued)

Nonadaptive connection weights are indicated in mcw (in Figs. 11.15 and 11.16) by a number (in a green shaded cell), but adaptive connection weights are indicated by a reference to the (self-model) state representing the adaptive value (in a peach-red shaded cell). This can be seen at the base level for states X12 to X54 (with self-model states X69 to X107 ). Similarly, at the first-order self-model level (see Fig. A4) this can be seen for states X78 to X95 (with self-model states X108 and X109 ). Role matrices for aggregation characteristics The network characteristics for aggregation are defined by the selection of combination functions from the library and values for their parameters. In role matrix mcfw it is specified by weights which state uses which combination function; see Figs. 11.17 and 11.18. In role matrix mcfp (see Figs. 11.19 and 11.20) it is indicated what the parameter values are for the chosen combination functions. Role matrices for timing characteristics In Figs. 11.21 and 11.22, the role matrix ms for speed factors is shown, which lists all speed factors. Next to it, the list of initial values can be found. Also for ms some entries are adaptive: the speed factors of X102 to X107 are represented by (second-order) self-model state X110 .

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G. Canbalo˘glu et al. mb base connectivy: first- and second-order self-model states Self-model states for team T1’s shared mental model

Self-model states for team T2’s shared mental model

Self-model states for A’s individual mental model based on team T2

Self-model states for B’s individual mental model

Self-model states for C’s individual mental model

Self-model states for team T3’s shared mental model

Self-model states for organisation O’s shared mental model

Second-order selfmodel states for control

nr

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X69 X70 X71 X72 X73 X74 X75 X76 X77

Wa_T1,b_T1 Wb_T1,c_T1 Wc_T1,d_T1 Wa_T2,b_T2 Wb_T2,go_c_T2 Wb_T2,nogo_c_T2 Wnogo_c_T2,a_T2 Wgo_c_T2,c_T2 Wc_T2,d_T2

X78 X79 X80 X81 X82 X83 X84 X85 X86 X87 X88 X89 X90 X91 X92 X93 X94 X95 X96 X97 X98 X99 X100 X101 X102 X103 X104 X105 X106 X107

Wa_A_T2,b_A_T2 Wb_A_T2,go_c_A_T2 Wb_A_T2,nogo_c_A_T2 Wnogo_c_A_T2,a_A_T2 Wgo_c_A_T2,c_A_T2 Wc_A_T2,d_A_T2 Wa_B,b_B Wb_B,go_c_B Wb_B,nogo_c_B Wnogo_c_B,a_B Wgo_c_B,c_B Wc_B,d_B Wa_C,b_C Wb_C,go_c_C Wb_C,nogo_c_C Wnogo_c_C,a_C Wgo_c_C,c_C Wc_C,d_C Wa_T3,b_T3 Wb_ T3,go_c_ T3 Wb_ T3,nogo_c_ T3 Wnogo_c_ T3,a_ T3 Wgo_c_ T3,c_ T3 Wc_ T3,d_ T3 Wa_O,b_O Wb_O,go_c_O Wb_O,nogo_c_O Wnogo_c_O,a_O Wgo_c_O,c_O Wc_O,d_O

X108 X109 X110

WW,TomsChoice WW,TomsSharing HW,institutionalisation

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2

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X33 X34 X35 X37 X38 X39 X40 X39 X41 X72 X73 X74 X75 X76 X77 X78 X79 X80 X81 X82 X83 X78 X79 X80 X81 X82 X83 X84 X85 X86 X87 X88 X89 X96 X97 X98 X99 X100 X101

X34 X35 X36 X38 X39 X40 X37 X41 X42 X78 X79 X80 X81 X82 X83 X84 X85 X86 X87 X88 X89 X90 X91 X92 X93 X94 X95 X90 X91 X92 X93 X94 X95

X69 X70 X71 X72 X73 X74 X75 X76 X77

X10

X63

X64 X57

X61

Fig. 11.14 Role matrices for the connectivity: mb for base connectivity for the first- and secondorder self-model states

11 Computational Analysis of the Role of Leadership Style for Its … mcw connection weights: base states World states for team T1

World states for team T2

A’s individual mental model states based on team T1

A’s individual mental model states based on team T2

B’s individual mental model states

C’s individual mental model states

Team T1’s shared mental model states

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X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17 X18 X19 X20 X21 X22 X23 X24 X25 X26 X27 X28 X29 X30 X31 X32 X33 X34 X35 X36 X37 X38 X39 X40 X41 X42

a_WS_T1 b_WS_T1 c_WS_T1 d_WS_T1 a_WS_T2 b_WS_T2 go_c_WS_T2 nogo_c_WS_T2 c_WS_T2 d_WS_T2 a_A_T1 b_A_T1 c_A_T1 d_A_T1 a_A_T2 b_A_T2 go_c_A_T2 nogo_c_A_T2 c_A_T2 d_A_T2 a_B b_B go_c_B nogo_c_B c_B d_B a_C b_C go_c_C nogo_c_C c_C d_C a_T1 b_T1 c_T1 d_T1 a_T2 b_T2 go_c_T2 nogo_c_T2 c_T2 d_T2

1 1 1 1 1 1 1 1 1 1 1 1 X69 X70 X71 1 X78 X79 X80 X82 X83 1 X84 X85 X86 X88 X89 1 X90 X91 X92 X94 X95 1 X69 X70 X71 1 X72 X73 X74 X76 X77

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X81

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1 1 1 1 1 1 1 1 1 1

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Fig. 11.15 Role matrices for the connectivity: mcw for connection weights for the base states

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Team T3’s shared mental model states

Organisation O’s shared mental model states

X43 X44 X45 X46 X47 X48 X49 X50 X51 X52 X53 X54

a_T3 b_T3 go_c_T3 nogo_c_T3 c_T3 d_T3 a_O b_O go_c_O nogo_c_O c_O d_O

1 X96 X97 X98 X100 X101 1 X102 X103 X104 X106 X107 1 1 1 1 1 1 1

X99

X55 X56 X57 X58 X59 X60 X61 X62 X63 X64 X65 X66 X67 X68

Anovice Dconsidersproposal Dapproves Econsidersproposal Fsupportsproposal Gsupportsproposal Eapproves conTeamsT1andT2Learn conTomsChoice conTomsSharing

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Wa_T1,b_T1 Wb_T1,c_T1 Wc_T1,d_T1 Wa_T2,b_T2 Wb_T2,go_c_T2 Wb_T2,nogo_c_T2 Wnogo_c_T2,a_T2 Wgo_c_T2,c_T2 Wc_T2,d_T2

1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1

X78 X79 X80 X81 X82 X83

Wa_A_T2,b_A_T2 Wb_A_T2,go_c_A_T2 Wb_A_T2,nogo_c_A_T2 Wnogo_c_A_T2,a_A_T2 Wgo_c_A_T2,c_A_T2 Wc_A_T2,d_A_T2

X108 X108 X108 X108 X108 X108

1 1 1 1 1 1

X105

-1

1

1 1 1 1 1 1 1

Fig. 11.15 (continued)

mcw connection weights: first- and second-order self-model states Self-model states for team T1’s shared mental model

Self-model states for team T2’s shared mental model

Self-model states for A’s individual mental model based on team T2

Fig. 11.16 Role matrices for the connectivity: mcw for connection weights for the first- and secondorder self-model states

11 Computational Analysis of the Role of Leadership Style for Its …

Self-model states for B’s individual mental model

Self-model states for C’s individual mental model

Self-model states for team T3’s shared mental model

Self-model states for organisation O’s shared mental model

Second-order selfmodel states for control

X84 X85 X86 X87 X88 X89 X90 X91 X92 X93 X94 X95 X96 X97 X98 X99 X100 X101 X102 X103 X104 X105 X106 X107

Wa_B,b_B Wb_B,go_c_B Wb_B,nogo_c_B Wnogo_c_B,a_B Wgo_c_B,c_B Wc_B,d_B Wa_C,b_C Wb_C,go_c_C Wb_C,nogo_c_C Wnogo_c_C,a_C Wgo_c_C,c_C Wc_C,d_C Wa_T3,b_T3 Wb_ T3,go_c_ T3 Wb_ T3,nogo_c_ T3 Wnogo_c_ T3,a_ T3 Wgo_c_ T3,c_ T3 Wc_ T3,d_ T3 Wa_O,b_O Wb_O,go_c_O Wb_O,nogo_c_O Wnogo_c_O,a_O Wgo_c_O,c_O Wc_O,d_O

X108 X109 X110

WW,TomsChoice WW,TomsSharing HW,institutionalisation

X109 X109 X109 X109 X109 X109 X109 X109 X109 X109 X109 X109 1 1 1 1 1 1 1 1 1 1 1 1 1

279 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1

1 1

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Fig. 11.16 (continued) mcfw combination function weights: base states World states for team T1

World states for team T2

A’s individual mental model states based on team T1

nr X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14

state a_WS_T1 b_WS_T1 c_WS_T1 d_WS_T1 a_WS_T2 b_WS_T2 go_c_WS_T2 nogo_c_WS_T2 c_WS_T2 d_WS_T2 a_A_T1 b_A_T1 c_A_T1 d_A_T1

1 2 alogistic steponce

3 hebb

4 compid

1 1 1 1 1 1 1 1 1 1 1 1 1 1

Fig. 11.17 Role matrices for the aggregation characteristics: mcfw for combination function weights for the base states

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A’s individual mental model states based on team T2

B’s individual mental model states

C’s individual mental model states

Team T1’s shared mental model states

Team T2’s shared mental model states

Team T3’s shared mental model states

Organisation O’s shared mental model states

Fig. 11.17 (continued)

X15 X16 X17 X18 X19 X20 X21 X22 X23 X24 X25 X26 X27 X28 X29 X30 X31 X32 X33 X34 X35 X36 X37 X38 X39 X40 X41 X42 X43 X44 X45 X46 X47 X48 X49 X50 X51 X52 X53 X54

a_A_T2 b_A_T2 go_c_A_T2 nogo_c_A_T2 c_A_T2 d_A_T2 a_B b_B go_c_B nogo_c_B c_B d_B a_C b_C go_c_C nogo_c_C c_C d_C a_T1 b_T1 c_T1 d_T1 a_T2 b_T2 go_c_T2 nogo_c_T2 c_T2 d_T2 a_T3 b_T3 go_c_T3 nogo_c_T3 c_T3 d_T3 a_O b_O go_c_O nogo_c_O c_O d_O

X55 X56 X57 X58 X59 X60 X61 X62 X63 X64 X65 X66 X67 X68

Anovice Dconsidersproposal Dapproves Econsidersproposal Fsupportsproposal Gsupportsproposal Eapproves conTeamsT1andT2Learn conTomsChoice conTomsSharing

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

11 Computational Analysis of the Role of Leadership Style for Its … mcfw combination function weights: first- and second-order self-model states Self-model states for team T1’s shared mental model

Self-model states for team T2’s shared mental model

Self-model states for A’s individual mental model based on team T2

Self-model states for B’s individual mental model

Self-model states for C’s individual mental model

Self-model states for team T3’s shared mental model

Self-model states for organisation O’s shared mental model

Second-order selfmodel states for control

nr

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X69 X70 X71 X72 X73 X74 X75 X76 X77

Wa_T1,b_T1 Wb_T1,c_T1 Wc_T1,d_T1 Wa_T2,b_T2 Wb_T2,go_c_T2 Wb_T2,nogo_c_T2 Wnogo_c_T2,a_T2 Wgo_c_T2,c_T2 Wc_T2,d_T2

X78 X79 X80 X81 X82 X83 X84 X85 X86 X87 X88 X89 X90 X91 X92 X93 X94 X95

Wa_A_T2,b_A_T2 Wb_A_T2,go_c_A_T2 Wb_A_T2,nogo_c_A_T2 Wnogo_c_A_T2,a_A_T2 Wgo_c_A_T2,c_A_T2 Wc_A_T2,d_A_T2 Wa_B,b_B Wb_B,go_c_B Wb_B,nogo_c_B Wnogo_c_B,a_B Wgo_c_B,c_B Wc_B,d_B Wa_C,b_C Wb_C,go_c_C Wb_C,nogo_c_C Wnogo_c_C,a_C Wgo_c_C,c_C Wc_C,d_C

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

X96 X97 X98 X99 X100 X101 X102 X103 X104 X105 X106 X107

Wa_T3,b_T3 Wb_ T3,go_c_ T3 Wb_ T3,nogo_c_ T3 Wnogo_c_ T3,a_ T3 Wgo_c_ T3,c_ T3 Wc_ T3,d_ T3

X108 X109 X110

WW,TomsChoice WW,TomsSharing HW,institutionalisation

1 1 1 1 1 1 1 1 1 1 1 1 1

Wa_O,b_O Wb_O,go_c_O Wb_O,nogo_c_O Wnogo_c_O,a_O Wgo_c_O,c_O Wc_O,d_O

1

281

2

3

4

1 1 1 1 1 1 1 1 1

1 1

Fig. 11.18 Role matrices for the aggregation characteristics: mcfw for combination function weights for the first- and second-order self-model states

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G. Canbalo˘glu et al. mcfp combination function parameters: base states World states for team T1

World states for team T2

A’s individual mental model states based on team T1

A’s individual mental model states based on team T2

B’s individual mental model states

C’s individual mental model states

Team T1’s shared mental model states

Team T2’s shared mental model states

Team T3’s shared mental model states

Organisation O’s shared mental model states

nr

state

X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17 X18 X19 X20 X21 X22 X23 X24 X25 X26 X27 X28 X29 X30 X31 X32 X33 X34 X35 X36 X37 X38 X39 X40 X41 X42 X43 X44 X45 X46 X47 X48 X49 X50 X51 X52 X53 X54

a_WS_T1 b_WS_T1 c_WS_T1 d_WS_T1 a_WS_T2 b_WS_T2 go_c_WS_T2 nogo_c_WS_T2 c_WS_T2 d_WS_T2 a_A_T1 b_A_T1 c_A_T1 d_A_T1 a_A_T2 b_A_T2 go_c_A_T2 nogo_c_A_T2 c_A_T2 d_A_T2 a_B b_B go_c_B nogo_c_B c_B d_B a_C b_C go_c_C nogo_c_C c_C d_C a_T1 b_T1 c_T1 d_T1 a_T2 b_T2 go_c_T2 nogo_c_T2 c_T2 d_T2 a_T3 b_T3 go_c_T3 nogo_c_T3 c_T3 d_T3 a_O b_O go_c_O nogo_c_O c_O d_O

X55 X56 X57 X58 X59 X60 X61 X62 X63 X64 X65 X66 X67 X68

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Fig. 11.20 Role matrices for the aggregation characteristics: mcfp for combination function parameters for the first- and second-order self-model states

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state a_WS_T1 b_WS_T1 c_WS_T1 d_WS_T1 a_WS_T2 b_WS_T2 go_c_WS_T2 nogo_c_WS_T2 c_WS_T2 d_WS_T2 a_A_T1 b_A_T1 c_A_T1 d_A_T1 a_A_T2 b_A_T2 go_c_A_T2 nogo_c_A_T2 c_A_T2 d_A_T2 a_B b_B go_c_B nogo_c_B c_B d_B a_C b_C go_c_C nogo_c_C c_C d_C a_T1 b_T1 c_T1 d_T1 a_T2 b_T2 go_c_T2 nogo_c_T2 c_T2 d_T2 a_T3 b_T3 go_c_T3 nogo_c_T3 c_T3 d_T3

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Fig. 11.21 Role matrix ms for the timing characteristics (speed factors) and initial values iv for the base states

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Fig. 11.21 (continued) ms speed factors and iv initial values: first- and second-order self-model states Self-model states for team T1’s shared mental model

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state Wa_T1,b_T1 Wb_T1,c_T1 Wc_T1,d_T1 Wa_T2,b_T2 Wb_T2,go_c_T2 Wb_T2,nogo_c_T2 Wnogo_c_T2,a_T2 Wgo_c_T2,c_T2 Wc_T2,d_T2 Wa_A_T2,b_A_T2 Wb_A_T2,go_c_A_T2 Wb_A_T2,nogo_c_A_T2 Wnogo_c_A_T2,a_A_T2 Wgo_c_A_T2,c_A_T2 Wc_A_T2,d_A_T2 Wa_B,b_B Wb_B,go_c_B Wb_B,nogo_c_B Wnogo_c_B,a_B Wgo_c_B,c_B Wc_B,d_B

0 0 0 0 0 0 0 0 0 0 0 0

Fig. 11.22 Role matrix ms for the timing characteristics (speed factors) and initial values iv for the first- and second-order self-model states

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References Canbalo˘glu, G., Treur, J.: Context-sensitive mental model aggregation in a second-order adaptive network model for organisational learning. In: Benito, R.M., Cherifi, C., Cherifi, H., Moro, E., Rocha, L.M., Sales-Pardo, M. (eds.) Complex Networks & Their Applications X. Proceedings of the Complex Networks 2021. Studies in Computational Intelligence, vol. 1015, pp 411–423. Springer Nature, Cham (2022a) Canbalo˘glu, G., Treur, J.: Using Boolean functions of context factors for adaptive mental model aggregation in organisational learning. In: Klimov, V.V., Kelley, D.J. (eds.) Biologically Inspired Cognitive Architectures 2021. BICA 2021. Studies in Computational Intelligence, vol. 1032, pp 54–68 Springer Nature, Cham (2022b). https://www.researchgate.net/publication/354402996 Canbalo˘glu, G., Treur, J., Wiewiora, A.: Computational modeling of multilevel organisational learning: from conceptual to computational mechanisms. In: Computational Intelligence, Proceedings of InCITe’22. Lecture Notes in Electrical Engineering, vol. 968, pp. 1–17. Springer Nature (2022a) Canbalo˘glu, G., Treur, J., Roelofsma, P.H.M.P.: Computational modeling of organisational learning by self-modeling networks. Cogn. Syst. Res. 73, 51–64 (2022b) Canbalo˘glu, G., Treur, J., Roelofsma, P.H.M.P.: An adaptive self-modeling network model for multilevel organisational learning. In: Proceedings of the 7th International Congress on Information and Communication Technology, ICICT’22, vol. 2. Lecture Notes in Networks and Systems, vol. 448, pp. 179–191. Springer Nature (2023a) Canbalo˘glu, G., Treur, J., Wiewiora, A.: Computational modeling of the role of leadership style for its context-sensitive control over multilevel organisational learning. In: Proceedings of the ICICT’22. Lecture Notes in Networks and Systems, vol. 447, pp. 223–239. Springer Nature (2023b) Canbalo˘glu, G., Treur, J., Wiewiora, A. (eds.): Computational Modeling of Multilevel Organisational Learning and Its Control Using Self-Modeling Network Models. Springer Nature (this volume) (2023c)

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Chang, A., Wiewiora, A., Liu, Y.: A socio-cognitive approach to leading a learning project team: a proposed model and scale development. Int. J. Project Manag. (2021) Crossan, M.M., Lane, H.W., White, R.E.: An organizational learning framework: from intuition to institution. Acad. Manag. Rev. 24, 522–537 (1999) Edmondson, A.C.: The local and variegated nature of learning in organizations: a group-level perspective. Org. Sci. 13, 128–146 (2002) Fiol, C.M., Lyles, M.A.: Organizational learning. Acad. Manag. Rev. 10, 803–813 (1985) Hannah, S.T., Lester, P.B.: A multilevel approach to building and leading learning organizations. Leadersh. Q. 20(1), 34–48 (2009) Hebb, D.O.: The Organization of Behavior: A Neuropsychological Theory. Wiley, New York (1949) Kim, D.H.: The link between individual and organizational learning. Sloan Manag. Rev. 37–50 (Fall 1993). Reprinted in: Klein, D.A. (ed.): The Strategic Management of Intellectual Capital. Routledge-Butterworth-Heinemann, Oxford (1993) Mazutis, D., Slawinski, N.: Leading organizational learning through authentic dialogue. Manag. Learn. 39(4), 437–456 (2008) Rizzolatti, G., Sinigaglia, C.: Mirrors in the Brain: How Our Minds Share Actions and Emotions. Oxford University Press (2008) Treur, J.: Network-Oriented Modeling for Adaptive Networks: Designing Higher-Order Adaptive Biological, Mental and Social Network Models. Springer Nature, Cham (2020) Treur, J., Van Ments, L. (eds.): Mental Models and Their Dynamics, Adaptation, and Control: A Self-modeling Network Modeling Approach. Springer Nature (2022) Van Gog, T., Paas, F., Marcus, N., Ayres, P., Sweller, J.: The mirror neuron system and observational learning: implications for the effectiveness of dynamic visualizations. Educ. Psychol. Rev. 21(1), 21–30 (2009) Wiewiora, A., Smidt, M., Chang, A.: The ‘how’ of multilevel learning dynamics: a systematic literature review exploring how mechanisms bridge learning between individuals, teams/projects and the organization. Eur. Manag. Rev. 16, 93–115 (2019) Wiewiora, A., Chang, A., Smidt, M.: Individual, project and organisational learning flows within a global project-based organisation: exploring what, how and who. Int. J. Project Manag. 38, 201–214 (2020)

Chapter 12

Computational Analysis of a Real-World Scenario of Organisational Learning for a Project Management Organisation Gülay Canbalo˘glu, Jan Treur, and Anna Wiewiora

Abstract This chapter describes how the recently developed self-modeling network modeling approach for multilevel organisational learning has been tested on applicability for a real-world case of a project-based organisation. The modeling approach was able to successfully address this complex case by designing a third-order adaptive network model. Doing this, as a form of further innovation three new features have been added to the modeling approach: recombination of selected high-quality mental model parts, refinement of mental model parts, and distinction between context-sensitive detailed control and global control. Keywords Project-based organisation · Project learning · Self-modeling networks · Third-order adaptive computational network model

12.1 Introduction An organisation’s ability to acquire learning from individuals and teams is important for its capability building and long-term survival. Multilevel organisational learning focuses on learning processes that connect individuals, teams and organisation, and has been an established area of research (Kim 1993; Crossan et al. 1999; Iftikhar and Wiewiora 2021; Wiewiora et al. 2019; Wiewiora et al. 2020). G. Canbalo˘glu · J. Treur (B) Social AI Group, Department of Computer Science, Vrije Universiteit Amsterdam, Amsterdam, Netherlands e-mail: [email protected] G. Canbalo˘glu e-mail: [email protected] A. Wiewiora School of Management, QUT Business School, Queensland University of Technology, Brisbane, Australia e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 G. Canbalo˘glu et al. (eds.), Computational Modeling of Multilevel Organisational Learning and Its Control Using Self-modeling Network Models, Studies in Systems, Decision and Control 468, https://doi.org/10.1007/978-3-031-28735-0_12

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Organisational learning begins with individuals. Individual learning resides in individual’s minds through their mental models, which can be described as deeply held internal images of how the world works (Senge 1991). Learning is activated when individual mental models are changed, for example during discussions, observations, negotiations or imitations of others. Often exchange of diverse individual mental models is activated with the change or adjustment of insights, which in turn results in new learning (Kim 1993). Organisational members are exposed to social networks, hence are in the position to exchange diverse mental models and create new learnings (Bogenrieder 2002). Organisational learning is created once individual mental models are shared and sufficiently spread throughout the organization (Kim 1993). Organisational learning can occur in feed-forward and feedback directions. Feed-forward learning occurs from individuals to teams and to the organisation. It can be activated by individuals sharing their mental models to create new learnings and institutionalising these learnings on the organisational level in a form of routines, processes, or guidelines. Feedback learning occurs from organisation to teams and to individuals and relates to exploiting existing and institutionalized knowledge by the teams and individuals (Crossan et al. 1999). Literature on multilevel organisational learning has been explored in management and organisational studies, and consists of mostly conceptual, exploratory and qualitative work. Only limited and recent work has begun investigating multilevel learning using computational analysis (Canbalo˘glu et al. 2022a, b, d, 2023a), see also Chaps. 5–7 and 11 of this volume (Canbalo˘glu et al. 2023b). Building on previous work on self-modeling networks and mental models (Treur 2020a, b; Treur and Van Ments 2022), recently an adaptive dynamical systems modeling approach has been developed that offers a platform for addressing multilevel organisational learning computationally (Canbalo˘glu et al. 2022a, b, d, 2023a). In the current chapter, this approach is applied to computationally analyse a real-world case for a large worldwide project-based organisation, as described in Wiewiora et al. (2020). As such, this research seeks to answer the following research question: how can computational modeling be used to capture multilevel learning in the real-world project-based learning scenario? Within the computational analysis addressed here, a number of new special features are introduced. One of these special features is that from sets of available mental models, in an informed manner the best quality mental model parts are selected and (re)combined into new mental models, which provides a kind of creative process that has some inspiration from and similarity to evolutionary recombination. Another special feature is that refinement of mental models is used to increase their quality by replacing tasks that occur in the mental model by a sequence of two (or more) simpler subtasks. Finally, yet another special feature is that detailed control and global control over the learning processes are distinguished from each other. To this end, adopting the self-modeling network approach (Treur 2020a, b), the following four different representational and computational levels are distinguished in the organisational learning processes:

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• the base level with mental states playing a role (usually describing tasks) in the considered mental models and the dynamics of these states, for example, based on internal simulation or observation • the first-order self-modeling level where states are used to explicitly represent the weights of the connections in mental models and their adaptation, recombination and refinement over time within the different learning processes • the second-order self-modeling level with states that control the learning processes in a detailed, context-sensitive manner • the third-order self-modeling level with states that control the learning processes globally Section 12.2 of this chapter provides a background knowledge on multi-level organisational learning in the context of a project-based organisation. Section 12.3 briefly summarises the self-modeling network modeling approach used in this research. Section 12.4 introduces the third-order adaptive computational network model. In Sect. 12.5 an example of a learning simulation, which demonstrates how learning is transferred between the levels, is discussed. Section 12.6 discusses results from the simulation and outlines research contribution. Section 12.7 is an appendix with a full specification of the introduced network model.

12.2 Multilevel Organisational Learning in the Context of a Project-Based Organisation 12.2.1 Mental Models Activate Organisational Learning The vast majority of organisational learning resides in individuals’ mental models, which are deeply held believes about the world. This process of organisational learning involves: (1) making explicit an individual’s mental model, and (2) providing space for individuals to exchange diverse and even conflicting mental models to create shared mental models (Kim 1993; Bogenrieder 2002). ‘As mental models are made explicit and actively shared, the base of shared meaning in an organisation expands, and the organisation’s capacity for effective coordinated action increases’ (Kim 1993, p. 48). In a parallel literature Craik (1943) noted that mental models are considered as relational structures that are learned and used for internal simulation in order to predict what happens next. Van Ments and Treur (2021) expand on these insights and describe a cognitive architecture for handling mental models. This cognitive architecture consists of three levels: (1) for dynamics of mental models by internal simulation or observation, (2) for adaptation of them, and (3) for control of the adaptation. For more details of application and computational formalisation of this cognitive architecture, see (Treur and Van Ments 2022). In this (network-oriented) formalisation, mental models are represented as subnetworks within a network with nodes for mental states and connections for their relations. Adaptation of these relations takes

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place using a (first-order) self-modeling level in the network with self-model states representing the connection weights and control of this adaptation is modeled by a second-order self-model level in the network; see Sect. 12.3 or (Treur and Van Ments 2022) for more details about this.

12.2.2 Multilevel Learning in the Context of Project-Based Organisation—A Case for Computational Simulation Project-based organisations offer a rich and complex context to demonstrate how multilevel learning occurs. Most organisations conduct at least some aspects of their work by projects and can be described as project-based. Projects are temporary endeavours, set up to create a novel product, service or process. The multidisciplinary nature of projects, in which experts from various areas come together to develop a new solution, provides a vast opportunity for learning. However, due to project temporality, these learnings are often difficult to capture (Bakker et al. 2011). This is because a project team disbands right after the project is delivered and they take valuable learnings with them. Mature project-based organisations deploy project management offices (PMOs) to assist projects in capturing learnings and transferring these learnings to the organisation or other projects (Pemsel and Wiewiora 2013). A PMO is a department or unit within on organisation that provides support to managing projects including development of project management standards, providing training and coaching to project managers (Project Management Institute 2013). For the case considered here, organisation Alpha is a large and global project-based organisation (all names have been replaced by anonymous ones). Alpha has 24 PMOs across its regions. In Alpha, members of the PMOs meet virtually on a regular basis to share learnings from their respective regions with the attempt to institutionalise that learning and improve project management practices. These formal meetings are called PMO Forums and provide opportunity for networking. The case addressed here, has been described in Wiewiora et al. (2020). Below, the example of multilevel learning involving projects and PMO is presented in sequences. Learning artefact that is being developed is a risk management practice. • In one of the PMO forums, members discussed approaches to capture and manage risks. PMO manager from USA—Roger (pseudo name) shared a risk management practice with the PMO network – This risk management practice was developed locally, by the project managers from Roger’s location. The practice was created through face to face and small team meeting amongst project managers. As such, Roger organised a meeting with the local project managers and asked them to share their individual riskmanagement practices. This way he provided project managers opportunity and space for sharing their mental models and interpreting of learning.

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– Roger then took the best parts from different solutions to create one riskmanagement process. This demonstrates evidence of initial institutionalisation of the learning practice on the local level. At present, this risk management approach is considered the best practice and allows to capture risk in a systematic and effective way. • At the PMO forum, other PMO members begun sharing risk management practices from their own locations. • At the subsequent PMO forum, PMO personnel begun drawing upon these practices and developed an improved version of the risk management practice that can be used by the entire organisation. • PMO Central took charge of this improved version and converted to a global risk management practice, which now can be used across the locations. This demonstrates evidence of institutionalisation of learning on the organisational level. This example demonstrates team level learnings: (1) informal between project managers, and (2) formal between PMO personnel at the PMO forum. It also demonstrates how the learning is institutionalised into a new practice, first on the local and later on the organisational level. In Fig. 12.1 a conceptual overview is shown to illustrate the addressed scenario. Table 12.1 provides an overview of this scenario with some interpretations in terms of organisational learning processes (Table 12.1).

Feed forward learning

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Fig. 12.1 Conceptual overview of the processes involved in the multilevel organisational learning case addressed. Here at the PMO Local level, A and B are project managers working in the local area with Roger as the PMO manager, whereas at the PMO Forum level, C and D are representatives of managers from other PMO departments

• The practice was developed locally, by the project managers from Roger’s location. The practice was created through face to face and small team meeting amongst project managers. As such, Roger organised a meeting with project managers and asked them to share their individual risk-management practices • Roger then took the best parts from different solutions to create one risk-management approach

• At the PMO forum, other PMO members begun sharing risk management practices from their own locations • At the subsequent PMO forum, PMO personnel begun drawing upon these practices and developed an improved version of the risk management practice that can be used by the entire organisation

PMO local

PMO forum

Feed forward learning by (re)combination of best mental model parts: Individual mental models of PMO Forum members → Shared mental model for PMO Forum Feedback learning: Shared PMO Forum mental model → Adjustment of mental models for PMO Forum

Feed forward learning by (re)combination of best mental model parts: Individual mental models of local team members → Shared local team mental model Feedback learning: Shared local team mental model → Adjustment of the individual mental models of members

Interpretations

PMO central • PMO Central took charge of this improved version and converted to Feed forward learning by refinement: a global risk management practice, which now can be used across Shared mental model for PMO Forum the locations → Shared mental model for organisation Feedback learning Institutionalised learning → Change of practice for organisation, team and individuals

Scenario fragments

Level

Table 12.1 Fragments of the considered case scenario with interpretations

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12.3 The Self-Modeling Network Modeling Approach Used In this section, the network-oriented modeling approach used is briefly introduced. A temporal-causal network model is characterised by; here X and Y denote nodes of the network, also called states (Treur 2020a, b): • Connectivity characteristics Connections from a state X to a state Y and their weights ωX,Y • Aggregation characteristics For any state Y, some combination function cY (..) defines the aggregation that is applied to the impacts ωX,Y X(t) on Y from its incoming connections from states X • Timing characteristics Each state Y has a speed factor ηY defining how fast it changes for given causal impact. The following canonical difference (or related differential) equations are used for simulation purposes; they incorporate these network characteristics ωX,Y , cY (..), ηY in a standard numerical format:     Y (t + t) = Y (t) + ηY cY ω X 1 ,Y X 1 (t), . . . , ω X k ,Y X k (t) − Y (t) t

(12.1)

for any state Y and where X 1 to X k are the states from which Y gets its incoming connections. The available dedicated software environment described in (Treur 2020, Chap. 9), includes a combination function library with currently around 50 useful basic combination functions. The above concepts enable to design network models and their dynamics in a declarative manner, based on mathematically defined functions and relations. The examples of combination functions that are applied in the model introduced here can be found in Table 12.2. The two combination functions as shown in Table 12.1 and available in the combination function library are called basic combination functions. For any network model some number m of them can be selected; they are represented in a standard format as bcf1 (..), bcf2 (..), …, bcfm (..). In principle, they use parameters π1,i,Y , π2,i,Y such as the λ, σ, and τ in Table 12.1. Including these parameters, the standard format used for basic combination functions is (with V 1 , …, V k the single causal impacts): bcf i (π1,i,Y , π2,i,Y , V1 , . . . , Vk ). For each state Y just one basic combination function can be selected, but also a number of them can be selected; this will be interpreted as a weighted average of them with combination function weights γi,Y as follows: cY (π1,1,Y , π2,1,Y , . . . , π1,m,Y , π2,m,Y , V1 , . . . , Vk )     γ1,Y bcf1 π1,1,Y , π2,1,Y , V1 , . . . , Vk + . . . + γm,Y bcfm π1,m,Y , π2,m,Y , V1 , . . . , Vk = γ1,Y + . . . + γm,Y

(12.2)

alogisticσ,τ (V 1 , …,V k )

steponceα,β (..)

Advanced logistic sum

Steponce

Notation − 1 1+eστ

 (1 + e−στ )

1 if time t is between α and β, else 0

1 1+e−σ(V1 +···+Vk −τ)

Formula 

Start time α; end time β

Steepness σ > 0; excitability threshold τ

Parameters

Table 12.2 Examples of combination functions for aggregation available in the library

Context states X48 -X50

All states except X48 -X50

Used for

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Selecting only one of them for state Y, for example, bcf i (..), is done by putting weight γi,Y = 1 and the other weights 0. This is a convenient way to indicate combination functions for a specific network model. The function cY (..) can then just be indicated by the weight factors γi,Y and the parameters πi,j,Y . Realistic network models are usually adaptive: often not only their states but also some of their network characteristics change over time. By using a self-modeling network (also called a reified network), a network-oriented conceptualization can also be applied to adaptive networks to obtain a declarative description using mathematically defined functions and relations for them as well; see (Treur 2020a, b). This works through the addition of new states to the network (called self-model states) which represent (adaptive) network characteristics. In the graphical 3D-format as shown in Sect. 12.4, such additional states are depicted at a next level (called self-model level or reification level), where the original network is at the base level. As an example, the weight ωX,Y of a connection from state X to state Y can be represented (at a next self-model level) by a self-model state named WX,Y ; such states are shortly called W-states. Similarly, all other network characteristics from ωX,Y , cY (..), ηY can be made adaptive by including self-model states for them. For example, an adaptive speed factor ηY can be represented by a self-model state named HY (an H-state). Such added self-model states are integrated in the network and therefore have their own incoming and outgoing connections. As an example, also connections between different W-states can be used, for example, a connection from a first-order self-model state WV,W to another first-order self-model state WX,Y . A multitude of such connections between W-states are actually used in the adaptive network model introduced in Sect. 12.4 to model how one mental model can be influenced by (or learned from) another one. As the outcome of a process of network reification is also a temporal-causal network model itself, as has been shown in (Treur 2020a, Chap. 10), this selfmodeling network construction can easily be applied iteratively to obtain multiple orders of self-models at multiple (first-order, second-order, …) self-model levels. For example, a second-order self-model may include a second-order self-model state WWV,W ,W X,Y representing the weight ωWV ,W ,W X,Y of the connection from first-order self-model state WV,W to first-order self-model state WX,Y , which in turn represent the weights ωV,W and ωX,Y of the connections from base state V to W and from base state X to Y, respectively. These types of second-order self-model states, shortly called WWW -states or higher-order W-states, are used in the introduced adaptive network model as a way to control multilevel organisational learning in a detailed manner. In the network model also third-order self-model states are used to obtain global control over the phases of the organisational learning: HWWW -states representing the speed factors of the WWW -states. This makes the introduced model a third-order adaptive network model.

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12.4 The Designed Controlled Adaptive Network Model The designed network model for the project management organisation PMO described in Sect. 12.2 is adaptive to address the different forms of multilevel organisational learning involved and in addition explicitly addresses global and detailed context-sensitive control over the different organisational learning processes. There are three different contexts with actors that play a main role: a. Roger’s own location L Roger is communicating with project managers from that location. Two examples A and B of such project managers are included in the model. Roger selects the best parts of their individual mental models to form an improved mental model by some form of recombination. This becomes a shared team mental model at the location (local feed forward learning at location L); based on this A and B improve their individual mental models (local feedback learning at location L) b. The PMO Forum F Here Roger communicates with representatives from other PMO departments. Two examples C and D of such representatives are included in the model. Roger and the other members use the best parts of their individual mental models to obtain an improved shared mental model for forum F (feed-forward learning at PMO Forum F); based on this, C and D improve their individual mental models (feedback learning at PMO Forum F) c. PMO Central P At this level of organisation the PMO personnel, by refinement adds further improvements to the shared mental model from PMO Forum F. The resulting mental model is proposed to be institutionalised as a shared mental model for the project-based organisation as a whole (feed forward learning at the organisation level). In the designed model, the mental models for the three different contexts have three different representations (indicated by namings R-L, PMO-F and PMO-P, respectively). The specific example mental models used in the model have multiple sequential branches (indicated by tasks a and b with subscripts) that can be followed in parallel as preparation for a final task c. Two types of operations on mental models have been addressed: d. Recombination Taking specific branches of different mental models and combine them to obtain another mental model; this operation is used at the local level L and in the forum F e. Refinement Refining one branch by splitting one task b into two tasks bi and bii; this operation is used by PMO Central to obtain the final proposal to be institutionalised

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To structure the process, as a form of global control the different contexts have been addressed according to three different phases: Phase 1: Local PMO Communication at Roger’s location of the individual mental models of A and B to Roger and aggregation of them by incorporating the best parts of them to obtain a shared mental model of the location (feed forward learning) and learning from this shared mental model (feedback learning). Phase 2 PMO Forum Communication at the PMO Forum F of the individual mental models of C and D and Roger, aggregation of them (feed forward learning), and learning from the resulting shared mental model (feedback learning). Phase 3 PMO Central By PMO Central personnel improving the individual mental model from forum F to obtain a proposal for institutionalisation (feed forward learning). Figure 12.2 depicts the base level of the network model. As can be seen, for each person or team a subnetwork (in total seven of them) is included that as an illustrative example represents (as discussed in Sect. 12.2) the mental model’s relational structure of the assumed mental model for a person or team. Here mental model states are depicted by nodes and the relations between these mental model states by connections. For the example, as illustration each mental model consists of an end state for task c, with a number of branches to it (indicated by tasks a and b with subscripts); these branches are also called mental model parts. In this way, from left to right, the following can be seen in Fig. 12.2: • the three mental model structures for A, B, and Roger (R-L) for Roger’s local situation: light pink nodes • the three mental model structures for C, D, and PMO Forum (PMO-F) for the forum: darker pink nodes • the mental model structure for the PMO Central personnel PMO-P: purple nodes • the three context states conph1 (light pink) for Phase 1, conph2 (darker pink) for Phase 2, and conph3 (purple) for Phase 3; these will be used as input for the global control level to initiate and control these phases Note the difference between solid arrows and dotted arrows in Fig. 12.2. The solid ones indicate connections that in the scenario used are initially known already, whereas the dotted arrows indicate connections that are learned during the process. The mental model states have activation levels that vary over time from 0 (not activated) to 1 (fully activated). Based on this, internal simulation takes place by assigning for each of the mental models activation levels 1 to the (left-hand) states for task a and then by propagating the activation to next connected states in the mental model network structure.

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In Fig. 12.3 the learning processes are addressed, thereby not yet taking into account the control of these learning processes. For each of the connections of the different mental models (depicted as arrows in Fig. 12.2), a self-model W-state is introduced that represents the weight of the connection. The W-states have activation levels between 0 and 1. Here 0 means no knowledge about this connection and 1 full knowledge; intermediate values mean having partial knowledge. The W-states provide an additional level of representation of mental models on top of that at the base level. For example, at the base level, A’s mental model (at Roger’s location) has 4 connections and the cluster of W-states for this mental model is Wa1 _A,b1 _A , Wb1 _A,c_A , Wa2 _A,b2 _A , Wb2 _A,c_A . The slightly darker shaded big ovals in the blue plane in Fig. 12.3 indicate 6 of such clusters, each belonging to one mental model. By the pink downward arrows from the blue plane to the pink plane it is specified that the values of these self-model W-states are used for activation of the related mental model states during the internal simulation processes at the base level. Within the (first-order) self-model, connections between different W-states (belonging to different mental models) are used for the organisational learning processes. These (horizontal) connections from left to right in the blue plane in a1_D a4_D

b3_B

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Fig. 12.2 The base level of the adaptive network model: mental model states involved and their internal simulation Wa1_D,b1_D

Wb1_D,c_D Wb4_PMO-P,c_PMO-P Wb4_PMO-F,c_PMO-F Wa4_PMO-P,b4_PMO-P Wa4_PMO-F,b4_PMO-F Wb3_PMO-F,c_PMO-F W bii _PMO-P,c_PMO-P 3 Wa3_R-L,b3_R-L Wb4_D,c_D Wbi3_PMO-P,bii3_PMO-P Wa4_D,b4_D Wb2_B,c_B Wb2_PMO-P,c_PMO-P Wb2_R-L,c_R-L Wa3_PMO-F,b3_PMO-F Wb2_PMO-F,c_PMO-F Wa2_R-L,b2_R-L Wa3_PMO-P,bi3_PMO-P Wa2_PMO-P,b2_PMO-P Wa2_PMO-F,b2_PMO-F Wb1_R-L,c_R-L Wb1_PMO-F,c_PMO-F Wb3_B,c_B

Wa3_B,b3_B Wa2_B,b2_B Wb2_A,c_A Wa2_A,b2_A

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Fig. 12.3 The two lower levels of the adaptive network model: the base level with the mental model states and the first-order self-model level with the corresponding W-states for these mental models to enable the learning of the mental model connections

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Fig. 12.3 are used for feed forward learning processes and the connections in the opposite direction for feedback learning processes. These connections can also be interpreted as communication or transfer channels by which the knowledge represented by the concerning (source) W-state at the starting point of the arrow is transferred to the other (destination) W-state at the end point of the arrow, thereby being aggregated with knowledge from other incoming arrows (by the logistic combination function indicated in Table 12.1). As described above, the horizontal connections between the W-states are the basis for the learning of the mental models. However, within an organisation such connections are not automatically used. Such pathways may potentially be present but can be left inactive due to different contextual circumstances, including leadership styles and related management decisions. To cover this essential aspect as well, two other selfmodeling levels were added to the network model for the control of the learning; see Fig. 12.4. Here the purple plane models detailed control decisions for the different channels between W-states. These control decisions adress the choice of mental model parts to be included in the feed forward learning processes. For example, the second-order self-model state WW1_A ,W1_R-L models the decision to let model part 1 of A be included in the mental model built locally by Roger (R-L). To this end it represents the weight of the connection (or channel) from Wa1 _A,b1 _A of A’s mental model to Wa1 _R-L,b1 _R-L of Roger’s local mental model. The blue upward connections from the blue plane to the purple plane assure make that this WW1_A ,W1_R-L is only activated if the mental model connection of A represented by Wa1 _A,b1 _A is strong and not in case of a weak connection. This creates a selection of strong mental models and lets weak mental models out of consideration within the feed forward learning process. By the downward pink arrows from the pruple plane to the blue plane these decisions are effectuated, so that the related channels between W-states are actually opened. Finally, in the top level (green) plane in Fig. 12.4, a form of overall control is modeled concerning the different phases of the addressed scenario. On this highest level there are the three HWWW -states that control the adaptation speed of the WWW states based on the considered context; here this context is modeled based on the three context states in the base level for Phase 1 to 3. The long blue upward arrows from lowest to highest level indicate how these HWWW -states adapt to a given context at hand. Once activated, they in return active the corresponding stats in the secondorder self-model level (purple plane) via their downward pink arrows (Figs. 12.5, 12.6, 12.7).

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HWW,WPMO-F

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Fig. 12.4 The overall third-order adaptive network model: base level for mental model states involved and their internal simulation (pink plane), level for learning of the mental model connections (blue plane), level for detailed control of the learning of the mental models (purple plane) and global control level for the three different phases (green plane)

12.5 Simulation of the Scenario In the example scenario discussed here, PMO Local for Roger with members A and B is active in Phase 1 from time 20 to time 60 (controlled via the third-order self-model state HWW,WR-L ). • Project manager A has a mental model with two parts 1 and 2 (branches) which together prepare for final task c: a1 → b1 → c a2 → b2 → c • Project manager B has only a mental model with one part 3 (branch) which prepares for final task c: a3 → b3 → c The states [a2 b2 c] are known states but B has no knowledge of relations yet.

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Fig. 12.5 Base level states of the introduced adaptive network model for organisational learning

Fig. 12.6 First-order self-model states of the introduced adaptive network model for organisational learning

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Fig. 12.7 Second- and third-order self-model states to control the organisational learning

Before Roger’s local actions: time 0 to 20 From time 0 to time 20 Project manager A is able to successfully use her own mental model. As can be seen in Fig. 12.8, upon a1 and a2 occurring (value 1 for both from time 0 on), both b1 and b2 from A’s mental model parts 1 and 2 start to increase to around level 0.85 (green line) and due to that c increases to a level close to 1 (lighter green line). Apparently, b1 and b2 (even while both have a level not higher than around 0.85) together provide enough preparation to get c done at a high level. For Project manager B it is different. Although for B state b3 from B’s mental model part 3 also reaches a level around 0.85 (green line), like for b1 and b2 , this only results in c reaching a level only just above 0.7 (the light brown line initially behind the blue line), as b3 does not provide enough preparation for c. Apparently, b3 at a level around 0.85 does not provide enough preparation for good performance for task c. In principle, B also knows of tasks a2 and b2 that play a role in A’s mental model, but he has no knowledge yet about their relations in this phase; therefore he does not use that mental model part 2 to supplement his mental model part 3 based on a3 and b3 .

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Fig. 12.8 Base level of the example simulation for the scenario: the base states

Roger’s local actions: time 20 to 60 For time 20 to 60, Roger develops an improved mental model for his local PMO group, based on the best parts of the mental models of the group members A and B. He interacts with A and acquires the two good mental model parts of her and adopts these two parts. This can be seen in Fig. 12.10, where the control WWW -states X91 and X92 for both parts come up just after time 20 (behind the green line). Similarly, he adopts the mental model part 3 from B, as that looks as strong as each of the mental model parts of A (the same green line). This does not happen for B’s potential mental model part 2 as for B this has no knowledge (yet). So, Roger has now obtained the following mental model: a1 → b1 → c a2 → b2 → c a3 → b3 → c This learning can be seen in Fig. 12.9 by the orange line starting just after time 20 (from A for 1 and 2 and from B for 3).

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Fig. 12.9 The adaptation level of the example simulation for the scenario: the first-order selfmodeling level W-states for the different levels of the organisation

Fig. 12.10 The control of the adaptations for the example simulation for the scenario: the secondorder self-modeling level WWW -states and third-order self-modeling level HWWW -states

Around times 25 to 30, interaction with B takes place about mental model part 2 for B: first the communication about 2 is opened (the purple line starting around 25) and next B is learning mental model part 2 (the orange line in Fig. 12.9 starting around time 30). As the interactions with A and B are bidirectional, due to that B finally also adopts the mental model part. a2 → b2 → c

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that Roger had obtained from A. Therefore, also for him now b2 gets a value around 0.85 (the dark red line in Fig. 12.8 starting around time 25 and joining the green line around time 55). Because of this additional preparation, now also c for B increases to close to 1 (the light brown line in Fig. 12.8 leaving the blue line just after time 20 and joining the green line close to 1 around time 40). The PMO Forum’s actions: time 80 to 120 At the nonlocal level of the PMO Forum, the mental model developed locally by Roger and his locals is one of the inputs, but also the mental models of Forum members C and D. This is an overview of this input: Roger: a1 → b1 → c a2 → b2 → c a3 → b3 → c Forum member C: a4 → b4 → c [a2 b2 c]

(known states without knowledge of relations yet)

Forum member D: a4 → b4 → c [a1 b1 c]

(known states without knowledge of relations yet)

In Fig. 12.9 the red line (based on context state conph2 for Phase 2) starting almost vertically at time 80 initiates that all channels from Forum members R-L, C and D to PMO-F (and back) are opened (see also Fig. 12.10). Soon after that, the W-states for the mental model parts 1 to 3 from Roger and 4 from C and D are transferred to the Forum (the multi-colour curve in Fig. 12.9 starting immediately after time 80). After that, the orange line in Fig. 12.9 starting around time 85 indicates the W-state of D for learning back mental model part 1 (previously contributed by Roger) from the forum. In Fig. 12.8 it can be seen that now D’s internal simulation becomes better. The light blue line in Fig. 12.8 indicates the level of c_D. While based on D’s initially available mental model part 4 it was at a lower level just above 0.7 in the

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period before time 85, it only becomes high (reaching a value close to 1 between 85 and 90) after D has learned additional mental model part 1 at the Forum. The PMO Personnel’s actions: time 140 to 180 After the previous phase the PMO Forum has knowledge: a1 → b1 → c a2 → b2 → c a3 → b3 → c a4 → b4 → c This is used as input for the Forum personnel; the opening of the channel from the PMO Forum to the PMO personnel is shown by the lighter blue line starting at time 140. The personnel decide to improve the model parts 1 and 3 by refining task b into two subtasks bi and bii so that the step from a to b is split into two steps: from a to bi and from bi to bii. Splitting each of the tasks b1 and b3 into two subtasks makes that c gets a better preparation and will be more successful. Due to this, the knowledge becomes. a1 → bi1 → bii1 → c a2 → b2 → c a3 → bi3 → bii3 → c a4 → b4 → c Developing this knowledge is depicted in Fig. 12.9 by the darker blue line starting just after time 140. Overall, in Fig. 12.8 it can be seen that during the process when more mental model parts are learned, the internal simulation becomes better and better. The light blue line in Fig. 12.8 indicates the level of c_D. It only becomes high after D has learned mental model part 1 in phase 2 at the Forum. Similarly, at the local level c_B only becomes high after B learned mental model part 2 from Roger (orange line in Fig. 12.8).

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How the learning control works All these learning processes take place in a controlled manner. In Fig. 12.10 the control states for this are shown. The highest-level states are the three HWWW -states that control the adaptation speed of the WWW -states based on the considered context, here modeled by Phase 1 (local level, the red block-like curve from 20 to 60) via Phase 2 (from local to Forum level, the blue block-like curve from 80 to 120) to Phase 3 (from Forum to personell level, the orange block-like curve from 140 to 180). But note that the actual activation of the WWW -states depends on the information flowing upward from the mental model parts represented by the W-states at the level below (the blue upward arrows to the WWW -states in Fig. 12.4). This means that only mental model parts that have values that are high enough will be learned. This is illustrated by the example simulation as follows. Within Phase 1, the green line starting right after time 20 indicates the WWW -states for the channels used for (feed forward) learning from A and B to Roger, whereas the purple curve starting after time 25 indicates the WWW -state for the channel for (feedback) learning from Roger to B. This is later than time 20 because first Roger had to learn that mental model part from A before B was able to learn it from Roger. The WWW -state for the channel between Roger and B for mental model part 2 was only opened when this mental model part 2 for Roger got high values, which is after time 25. Similarly, the orange curve starting immediately after time 80 indicates the WWW -states for the channels within the Forum, and the blue curve starting just after time 140 indicates the WWW -states for the channels for the modifications made by the Forum personnel.

12.6 Discussion This chapter is based on material from (Canbalo˘glu et al. 2022c). This study used computational modeling to capture multilevel learning in the context of a projectbased organisation. More specifically, the chapter described how a recently developed modeling approach (Canbalo˘glu et al. 2022a, b, d, 2023a) for multilevel organisational learning has been tested on applicability for the real-world case of a projectbased organisation described in Wiewiora et al. (2020). This study offers three useful contributions to theory and practice. First, this multidisciplinary study uniquely combines insights from management science and computational modeling disciplines to describe and test how learning is transferred from individuals to teams and to organisation, using a learning scenario from the real-world. Studies on organisational learning have recognised that learning occurs on different interacting levels (Crossan et al. 1999) and begun exploring and operationalising learning across different levels using predominantly qualitative methodologies such as interviews or case studies (e.g. Berends and Lammers 2010;

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Wiewiora et al. 2020). The field of artificial intelligence and computational modeling has only recently begun using models to describe complex and multilevel social phenomena, with recent work investigating multilevel learning using computational analysis (Canbalo˘glu et al. 2022a, b, d, 2023a). The current study, presented in this chapter, advances existing research by using computational modeling to describe complex learning processes between individuals, teams and organisation. Second, this study advances the field of computational modeling. Using a designed third-order adaptive self-modeling network model, this research was able to map a complex multilevel learning scenario. During this test, three new features have been added to the modeling approach: recombination of selected high-quality mental model parts, refinement of mental model parts, and distinction between global control and context-sensitive detailed control. This has provided further innovation to the modeling approach as compared to (Canbalo˘glu et al. 2022a, b, d, 2023a). Third, the study offers a promising contribution to practice. Computational modeling can assist organisations in making more effective decisions about structuring learning processes. As demonstrated in our scenario, changes to (the settings of) the model can predict changes to the learning outcomes. Therefore, using computational modeling enables to manipulate variables and forecast different learning scenarios, which then provide basis for more informed managerial decisions about providing best conditions for learning. Future research can utilise self-modeling network modeling approach presented in this study to map different learning scenarios. A new learning scenario can introduce further nuances and additional organisational complexities into the models. This can be done for example, by adding to the models more interactions between individuals and teams, including different leadership styles and organisational cultures, which have been found to influence learning.

12.7 Appendix: Full Specification of the Network Model by Role Matrices In Figs. 12.11, 12.12, 12.13, 12.14, 12.15, 12.16, the different role matrices are shown that provide a full specification of the network characteristics defining the adaptive network model in a standardised table format. In each role matrix, each state has its row where it is listed which are the impacts on it from that role. Role matrices for connectivity characteristics The connectivity characteristics are specified by role matrices mb (in Figs. 12.11, 12.12, 12.13) and mcw (in Figs. 12.14, 12.15, 12.16). Role matrix mb lists the other states (at the same or lower level) from which the indicated state in the left columns its incoming connections, whereas in role matrix mcw the connection weights are listed for these connections.

12 Computational Analysis of a Real-World Scenario of Organisational … mb base connectivity: base states

A’s individual mental model states

B’s individual mental model states

R-L’s individual mental model states

C’s individual mental model states

D’s individual mental model states

PMO-F’s mental model states

PMO-P’s mental model states

Context states

nr

state

X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17 X18 X19 X20 X21 X22 X23 X24 X25 X26 X27 X28 X29 X30 X31 X32 X33 X34 X35 X36 X37 X38 X39 X40 X41 X42 X43 X44 X45 X46 X47 X48 X49 X50

a1_A b1_A a2_A b2_A c_A a2_B b2_B a3_B b3_B c_B a1_R-L b1_ R-L a2_ R-L b2_ R-L a3_ R-L b3_ R-L c_ R-L a2_C b2_C a4_C b4_C c_C a1_D b1_D a4_D b4_D c_D a1_PMO-F b1_ PMO-F a2_ PMO-F b2_ PMO-F a3_ PMO-F b3_ PMO-F a4_ PMO-F b4_ PMO-F c_ PMO-F a1_PMO-P bi1_ PMO-P bii1_ PMO-P a2_ PMO-P b2_ PMO-P a3_ PMO-P bi3_ PMO-P bii3_ PMO-P a4_ PMO-P b4_ PMO-P c_ PMO-P

conph1 conph2 conph2

1 X1 X1 X3 X3 X2 X6 X6 X8 X8 X7 X11 X11 X13 X13 X15 X15 X12 X18 X18 X20 X20 X19 X23 X23 X25 X25 X24 X28 X28 X30 X30 X32 X32 X34 X34 X29 X37 X37 X38 X40 X40 X42 X42 X43 X45 X45 X39 X48 X49 X50

2

3

311 4

X4

X9

X14

X16

X21

X26

X31

X33

X35

X41

X44

X46

Fig. 12.11 Role matrix mb for the base connectivity: the base states

5

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Self-model states for B’s mental model

nr

3

4

X59 X60

X51 X52

X55

X75 X77 X78 X79

X61 X62 X63 X64

X56 X53 X54 X58

Wa2_C,b2_C Wa4_C,b4_C Wb2_C,c_C

X74 X76 X78

X65 X66 X67

Wb4_C,c_C Wa1_C,b1_C Wa4_C,b4_C Wb1_C,c_C

X80 X73 X76 X77

X68 X69 X70 X71

X72

Wb4_C,c_C

X80

X72

X73 X74 X75 X76 X77

Wa1_PMO-F,b1_PMO-F Wa2_PMO-F,b2_PMO-F Wa3_PMO-F,b3_PMO-F Wa4_PMO-F,b4_PMO-F Wb1_PMO-F,c_PMO-F

X81 X83 X84 X86 X87

X82 X74 X85 X76 X77

X73 X60 X75 X66 X62

X59 X65 X61 X70 X71

X78 X79 X80

Wb2_PMO-F,c_PMO-F Wb3_PMO-F,c_PMO-F Wb4_PMO-F,c_PMO-F

X88 X89 X90

X78 X79 X80

X63 X64 X68

X67 X85 X72

X81 X82 X83

Wa1_PMO-F,bi1_PMO-F Wbi1_PMO-F,bii1_PMO-F Wa2_PMO-F,b2_PMO-F

X81 X82 X83

X73 X73 X74

X84 X85 X86

Wa3_PMO-F,bi3_PMO-F Wbi3_PMO-F,bii3_PMO-F Wa4_PMO-F,b4_PMO-F

X84 X85 X86

X75 X75 X76

X87 X88 X89 X90

Wbii1_PMO-F,c_PMO-F Wb2_PMO-F,c_PMO-F Wbii3_PMO-F,c_PMO-F Wb4_PMO-F,c_PMO-F

X87 X88 X89 X90

X77 X78 X79 X80

X51 X52 X53 X54 X55 X56 X57 X58 X59

Self-model states for R-L’s mental model

Self-model states for C’s mental model

Self-model states for D’s mental model

Self-model states for PMO-F’s mental model

Self-model states for PMO-P’s mental model

X60 X61 X62 X63 X64 X65 X66 X67 X68 X69 X70 X71

state

1

2

Wa1_A,b1_A

X59

X51

Wa2_A,b2_A Wb1_A,c_A Wb2_A,c_A Wa2_B,b2_B

X60 X62 X63 X60

X52 X53 X54 X55

Wa3_B,b3_B Wb2_B,c_B Wb3_B,c_B

X61 X63 X64

X56 X57 X58

Wa1_R-L,b1_R-L Wa2_R-L,b2_R-L

X73 X74

Wa3_R-L,b3_R-L Wb1_R-L,c_R-L Wb2_R-L,c_R-L Wb3_R-L,c_R-L

5

X57

Fig. 12.12 Role matrix mb for the base connectivity: the first-order self-model states

X69

X82

12 Computational Analysis of a Real-World Scenario of Organisational … mb base connectivy: second- and third-order self-model states

Second-order selfmodel states for control

nr

state

1

313

2

3

4

5

X91 X92 X93 X94 X95

WW1_A,W1_R-L WW2_A,W2_R-L WW2_B,W2_R-L WW3_B,W3_R-L WW1_CD,W1_PMO-F

X51 X52 X55 X56 X69

X53 X54 X57 X58 X71

X59 X60 X60 X61 X59

X62 X63 X63 X64 X62

X96 X97 X98

WW2_CD,W2_PMO-F WW3_CD,W3_PMO-F WW4_CD,W4_PMO-F

X65 X61 X66

X67 X64 X68

X60

X63

X70

X72

X99 X100 X101 X102

X73 X74 X75 X76

X77 X78 X79 X80

X103

WW1_PMO-F,W1_PMO-P WW2_PMO-F,W2_PMO-P WW3_PMO-F,W3_PMO-P WW4_PMO-F,W4_PMO-P HWW,WR-L

X48

X104

HWW,WPMO-F

X49

X105

HWWPMO-F,WPMO-P

X50

Fig. 12.13 Role matrix mb for the base connectivity: the second- and third-order self-model states

Nonadaptive connection weights are indicated in mcw (in Figs. 12.14, 12.15, 12.16) by a number (in a green shaded cell), but adaptive connection weights are indicated by a reference to the (self-model) state representing the adaptive value (in a peach-red shaded cell). This can be seen at the base level and first-order self-modeling level for many of the states, as many connections are adaptive. Role matrices for aggregation characteristics The network characteristics for aggregation are defined by the selection of combination functions from the library and values for their parameters. In role matrix mcfw it is specified by weights which state uses which combination function; see Figs. 12.17, 12.18, 12.19. In role matrix mcfp (see Figs. 12.20, 12.21, 12.22) the parameters are specified. Role matrices for timing characteristics In Figs. 12.23, 12.24, 12.25, the role matrix ms for speed factors is shown, which lists all speed factors. Next to it, the list of initial values iv can be found. Also, for ms some entries are adaptive: the speed factors of second-order self-model states X91 to X102 are represented by (second-order) self-model state X103 to X105 (see Fig. 12.25).

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mcw connection weights: base states

A’s individual mental model states

B’s individual mental model states

R-L’s individual mental model states

C’s individual mental model states

D’s individual mental model states

PMO-F’s mental model states

PMO-P’s mental model states

Context states

nr

state

X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17 X18 X19 X20 X21 X22 X23 X24 X25 X26 X27 X28 X29 X30 X31 X32 X33 X34 X35 X36 X37 X38 X39 X40 X41 X42 X43 X44 X45 X46 X47 X48 X49 X50

a1_A b1_A a2_A b2_A c_A a2_B b2_B a3_B b3_B c_B a1_R-L b1_ R-L a2_ R-L b2_ R-L a3_ R-L b3_ R-L c_ R-L a2_C b2_C a4_C b4_C c_C a1_D b1_D a4_D b4_D c_D a1_PMO-F b1_ PMO-F a2_ PMO-F b2_ PMO-F a3_ PMO-F b3_ PMO-F a4_ PMO-F b4_ PMO-F c_ PMO-F a1_PMO-P bi1_ PMO-P bii1_ PMO-P a2_ PMO-P b2_ PMO-P a3_ PMO-P bi3_ PMO-P bii3_ PMO-P a4_ PMO-P b4_ PMO-P c_ PMO-P

conph1 conph2 conph2

1 1 X51 1 X52 X53 1 X55 1 X56 X57 1 X59 1 X60 1 X61 X62 1 X65 1 X66 X67 1 X69 1 X70 X71 1 X73 1 X74 1 X75 1 X76 X77 1 X81 X82 1 X83 1 X84 X85 1 X86 X87

2

3

4

5

X54

X58

X63

X64

X68

X72

X78

X79

X80

X88

X89

X90

1 1 1

Fig. 12.14 Role matrices for the connectivity: mcw for connection weights for the base states

12 Computational Analysis of a Real-World Scenario of Organisational … mcw connection weights: first-order self-model states Self-model states for A’s mental model

Self-model states for B’s mental model

Self-model states for R-L’s mental model

Self-model states for C’s mental model

Self-model states for D’s mental model

Self-model states for PMO-F’s mental model

Self-model states for PMO-P’s mental model

nr

state

1

2

315

3

4

X51 X52 X53 X54 X55 X56 X57 X58

Wa1_A,b1_A Wa2_A,b2_A Wb1_A,c_A Wb2_A,c_A Wa2_B,b2_B Wa3_B,b3_B Wb2_B,c_B Wb3_B,c_B

X91 X92 X91 X92 X93

1 1 1 1 1

X94 X93 X94

1 1 1

X59 X60

Wa1_R-L,b1_R-L Wa2_R-L,b2_R-L Wa3_R-L,b3_R-L Wb1_R-L,c_R-L Wb2_R-L,c_R-L Wb3_R-L,c_R-L Wa2_C,b2_C

X95 X96 X97

1 1 1

X91 X92 X94

X93

1 1 1 1 1 1 1

X91 X92 X94

X93

Wa4_C,b4_C Wb2_C,c_C Wb4_C,c_C

X95 X96 X97 X96 X98 X96 X98

Wa1_C,b1_C Wa4_C,b4_C Wb1_C,c_C Wb4_C,c_C

X95 X98 X95 X98

1 1 1 1

X73 X74

Wa1_PMO-F,b1_PMO-F Wa2_PMO-F,b2_PMO-F

X99 X100

X99 1

1 X96

X95 X96

X75 X76 X77 X78

Wa3_PMO-F,b3_PMO-F Wa4_PMO-F,b4_PMO-F Wb1_PMO-F,c_PMO-F Wb2_PMO-F,c_PMO-F

X79 X80

Wb3_PMO-F,c_PMO-F Wb4_PMO-F,c_PMO-F

X101 X102 X99 X100 X101 X102

X101 1 1 1 1 1

1 X98 X95 X96 X97 X98

X97 X98 X95 X96 X101 X98

X81 X82 X83 X84 X85 X86 X87

Wa1_PMO-F,bi1_PMO-F Wbi1_PMO-F,bii1_PMO-F Wa2_PMO-F,b2_PMO-F Wa3_PMO-F,bi3_PMO-F Wbi3_PMO-F,bii3_PMO-F Wa4_PMO-F,b4_PMO-F Wbii1_PMO-F,c_PMO-F

1 1 1

X99 X99 X100

1 1 1 1

X101 X101 X102 X99

X88 X89 X90

Wb2_PMO-F,c_PMO-F Wbii3_PMO-F,c_PMO-F Wb4_PMO-F,c_PMO-F

1 1 1

X100 X101 X102

X61 X62 X63 X64 X65 X66 X67 X68 X69 X70 X71 X72

5

X95

X99

Fig. 12.15 Role matrices for the connectivity: mcw for connection weights for the first-order self-model states

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mcw connection weights: second- and third-order self-model states

Second-order selfmodel states for control

nr

state

1

2

3

4

5

X91 X92 X93 X94 X95 X96

WW1_A,W1_R-L WW2_A,W2_R-L WW2_B,W2_R-L WW3_B,W3_R-L WW1_CD,W1_PMO-F WW2_CD,W2_PMO-F

1 1 1 1 1 1

1 1 1 1 1 1

1 1 1 1 1 1

1 1 1 1 1 1

X97 X98 X99

WW3_CD,W3_PMO-F WW4_CD,W4_PMO-F WW1_PMO-F,W1_PMO-P

1 1 1

1 1 1

1

1

X100 X101 X102 X103

WW2_PMO-F,W2_PMO-P WW3_PMO-F,W3_PMO-P WW4_PMO-F,W4_PMO-P HWW,WR-L

1 1 1

1 1 1

1

X104

HWW,WPMO-F

1

X105

HWWPMO-F,WPMO-P

1

Fig. 12.16 Role matrices for the connectivity: mcw for connection weights for the second- and third-order self-model states mcfw combination function weights: base states

A’s individual mental model states

B’s individual mental model states

R-L’s individual mental model states

C’s individual mental model states

nr

state

X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17 X18 X19 X20 X21 X22

a1_A b1_A a2_A b2_A c_A a2_B b2_B a3_B b3_B c_B a1_R-L b1_ R-L a2_ R-L b2_ R-L a3_ R-L b3_ R-L c_ R-L a2_C b2_C a4_C b4_C c_C

1 steponce

2 alogistic 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Fig. 12.17 Role matrices for the aggregation: mcfw for combination function weights for the base states

12 Computational Analysis of a Real-World Scenario of Organisational …

D’s individual mental model states

PMO-F’s mental model states

PMO-P’s mental model states

Context states

X23 X24 X25 X26 X27 X28 X29 X30 X31 X32 X33 X34 X35 X36 X37 X38 X39 X40 X41 X42 X43 X44 X45 X46 X47 X48 X49 X50

a1_D b1_D a4_D b4_D c_D a1_PMO-F b1_ PMO-F a2_ PMO-F b2_ PMO-F a3_ PMO-F b3_ PMO-F a4_ PMO-F b4_ PMO-F c_ PMO-F a1_PMO-P bi1_ PMO-P bii1_ PMO-P a2_ PMO-P b2_ PMO-P a3_ PMO-P bi3_ PMO-P bii3_ PMO-P a4_ PMO-P b4_ PMO-P c_ PMO-P

conph1 conph2 conph2

317 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1

Fig. 12.17 (continued) mcfw combination function weights: firstorder self-model states Self-model states for A’s mental model

Self-model states for B’s mental model

nr X51 X52 X53 X54 X55 X56 X57 X58 X59 X60

Self-model states for R-L’s mental model

Self-model states for C’s mental model

X61 X62 X63 X64 X65 X66 X67 X68

state

1 steponce

2 alogistic

Wa1_A,b1_A Wa2_A,b2_A Wb1_A,c_A Wb2_A,c_A Wa2_B,b2_B Wa3_B,b3_B Wb2_B,c_B Wb3_B,c_B

1 1 1 1 1

Wa1_R-L,b1_R-L Wa2_R-L,b2_R-L Wa3_R-L,b3_R-L

1 1 1 1 1 1 1 1 1 1

Wb1_R-L,c_R-L Wb2_R-L,c_R-L Wb3_R-L,c_R-L Wa2_C,b2_C Wa4_C,b4_C Wb2_C,c_C Wb4_C,c_C

1 1 1

Fig. 12.18 Role matrices for the aggregation: mcfw for combination function weights for the first-order self-model states

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Self-model states for D’s mental model

Self-model states for PMO-F’s mental model

Self-model states for PMO-P’s mental model

X69 X70 X71 X72

Wa1_C,b1_C Wa4_C,b4_C Wb1_C,c_C Wb4_C,c_C

1 1 1 1

X73 X74

Wa1_PMO-F,b1_PMO-F Wa2_PMO-F,b2_PMO-F

1 1

X75 X76 X77 X78 X79 X80

Wa3_PMO-F,b3_PMO-F Wa4_PMO-F,b4_PMO-F Wb1_PMO-F,c_PMO-F Wb2_PMO-F,c_PMO-F Wb3_PMO-F,c_PMO-F Wb4_PMO-F,c_PMO-F

1 1 1 1 1 1

X81 X82 X83 X84

Wa1_PMO-F,bi1_PMO-F Wbi1_PMO-F,bii1_PMO-F Wa2_PMO-F,b2_PMO-F Wa3_PMO-F,bi3_PMO-F

1 1 1

X85 X86 X87 X88 X89 X90

Wbi3_PMO-F,bii3_PMO-F Wa4_PMO-F,b4_PMO-F Wbii1_PMO-F,c_PMO-F Wb2_PMO-F,c_PMO-F Wbii3_PMO-F,c_PMO-F Wb4_PMO-F,c_PMO-F

1 1 1 1 1 1 1

Fig. 12.18 (continued) mcfw combination function weights: second- and third-order self-model states

Second-order selfmodel states for control

nr

state

1 steponce

2 alogistic

X91 X92 X93 X94 X95 X96

WW1_A,W1_R-L WW2_A,W2_R-L WW2_B,W2_R-L WW3_B,W3_R-L WW1_CD,W1_PMO-F WW2_CD,W2_PMO-F

X97 X98 X99

WW3_CD,W3_PMO-F WW4_CD,W4_PMO-F WW1_PMO-F,W1_PMO-P

X100 X101 X102 X103

WW2_PMO-F,W2_PMO-P WW3_PMO-F,W3_PMO-P WW4_PMO-F,W4_PMO-P HWW,WR-L

1 1 1

X104

HWW,WPMO-F

1

X105

HWWPMO-F,WPMO-P

1

1 1 1 1 1 1 1 1 1

1

Fig. 12.19 Role matrices for the aggregation: mcfw for combination function weights for the second-order and third-order self-model states

12 Computational Analysis of a Real-World Scenario of Organisational … mcfp combination function parameters: base states

A’s individual mental model states

B’s individual mental model states

R-L’s individual mental model states

C’s individual mental model states

D’s individual mental model states

PMO-F’s mental model states

PMO-P’s mental model states

Context states

nr

state

X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17 X18 X19 X20 X21 X22 X23 X24 X25 X26 X27 X28 X29 X30 X31 X32 X33 X34 X35 X36 X37 X38 X39 X40 X41 X42 X43 X44 X45 X46 X47 X48 X49 X50

a1_A b1_A a2_A b2_A c_A a2_B b2_B a3_B b3_B c_B a1_R-L b1_ R-L a2_ R-L b2_ R-L a3_ R-L b3_ R-L c_ R-L a2_C b2_C a4_C b4_C c_C a1_D b1_D a4_D b4_D c_D a1_PMO-F b1_ PMO-F a2_ PMO-F b2_ PMO-F a3_ PMO-F b3_ PMO-F a4_ PMO-F b4_ PMO-F c_ PMO-F a1_PMO-P bi1_ PMO-P bii1_ PMO-P a2_ PMO-P b2_ PMO-P a3_ PMO-P bi3_ PMO-P bii3_ PMO-P a4_ PMO-P b4_ PMO-P c_ PMO-P

conph1 conph2 conph2

319

1 steponce

2 alogistic

α

β

20 80 140

60 120 180

σ 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

τ 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

Fig. 12.20 Role matrices for aggregation characteristics: mcfp for combination function parameters for the base states

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mcfp combination function parameters: first-order self-model states

Self-model states for A’s mental model

Self-model states for B’s mental model

Self-model states for R-L’s mental model

Self-model states for C’s mental model

Self-model states for D’s mental model

Self-model states for PMO-F’s mental model

Self-model states for PMO-P’s mental model

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state

α X51 X52 X53 X54 X55 X56 X57 X58 X59 X60 X61 X62 X63 X64

Wa1_A,b1_A Wa2_A,b2_A Wb1_A,c_A Wb2_A,c_A Wa2_B,b2_B Wa3_B,b3_B Wb2_B,c_B Wb3_B,c_B Wa1_R-L,b1_R-L Wa2_R-L,b2_R-L Wa3_R-L,b3_R-L Wb1_R-L,c_R-L

X65 X66 X67 X68 X69 X70 X71 X72

Wb2_R-L,c_R-L Wb3_R-L,c_R-L Wa2_C,b2_C Wa4_C,b4_C Wb2_C,c_C Wb4_C,c_C Wa1_C,b1_C Wa4_C,b4_C Wb1_C,c_C Wb4_C,c_C

X73 X74 X75 X76 X77 X78 X79

Wa1_PMO-F,b1_PMO-F Wa2_PMO-F,b2_PMO-F Wa3_PMO-F,b3_PMO-F Wa4_PMO-F,b4_PMO-F Wb1_PMO-F,c_PMO-F Wb2_PMO-F,c_PMO-F Wb3_PMO-F,c_PMO-F

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Wa1_PMO-F,bi1_PMO-F Wbi1_PMO-F,bii1_PMO-F Wa2_PMO-F,b2_PMO-F Wa3_PMO-F,bi3_PMO-F Wbi3_PMO-F,bii3_PMO-F Wa4_PMO-F,b4_PMO-F Wbii1_PMO-F,c_PMO-F Wb2_PMO-F,c_PMO-F

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Wbii3_PMO-F,c_PMO-F Wb4_PMO-F,c_PMO-F

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20 20 20 20 20 20 20 20 20 20

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Fig. 12.21 Role matrices for aggregation characteristics: mcfp for combination function parameters for the first-order self-model states

12 Computational Analysis of a Real-World Scenario of Organisational …

mcfp combination function parameters: second- and third-order self-model states

Second-order self-model states for detailed control

Third-order self-model states for global control

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WW4_CD,W4_PMO-F WW1_PMO-F,W1_PMO-P WW2_PMO-F,W2_PMO-P WW3_PMO-F,W3_PMO-P WW4_PMO-F,W4_PMO-P HWW,WR-L

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Fig. 12.22 Role matrices for aggregation characteristics: mcfp for combination function parameters for the second- and third-order self-model states

speed factors ms and initial values iv: base states

A’s individual mental model states

B’s individual mental model states

R-L’s individual mental model states

C’s individual mental model states

D’s individual mental model states

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a1_A b1_A a2_A b2_A c_A a2_B b2_B a3_B b3_B c_B a1_R-L b1_ R-L a2_ R-L b2_ R-L a3_ R-L b3_ R-L c_ R-L a2_C b2_C a4_C b4_C c_C a1_D b1_D a4_D b4_D c_D

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0 1 0 1 1 0 1 0 1 1 0 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1

1 0 1 0 0 1 0 1 0 0 1 0 1 0 1 0 0 1 0 1 0 0 1 0 1 0 0

Fig. 12.23 Role matrix ms for the timing characteristics (speed factors) and initial values iv for the base states

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PMO-F’s mental model states

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Context states

X28 X29 X30 X31 X32 X33 X34 X35 X36 X37 X38 X39 X40 X41 X42 X43 X44 X45 X46 X47 X48 X49 X50

a1_PMO-F b1_ PMO-F a2_ PMO-F b2_ PMO-F a3_ PMO-F b3_ PMO-F a4_ PMO-F b4_ PMO-F c_ PMO-F a1_PMO-P bi1_ PMO-P bii1_ PMO-P a2_ PMO-P b2_ PMO-P a3_ PMO-P bi3_ PMO-P bii3_ PMO-P a4_ PMO-P b4_ PMO-P c_ PMO-P

conph1 conph2 conph2

0 1 0 1 0 1 0 1 1 0 1 1 0 1 0 1 1 0 1 1 2 2 2

1 0 1 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 0 0 0

Fig. 12.23 (continued) speed factors ms and initial values iv: firstorder self-model states

nr

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state Wa1_A,b1_A Wa2_A,b2_A Wb1_A,c_A Wb2_A,c_A Wa2_B,b2_B Wa3_B,b3_B Wb2_B,c_B Wb3_B,c_B Wa1_R-L,b1_R-L Wa2_R-L,b2_R-L Wa3_R-L,b3_R-L Wb1_R-L,c_R-L Wb2_R-L,c_R-L Wb3_R-L,c_R-L Wa2_C,b2_C Wa4_C,b4_C Wb2_C,c_C Wb4_C,c_C Wa1_C,b1_C Wa4_C,b4_C Wb1_C,c_C Wb4_C,c_C

ms

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0 0 0

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0 0 0 1

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0 1 0

0.2 0.2 0.2

1 0 1

Fig. 12.24 Role matrix ms for the timing characteristics (speed factors) and initial values iv for the first-order self-model states

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Self-model states for PMO-F’s mental model

X73 X74 X75 X76 X77 X78 X79 X80

Wa1_PMO-F,b1_PMO-F Wa2_PMO-F,b2_PMO-F Wa3_PMO-F,b3_PMO-F Wa4_PMO-F,b4_PMO-F Wb1_PMO-F,c_PMO-F Wb2_PMO-F,c_PMO-F Wb3_PMO-F,c_PMO-F Wb4_PMO-F,c_PMO-F

0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

0 0 0 0 0 0 0 0

Self-model states for PMO-P’s mental model

X81 X82 X83 X84 X85 X86 X87 X88 X89 X90

Wa1_PMO-F,bi1_PMO-F Wbi1_PMO-F,bii1_PMO-F Wa2_PMO-F,b2_PMO-F Wa3_PMO-F,bi3_PMO-F Wbi3_PMO-F,bii3_PMO-F Wa4_PMO-F,b4_PMO-F Wbii1_PMO-F,c_PMO-F Wb2_PMO-F,c_PMO-F Wbii3_PMO-F,c_PMO-F Wb4_PMO-F,c_PMO-F

0.2 0.2 0.2 0.2 0.2

0 0 0 0 0

0.2 0.2 0.2

0 0 0

0.2 0.2

0 0

Fig. 12.24 (continued)

speed factors ms and initial values iv: second- and thirdorder self-model states

nr

Second-order self-model states for control

X91 X92 X93 X94 X95 X96 X97 X98 X99 X100 X101 X102

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ms

iv

X103 X103 X103 X103 X104 X104 X104 X104 X105 X105 X105 X105

0 0 0 0 0 0 0 0 0 0 0 0

X103

WW1_A,W1_R-L WW2_A,W2_R-L WW2_B,W2_R-L WW3_B,W3_R-L WW1_CD,W1_PMO-F WW2_CD,W2_PMO-F WW3_CD,W3_PMO-F WW4_CD,W4_PMO-F WW1_PMO-F,W1_PMO-P WW2_PMO-F,W2_PMO-P WW3_PMO-F,W3_PMO-P WW4_PMO-F,W4_PMO-P HWW,WR-L

2

0

X104

HWW,WPMO-F

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HWWPMO-F,WPMO-P

2

0

Fig. 12.25 Role matrix ms for the timing characteristics (speed factors) and initial values iv for the second- and third-order self-model states

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References Bakker, R.M., Cambré, B., Korlaar, L., Raab, I.: Managing the project learning paradox: a settheoretic approach toward project knowledge transfer. Int. J. Project Manag. 29, 494–503 (2011) Berends, H., Lammers, I.: Explaining discontinuity in organizational learning: a process analysis. Organ. Stud. 31, 1045–1068 (2010) Bogenrieder, I.: Social architecture as a prerequisite for organizational learning. Manag. Learn. 33, 197–212 (2002) Canbalo˘glu, G., Treur, J., Wiewiora, A.: Computational modeling of the role of leadership style for its context-sensitive control over multilevel organizational learning. In: Proceedings of the 7th International Congress on Information and Communication Technology, ICICT’22. Lecture Notes in Networks and Systems, vol. 447, pp. 223–239. Springer Nature Switzerland AG (2022a). https://www.researchgate.net/publication/355186556 Canbalo˘glu, G., Treur, J., Wiewiora, A.: Computational modeling of multilevel organizational learning: from conceptual to computational mechanisms. In: Proceedings InCITe’22. Lecture Notes in Electrical Engineering, vol. 968, pp. 1–17. Springer Nature Switzerland AG (2022b). https://www.researchgate.net/publication/354617515 Canbalo˘glu, G., Treur, J., Wiewiora, A.: Multilevel organisational learning in a project-based organisation: computational analysis based on a 3rd-order adaptive network model. Procedia Computer Science 213, 1–82 (2022c) Canbalo˘glu, G., Treur, J., Roelofsma, P.H.M.P.: Computational modeling of organizational learning by self-modeling networks. Cogn. Syst. Res. 73, 51–64 (2022d) Canbalo˘glu, G., Treur, J., Wiewiora, A. (eds.).: Computational Modeling of Multilevel Organizational Learning and its Control Using Self-Modeling Network Models. Springer Nature Switzerland AG (2023b). https://www.researchgate.net/publication/355582177 (this volume) Canbalo˘glu, G., Treur, J., Roelofsma, P.H.M.P.: An adaptive self-modeling network model for multilevel organisational learning. In: Proceedings of the 7th International Congress on Information and Communication Technology, ICICT’22, vol. 2. Lecture Notes in Networks and Systems, vol. 448, pp. 179–191. Springer Nature (2023a) Craik, K.J.W.: The Nature of Explanation. University Press, Cambridge, MA (1943) Crossan, M.M., Lane, H.W., White, R.E.: An organizational learning framework: from intuition to institution. Acad. Manag. Rev. 24, 522–537 (1999) Iftikhar, R., Wiewiora, A.: Learning processes and mechanisms for interorganizational projects: insights from the Islamabad-Rawalpindi metro bus project. IEEE Trans. Eng. Manage. (2021). https://doi.org/10.1109/TEM.2020.3042252 Kim, D.H.: The link between individual and organizational learning. Sloan Manag. Rev. Fall 37–50. Reprinted in: Klein, D.A. (ed.) The Strategic Management of Intellectual Capital. RoutledgeButterworth-Heinemann, Oxford (1993) Pemsel, S., Wiewiora, A.: Project management office a knowledge broker in project-based organizations. Int. J. Project Manag. 31(1), 31–42 (2013) Project Management Institute, I.: A Guide to the Project Management Body of Knowledge: (PMBOK guide), 5 edn. Pennsylvania: Project Management Institute, Inc. (2013) Senge, P.M.: The Fifth Discipline: The Art and Practice of the Learning Organization. Currency Doubleday (1990) Senge, P.M. The fifth discipline, the art and practice of the learning organization. Perform. Instr. 30, 37 (1991) Treur, J., Van Ments, L. (eds.): Mental Models and their Dynamics, Adaptation, and Control: A Self-Modeling Network Modeling Approach. Springer Nature, Cham, Switzerland (2022) Treur, J.: Network-Oriented Modeling for Adaptive Networks: Designing Higher-Order Adaptive Biological, Mental and Social Network Models. Springer Nature, Cham, Switzerland (2020a) Treur, J.: Modeling multi-order adaptive processes by self-modeling networks (keynote speech). In: Tallón-Ballesteros, A.J., Chen, C.-H. (eds.) Proceedings of the 2nd International Conference

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on Machine Learning and Intelligent Systems, MLIS’20. Frontiers in Artificial Intelligence and Applications, vol. 332, pp. 206–217. IOS Press (2020b) Van Ments, L., Treur, J.: Reflections on dynamics, adaptation and control: a cognitive architecture for mental models. Cogn. Syst. Res. 70, 1–9 (2021) Wiewiora, A., Smidt, M., Chang, A.: The ‘how’ of multilevel learning dynamics: a systematic literature review exploring how mechanisms bridge learning between individuals, teams/projects and the organization. Eur. Manag. Rev. 16, 93–115 (2019) Wiewiora, A., Chang, A., Smidt, M.: Individual, project and organizational learning flows within a global project-based organization: exploring what, how and who. Int. J. Project Manag. 38, 201–214 (2020)

Chapter 13

Computational Analysis of the Influence of Leadership and Communication on Learning Within an Organisation Debby Bouma, Gülay Canbalo˘glu, Jan Treur, and Anna Wiewiora

Abstract This research addresses the influence of leadership and communication on learning within an organisation by direct mutual interactions in dyads. This is done in combination with multilevel organisational learning as an alternative route, which includes feed forward and feedback learning. The results show that effective communication (triggered by the active team leader, and/or by natural, informal communication), leads to a faster learning process within an organisation compared to the longer route via feed forward and feedback formal organisational learning. However, this more direct form of bilateral learning in general may take more of the employee’s time, as a quadratic number of dyadic interactions in general is less efficient than a linear number of interactions needed for feed forward and feedback organisational learning. Keywords Adaptive network model · Communication · Leadership · Mental models · Organisational learning

D. Bouma · G. Canbalo˘glu · J. Treur (B) Social AI Group, Department of Computer Science, Vrije Universiteit Amsterdam, Amsterdam, Netherlands e-mail: [email protected] D. Bouma e-mail: [email protected] G. Canbalo˘glu e-mail: [email protected] J. Treur · A. Wiewiora QUT Business School, Queensland University of Technology, Brisbane, Australia e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 G. Canbalo˘glu et al. (eds.), Computational Modeling of Multilevel Organisational Learning and Its Control Using Self-modeling Network Models, Studies in Systems, Decision and Control 468, https://doi.org/10.1007/978-3-031-28735-0_13

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13.1 Introduction The concept of multilevel organisational learning (Crossan et al. 1999; Wiewiora et al. 2019) is not new, however, combining it with artificial intelligence to obtain possibilities for computer simulation has emerged only in recent years, e.g., (Canbalo˘glu et al. 2022, 2023a), see also Chaps. 5–12 in this volume (Canbalo˘glu et al. 2023b). Organisational learning is a shared knowledge development process involving individuals, groups and the organisation. It occurs through (1) the exchange and formation of shared mental models between team or projects members and (2) institutionalisation of these shared mental models on the organisational level for future use. This process is referred to feed-forward learning. Learning also occurs in the feedback direction when the institutionalised learning and the shared mental models are being transferred and used by teams and individuals. Computer simulations can be used to determine the best possible way to learn, so that an organisation can share their knowledge as quick and efficient as possible. This research explores the link between leadership, communication and learning within an organisation. This is done by simulating four scenarios, based on an active or inactive team leader, as well as high or low extent of natural communication. This chapter consists of eight sections. In the second section background information about (shared) mental models, organisational learning and different types of leadership styles are introduced. In the section thereafter, the self-modeling network modeling approach used is briefly introduced. Next, a real-life situation, addressed in this chapter will be discussed. In Sect. 13.5, the designed model is described in more detail. Example simulation results can be found in Sect. 13.6 and 13.7. Section 13.8 is a discussion. Finally, Sect. 13.9 is a section that discusses limitations as well as possible further research and Sect. 13.10 is a Appendix section with the full specification of the model in role matrices format.

13.2 Background Knowledge 13.2.1 (Shared) Mental Models Craik (1943) suggested that the human brain constructs ‘small-scale models’ of reality; this phenomenon was later referred to as mental models. Mental models can represent events and processes, spatial relations, and the operations of complex systems (Glasgow and Ram 1994; Hegarty 1992; Moray and Gopher 1999; Treur and Van Ments 2022; Van Ments and Treur 2021). They are working models of situations or processes from the world, and include information we know, as well as our beliefs (Glasgow and Ram 1994; Johnson-Laird 2001; Paoletti et al. 2019). Through a person’s mental manipulation or internal simulation, mental models are capable of understanding and explaining phenomena, and thus react appropriately (Greca and Moreira 2000). Mental models are also termed analogical representations of reality (Greca and Moreira 2000).

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When working in teams, every individual person has their own mental model. Teams learn by sharing individual mental models with each other, and then forming a shared mental model. These shared mental models, in combination with common beliefs that are institutional are very important in organisational learning (Kim 1993; Canbalo˘glu et al. 2022, 2023a).

13.2.2 Organisational Learning Humans have the ability to act in groups and through joint action. In such joint action, the group creates a set of intersubjective meanings that are expressed in their communication, either verbal or nonverbal, or through acts, or even objects. Communication includes metaphors, myths, etc. These are shared within the group. New members will initially have little to no idea of the communication within that group, but with time they learn (Cook and Yanow 2011). Groups and organisations also can trigger learning to other levels (Crossan et al. 1999). According to Levitt and March (1988), organisational learning looks at how people learn from other people and their experience; in parallel individuals simultaneously adapt their behaviour based on organisational routines and processes (Levitt and March 1988). According to Levitt and March (1988), there are three observations that form organisational learning, these are (1) organisational behaviour is based on routines, (2) actions made by organisations are often history-dependent, and lastly (3) organisations are oriented to targets. In this scenario routines include “forms, rules, procedures, conventions, strategies, and technologies” (Levitt and March 1988) constructed in organisations. Organisational learning is considered a multilevel phenomenon that involves individuals, teams and organisations and the connections between those Fiol and Lyles (1985), Crossan et al. (1999). This learning process works in feed forward and feedback directions. Feed forward learning means that organisations can learn from individuals and teams. Feedback learning refers to the utilization of already existing and institutionalized knowledge and sharing this with individuals and teams (Crossan et al. 1999; Wiewiora et al. 2019; Canbalo˘glu et al. 2022, 2023a). Features of individual memories have an influence on the organisational learning. The formation of shared mental models is usually part of (feed forward) organisational learning. Multilevel organisational learning can be depicted as shown in Fig. 13.1.

13.2.3 Leadership There is an established link between leadership and organisational learning (Senge 1990, 1994; Tushman and Nadler 1986). In 1939 psychologist Kurt Lewin and his group identified different styles of leadership. They identified three different styles; since then, more styles have been added (Lewin 1951). In Lewin’s study, children were divided into three groups with a different leadership style: (1) authoritarian, (2)

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Feed forward learning

ORGANIZATION

Learning within and between teams or projects

TEAMS or PROJECTS

Learning within and between individuals

INDIVIDUALS

Feedback learning

Fig. 13.1 Multilevel organisational learning (Canbalo˘glu et al. 2023a)

participative, and (3) delegative. Later, transformational and transactional leaderships were added to this list. For authoritarian leadership, the leader provides clear instructions of what is needed and expected. This leadership style assumes a strong leader and people who (willingly) follow this. In this style, there is a strong distinction between the leader and the rest of the group. The leaders make the decisions with little to no input from the rest. This style of leadership is often negatively presented, because it can be seen as controlling, or close-minded, and in Lewin’s research it was also found as the group where the creativity was the lowest. However, in situations where a lot of decisions need to be made quickly, or where the group needs a lot of direction, it could be beneficial. Another benefit is that this style maintains a sense of order well; see also (What Are Prominent Leadership Styles and Frameworks You Should Know? 2021). A participative leadership style involves a leader who is very involved with the group and involves other members in the decision making as well as providing guidance when needed. Lewin’s study concluded that this was the most effective leadership. The children in Lewin’s participative study group were not as productive as the children in the authoritarian group, but the inputs provided were of higher quality. While the rest of the group is involved in the decision making in this style, the leader does have the last say. The third and last style Lewin and his group came up with was the delegative leadership style. According to the scientists, this was the least productive group. There were more demands made on the leader, and the children showed little cooperation, while also not being able to work independently. While this style can work with qualified experts, it often leads roles which are not well-defined as well as a lack of motivation. According to Lewin, children in this group often lacked direction,

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blamed others for mistakes thus not accepting responsibilities, as well as making less progress and producing less work. A relatively newly distinguished leadership style is transformational leadership; in these groups, leaders inspire their followers. These leaders help both fulfil the goals of the organisation, as well as helping members reach their potential. According to research, the transformational leadership style has a positive effect on organisational learning (Noruzy et al. 2012; Radzi et al. 2013). The last, also relatively newly identified leadership style is the transactional one. This is often seen in work environments with an employer and an employee. The employee has a role of follower, in exchange for a compensation, often money. This type of leadership creates clear roles and provides supervision and direction when needed. This style of leadership can have a negative effect on creativity. These leadership styles will be addressed and compared in the different scenarios, to analyse how they affect the learning within the organisation.

13.3 Real-World Scenario For a case study used to evaluate the model, the case described by Edmondson (2002) was used. This paper looks at the role of learning within teams. This is done by observing several teams, and the collective learning process is investigated by looking at the team’s reflection, and action. The paper describes an organisation with 12 different teams, according to 5 different team types: top management team (TMT), middle management team (MMT), product development team (PDT), internal services team (IS), and production team (PT). These teams were divided into three different groups: (1) reflection and action, (2) reflection without action, and (3) neither action nor reflection. In Edmondson (2002)’s explanation of group division, different types of leadership can be recognized, and in the current chapter it is explored how organisational learning was influenced by this. To make the comparison as fair as possible, the different groups should be of the same team type. The team type of product development was chosen. This team occurs in two different ways (1 and 2) and these team types (PDT) were discussed in-depth in Edmondson’s paper. This enabled us to grasp what was going on in the team, and thus model it more realistically. In this way, the following situation was assumed: There is a team, whose job it is to promote a new product. The relevant team members in this situation are the team leader (TL), the marketing consultant (M), the designer (D), and the financial representative (F). The marketing consultant suggests billboards as a way to advertise a new product, while the designer suggests social media. For both ideas there is money needed from the financial representative. The team leader suggests that both team members talk to the financial representative. In next sections, O represents the organisation as a whole, and how this learns, and is represented to show the connections between the people, and organisation.

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13.4 The Self-modeling Network Modeling Approach Used In this section, the network-oriented modeling approach used is briefly introduced. A (temporal-causal) network model is characterised as follows; here X and Y denote nodes of the network, also called states (Treur 2020a, b): ● Connectivity characteristics Connections from a state X to a state Y and their weights ωX,Y ● Aggregation characteristics For any state Y, some combination function cY (..) defines the aggregation that is applied to the impacts ωX,Y X(t) on Y from its incoming connections from states X ● Timing characteristics Each state Y has a speed factor ηY defining how fast it changes for given causal impact. The following canonical difference (or related differential) equations are used for simulation purposes; they incorporate these network characteristics ωX,Y , cY (..), ηY in a standard numerical format: Y (t + ∆t) = Y (t) + ηY [cY (ω X 1 ,Y X 1 (t), . . . , ω X k ,Y X k (t)) − Y (t)]∆t

(13.1)

for any state Y and where X 1 to X k are the states from which Y gets its incoming connections. The available dedicated software environment described in Treur (2020a, Chap. 9), includes a combination function library with currently around 50 useful basic combination functions. The above concepts enable us to design network models and their dynamics in a declarative manner, based on mathematically defined functions and relations. The examples of combination functions that are applied in the model introduced here can be found in Table 13.1. Combination functions as shown in Table 13.1 and available in the combination function library are called basic combination functions. For any network model some number m of them can be selected; they are represented in a standard format as bcf1 (..), bcf2 (..), …, bcfm (..). In principle, they use parameters π1,i,Y , π2,i,Y such as the α, β, σ, and τ in Table 13.1. Including these parameters, the standard format used for basic combination functions is (with V 1 , …, V k the single causal impacts): bcf i (π1,i,Y , π2,i,Y , V1 , . . . , Vk ). Table 13.1 The combination functions used in the introduced self-modeling network model Notation

Formula 

 − 1+e1στ ) (1 +

Parameters Steepness σ > 0 Excitability threshold τ

Advanced logistic sum

alogisticσ,τ (V 1 ,…,V k )

1 1+e−σ(V1 +···+Vk −τ) e−στ )

Steponce

steponceα,β (..)

1 if time t is between α and β, else Start time α 0 End time β

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For each state Y just one basic combination function can be selected, but also a number of them can be selected by weights γi,Y ; this will be interpreted as a weighted average of them. A function cY (..) can then be specified by these weight factors γi,Y and the parameters πi,j,Y . Realistic network models are usually adaptive: often not only their states but also some of their network characteristics change over time. By using a self-modeling network (also called a reified network), a similar network-oriented conceptualization can also be applied to adaptive networks to obtain a declarative description using mathematically defined functions and relations for them as well; see Treur (2020a, b). This works through the addition of new states to the network (called self-model states) which represent (adaptive) network characteristics. In the graphical 3D-format as shown in Sect. 13.5, such additional states are depicted at a next level (called self-model level or reification level), where the original network is at the base level. As an example, the weight ωX,Y of a connection from state X to state Y can be represented (at a next self-model level) by a self-model state named WX,Y . Such firstorder W-states will be used in the model introduced here to model learning within an organisation. Similarly, all other network characteristics from ωX,Y , cY (..), ηY could be made adaptive by including self-model states for them. This self-modeling network construction can easily be applied iteratively to obtain multiple orders of self-models at multiple (first-order, second-order, …) self-model levels. For example, a second-order self-model may include a second-order self-model state WWV,W ,W X,Y representing the weight of the connection from first-order self-model state WV,W to first-order self-model state WX,Y . Such higher-order WWW -states can be used to control the learning processes that are modeled by the W-states; they will be used as well in the model introduced here.

13.5 The Second-Order Adaptive Network Model The introduced second-order adaptive network model addresses the effect of communication and leadership on learning within an organisation. Communication can occur by either natural communication or communication organised by the team leader. In this chapter, natural communication is described as communication that happens naturally, without extra encouragement from the team leader, within a team. Examples of natural communication are team members who talk with each other within or outside meetings. This includes talking to each other about a project without prompting from their team leader. The team leader can also influence communication, by for example, regulating meetings or encouraging team members to communicate among themselves. In this model, certain assumptions are made: ● Natural communication is a spectrum from completely off (low) to completely on (high), and this natural communication can be adjusted for every dyad.

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● The level of encouragement from the team leader to communicate is also a spectrum. Communication within team members (in dyads) as well as the relations between team members can be adjusted by the team leader. ● There is also a spectrum from feedback and feed forward learning. ● If the team leader states that something will happen, it will happen. This means nobody overrules the team leader. ● The simulation by the model follows three phases; these phases do not overlap: – First, the natural communication and the team leader interaction (time 20–60) Employees are learning by mutual interaction in dyads – Feedforward learning (time 60–120) A shared mental model is formed (O) – Feedback learning (time 140–180) So, the model shows three different types of learning processes within an organisation. The benefit of this model is that the relationships between members can be adjusted separately. This ensures that the model can be made as realistic as possible and can show many different scenarios. In the scenarios addressed, for the sake of simplicity we assumed that all relationships between people are either completely off or completely on. Four different scenarios will be presented. Details were added to make the model more realistic and fitting for a specific scenario. ● Scenario 1 is the base scenario. In this scenario we will assume that there is neither an active team leader nor a high extent of natural communication. In this scenario people do not learn from each other in Phase 1, only from feedback learning in Phase 3 (after feed forward learning in Phase 2). An example case in which this happens is when individuals work in a temporary team which has been recently assembled. We assume that they have not worked with each other. This can happen when the team members come from different departments, organisations, or when the team is virtual and thus does not have many opportunities to communicate with each other. The team leader can also influence the team’s communication in several ways that have a negative effect. For example, (1) the team leader might not be very comfortable with taking the lead due to having a new position, (2) the team leader might be busy with other responsibilities, or (3) the team leader exercises their position of power by limiting learning opportunities. When the team members have a hard time communicating with each other, and the team leader does not encourage communication, we have this first scenario. ● Scenario 2 describes that of an inactive team leader, but a high extent of natural communication within the team. This is similar to a delegative leadership style. This is because the leader only delegates their tasks. It is up to the team members to ensure the quality they deliver. There are several reasons why a team may come to this scenario. It might be that the team leader feels like the team is capable to handle things on their own, and thus not feel the need for regular meetings. They assume that the members will come to them if they have any problems. The team leader might expect this because the team members have worked together in the past and feel comfortable reaching out to each other when they need help from another member. When the team members have worked together in the past, but

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the team leader is new, they might have a difficult time taking instructions from the leader. However, it is also possible that the team leader has a lot of other responsibilities, and therefore does not take an active role in leading the team. ● In Scenario 3, we describe an active team leader and a low natural communication, this type of leadership is consistent with transactional or authoritarian leadership. Here, every team member gets a specific task, reducing the need for team members to talk with each other. Instances where this scenario is realistic, is a new team with an experienced team leader who knows exactly what needs to be done or a team in which the leader purposefully limits communication opportunities because he/she wants to retain position of power and control the extend of the teamwork. The team leader is comfortable taking the lead and organises regular meetings in which the whole team gets updates, however team members are not encouraged to propose or share new ideas. Because of this, communication mainly goes through the team leader. The team leader could also use this position of power to control team members and tell them what to do, to maintain their powerful position. ● In Scenario 4, we assume an active team leader and high natural communication. This scenario fits with a participative or transformational leadership style. In both these leadership styles the team leader plays an active role in the team, both as a worker and as an inspirer. This scenario could happen when the team members, including the team leader, are familiar with each other and the team leader is comfortable with taking the lead. The team leader organises regular meetings in which they provide updates about the project, initiative and work and motivates the team members to provide input, participate in the discussions and share ideas. The team members feel comfortable reaching out to other members when they need help. This is encouraged by the team leader who supports their team members in sharing knowledge and provides opportunities for exchanging ideas and communication. For the detailed design of the network model, Figs. 13.3, 13.4 and 13.5 explain every state, and the influence of states on each other can be seen in the graphical connectivity representation in Fig. 13.2. All states use the combination function alogistic from Table 13.1, except the three states X44 to X46 for the control of Phase 1 to Phase 3 that use the function steponce from Table 13.1 to control the time intervals for these phases. In Fig. 13.2, as well as in Fig. 13.3, at the base level (lower plane) it is shown how the internal simulation of a mental model by the different individuals is modeled: the team leader (TL), the marketing consultant (M), the designer (D), and the financial representative (F). Every individual has their own mental model of the same situation. In this model, a_X, where X can be swapped out for any team member, stands for the mental model state (at the base level: the lower plane in Fig. 13.2) for starting of the meeting, b_X for getting more money from the financial representative; c_X and d_X stand for, respectively, mental model states for starting a social media strategy and starting a billboard strategy. Finally, e_X stands for mental model states for having an improved marketing strategy.

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Fig. 13.2 Connectivity of the second-order adaptive network model

As can be seen in Figs. 13.2 and 13.3, the financial representative only has mental model states for a and b. This is because they, outside of granting more funds for the marketing strategy, are not directly involved further in the process. The solid arrows represent things that the team member is already sure off; the financial representative is sure that there is money available, making a_F to b_F a solid arrow. The dashed arrows indicate relations that are initially not (completely) known yet; the team leader only knows this after either (1) communication with the financial representative, or (2) feedback learning. In this graphical representation, the O stands for the organisation. The first-order self-model level includes self-model states WX,Y where X and Y are two subsequent base level mental model states; for example, Wa_TL,b_TL , see Fig. 13.4 and the middle plane in Fig. 13.1. The upward connections are depicted by blue arrows, and the downward arrow shows how the value from WX,Y is used in the activation of base state Y. Changes in values for these W-states represent learning. To this end, the WX,Y states from all dyads of different team members are linked by black or grey arrows, these model their mutual communication; they only differ in colour to keep the graphical representation as clear as possible. This means that they

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Explanation Starting meeting for the team leader Getting more money from the FD for the team leader Starting social media strategy for the team leader Starting billboard strategy for the team leader Having improved marketing strategy for the team leader Starting meeting for the designer Getting more money from the FD for the designer Starting social media strategy for the designer Starting billboard strategy for the designer Having improved marketing strategy for the designer Starting meeting for the marketeer Getting more money from the financial department for the marketeer Starting social media strategy for the marketeer Starting billboard strategy for the team leader Having improved marketing strategy for the marketeer Shared mental model for the start of the meeting Shared mental model for getting more money from the financial department Shared mental model for starting social media strategy Shared mental model for starting billboard strategy Shared mental model for having improved marketing strategy Starting meeting for the financial department Giving more money to the other departments from the financial department

Fig. 13.3 Base states

can learn from each other. How much they learn from each other is determined by the second-order self-model level. The second-order self-model level models the control for how the team members learn from each other; see Fig. 13.5 and the upper plane in Fig. 13.2. This directly relates to how learning is represented in the first-order self-model level. These WWW states represent the weights of the (communication) channels between the W-states for different mental models. At this level, they are grouped per team member instead of a different state for every task. This is done to keep the representation as clear as possible. Every WWW -state has incoming arrows that provide the context information that is relevant for the processes it controls, and a downward (control effectuating) arrow to the first-order self-model level to determine how it influences the processes for the respective W-states. These W-states have (horizontal) black incoming arrows, these represent the (potential) communication, and the feedback and feedforward learning channels. The first phase has influences on the communication state and the team leader state, which in their turn influence all team member states from the first-order level, thus excluding O. Phase 2 models the feed forward learning, so from team members to O. Lastly, Phase 3 models the feedback learning, from O to the team members. The fact that all these states, and their effect on other states can be adapted individually, ensures that this network model is highly adaptive.

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Explanation First-order self-model for the weight of the connection from a to b within the shared mental model of the team leader First-order self-model for the weight of the connection from b to c within the shared mental model of the team leader First-order self-model for the weight of the connection from b to d within the shared mental model of the team leader First-order self-model for the weight of the connection from c to e within the shared mental model of the team leader First-order self-model for the weight of the connection from d to e within the shared mental model of the team leader First-order self-model for the weight of the connection from a to b within the shared mental model of the designer First-order self-model for the weight of the connection from b to c within the shared mental model of the designer First-order self-model for the weight of the connection from b to d within the shared mental model of the designer First-order self-model for the weight of the connection from c to e within the shared mental model of the designer First-order self-model for the weight of the connection from d to e within the shared mental model of the designer First-order self-model for the weight of the connection from a to b within the shared mental model of the marketeer First-order self-model for the weight of the connection from b to c within the shared mental model of the marketeer First-order self-model for the weight of the connection from b to d within the shared mental model of the marketeer First-order self-model for the weight of the connection from c to e within the shared mental model of the marketeer First-order self-model for the weight of the connection from d to e within the shared mental model of the marketeer First-order self-model for the weight of the connection from a to b within the shared mental model of organisation O First-order self-model for the weight of the connection from b to c within the shared mental model of organisation O First-order self-model for the weight of the connection from b to d within the shared mental model of organisation O First-order self-model for the weight of the connection from c to e within the shared mental model of organisation O First-order self-model for the weight of the connection from d to e within the shared mental model of organisation O

Phase 1: Learning through communication Phase 2: Shared mental model is formed Phase 3: Feedback Context states Team leader states

Fig. 13.4 First-order self-model states

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Explanation Second-order self-model state for the weights of the connections from the first-order self-model states of the shared mental model of the team leader to the first-order self-model states of the shared organisational model. Second-order self-model state for the weights of the connections from the first-order self-model states of the shared mental model of designer to the first-order self-model states of the shared organisational model. Second-order self-model state for the weights of the connections from the first-order self-model states of the shared mental model of the marketeer to the first-order self-model states of the shared organisational model. Second-order self-model state for the weights of the connections from the first-order self-model states of the shared mental model of the financial department to the first-order self-model states of the shared organisational model. Second-order self-model state for the weights of the connections from the first-order self-model states of the shared mental model of the organisation to the first-order self-model states of the team leader. Second-order self-model state for the weights of the connections from the first-order self-model states of the shared mental model of the organisation to the first-order self-model states of the designer. Second-order self-model state for the weights of the connections from the first-order self-model states of the shared mental model of the organisation to the first-order self-model states of the marketeer. Second-order self-model state for the weights of the connections from the first-order self-model states of the shared mental model of the team leader to the first-order self-model states of the designer as well as second-order self-model state for the weights of the connections from the first-order self-model states of the shared mental model of the designer to the first -order self-model states of the team leader. Second-order self-model state for the weights of the connections from the first-order self-model states of the shared mental model of the team leader to the first-order self-model states of the marketeer as well as second-order self-model state for the weights of the connections from the first-order self-model states of the shared mental model of the team leader to the first -order selfmodel states of the marketeer. Second-order self-model state for the weights of the connections from the first-order self-model states of the shared mental model of the team leader to the first-order self-model states of the financial department as well as second-order self-model state for the weights of the connections from the first-order self-model states of the shared mental model of the team leader to the first -order self-model states of the financial department. Second-order self-model state for the weights of the connections from the first-order self-model states of the shared mental model of the designer to the first-order self-model states of the marketeer as well as second-order self-model state for the weights of the connections from the first-order self-model states of the shared mental model of the designer to the first -order self-model states of the marketeer. Second-order self-model state for the weights of the connections from the first-order self-model states of the shared mental model of the designer to the first-order self-model states of the financial department as well as second-order self-model state for the weights of the connections from the first-order self-model states of the shared mental model of the designer to the first -order selfmodel states of the financial department. Second-order self-model state for the weights of the connections from the first-order self-model states of the shared mental model of the marketeer to the first-order self-model states of the financial department as well as second-order self-model state for the weights of the connections from the first-order self-model states of the shared mental model of the marketeer to the first -order self-model states of the financial department.

Fig. 13.5 Second-order self-model states

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In the Appendix section the full specification of the model by role matrices is shown.

13.6 Simulation Results The available dedicated software environment in MATLAB was used to run a number of simulations, in particular for Scenario 1 to 4 as described in Sect. 13.5. Because communication is influenced by both the team leader states TLS and the context states CS (for natural communication), and by both feedback and feedforward learning, we decided to focus on these states. Both feedforward and feedback learning have an influence on the knowledge of each person. When the feedforward is (partially) missing, the individual has to learn this process through feedback learning (from the organisation). In the base Scenario 1, there is no natural communication for dyads, nor dyad communication initiated by the team leader; therefore, the individuals only learn after the feedback learning, which takes longer. In all other scenarios, there is at least one state which leads to dyad learning. This leads to (partial or complete) dyad learning and completing this with feed forward and feedback organisational learning. For an overview, see Fig. 13.6.

13.6.1 Scenario 1: Inactive Team Leader and Low Natural Communication As mentioned before, this scenario has no communication during Phase 1 (time 20– 60), see Fig. 13.7. Neither through natural communication nor through an active team leader. It can indeed be seen that there is no learning during Phase 1, the learning only starts in Phase 2 (time 60–120). This learning is only feed forward organisational learning. Thus, the organisation is learning, but team members are not yet. The team members only start learning in the feedback learning phase, Phase 3 (time 140–180).

Natural communication Team-leader-initiated communication CS Context states TLS Team leader states

Fig. 13.6 Overview of scenarios 1 to 4

Scenario 1 0 0

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Fig. 13.7 Simulation results for Scenario 1

13.6.2 Scenario 2: Inactive Team Leader and High Natural Communication This Scenario 2 has an inactive team leader, but a high natural communication, see Fig. 13.8. Because of this, the team members are already learning during Phase 1. In addition, organisational learning happens in Phase 2, like in Scenario 1. However, since the team members have a good communication, the knowledge is already shared.

13.6.3 Scenario 3: An Active Team Leader and a Low Natural Communication Similar to Scenario 2, the team members are already learning in the first phase, see Fig. 13.9. This is because the team leader makes sure there is communication within the team. Because of this, the team members are already learning in Phase 1, and in

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Fig. 13.8 Simulation results for Scenario 2

addition the information is learned by the organisation through feed forward learning in Phase 2.

13.6.4 Scenario 4: An Active Team Leader and a High Natural Communication Comparable to the previous two scenarios, in this scenario the learning is too happening in Phase 1, see Fig. 13.10 In this case the communication can happen naturally, or through the team leader. This ensures that there is enough communication between the team members to establish a shared learning process in Phase 1. In Phase 2 this knowledge is shared with the organisation, during the feed forward learning. Finally in Phase 3, the feedback learning is updating the individual mental models, as far as needed.

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Fig. 13.9 Simulation results for Scenario 3

13.7 Addressing Variations in Imperfect Communication In this section it is discussed and illustrated how the proposed computational model can also address imperfect communication and variations in the strength of communication between individuals. Two new scenarios are illustrating this: Scenario 5 and Scenario 6.

13.7.1 Scenarios 5 and 6 ● Scenario 5 describes a scenario in which some colleagues know each other better than other colleagues. In this scenario, the financial representative has a higher natural communication with the designer than with marketing director. Apart from this, the team leader is inactive. This could happen, for example, when the financial representative and the designer have been colleagues before. It has some similarity to Scenario 2, where there is a delegative team leader style, however

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Fig. 13.10 Simulation results for Scenario 4

with the marketing director being a new addition, the natural communication might be weaker than with the financials’ representative other colleagues. ● In Scenario 6, we, again, describe a situation where some colleagues have stronger natural communication than other colleagues. In this scenario, there is also an active team leader. This could happen in a participative, or transformational leadership, where two colleagues in the team get along less than the other colleagues. This may happen for all sorts of reasons, it is natural to have different friendliness levels with different colleagues.

13.7.2 Simulation Results for Scenarios 5 and 6 In Fig. 13.11 the outcomes for Scenario 5 are shown: there are certain colleagues who know each other better than other colleagues, due to an inactive team leader, there is quite some difference in the different phases. Because there is natural communication between some colleagues, and not between others, there are some lines which start earlier than others, or do not rise all the way to one, meaning they do not learn

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Fig. 13.11 Simulation results for Scenario 5

everything in phase 1, but still completed their knowledge in phase 3 with feedback learning. In Fig. 13.12 the results for Scenario 6 are shown. In this case there are also colleagues who have different levels of knowledge from each other, but in this scenario there is a more active team leader. You can see that the outcomes of this scenario are similar to Scenario 2, 3, and 4. However, there are some small differences. There are some lines that do not reach quite as high, this is due to the lower communication between colleagues. Because the team leader is active, the colleagues who are lesser known still get to share almost all of the knowledge, and this will be completed in phase 3.

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Fig. 13.12 Simulation results for Scenario 6

13.8 Discussion This chapter uses material from Bouma et al. (2023). This research addressed the influence of leadership and communication on learning within an organisation by direct mutual dyadic interactions. This is done in combination with multilevel organisational learning as an alternative route, including feed forward and feedback learning. The results show that when good communication is present (either due to the team leader, or due to the natural communication, or both), this can lead to a faster learning process within an organisation than the longer route via feed forward and feedback learning. However, this more direct form of learning in general may take more of the employee’s time, as a quadratic number of dyadic interactions in general requires more invested time than a linear number of interactions needed for feed forward and feedback learning.

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As can be seen in the graphs in Sects. 13.6 and 13.7, learning between team members takes place when there is at least one basis for communication. In this case, Scenario 1 lacks such a basis but for Scenario 2 to 4 this basis was there: either an active team leader, a high level of natural communication, or both. Therefore, the outcomes for latter three scenarios are quite similar. More differences were shown in Scenario 5 and 6 where variations in strengths of communications were addressed. Due to this, different levels of imperfectness of knowledge occurred which only were resolved after feedforward and feedback (organisational) learning. When there is only an active team leader, this person is often seen as the boss, and treated as such. This team leader is very important, because they make sure that everything that needs to get done, will be done. However, this can lead to the ‘hierarchical mum effect’, which is defined as “individuals’ reluctance to provide negative feedback to another for fear of being associated with the message, …”. This means that people are less likely to say something to their superior, even if this is at the expense of task accomplishments, because they want to maintain a positive relationship. This can be seen specifically in work relationships. Another factor is that team members are more likely to expect negative feedback from their team leader than the team leader expects negative feedback from them. This may negatively influence team members to expressing their feedback (Bisel et al. 2012). Other research has shown that when there is a two-way symmetrical communication system, which also includes internal team peer communication, the likelihood of employees’ job satisfaction increases as well as their participation and commitment. Internal communication helps team leaders connect with their members, and so help the organisation with bettering its’ environment (García-Morales et al. 2011). So, the presence of an active team leader as well as natural communication leads to a more satisfactory work experience. When there is only a high level of natural communication, team members may learn a lot from each other, but things could still be missing. Like mentioned before, a team leader is important because they ensure that everything that needs to be done, will be done (Bisel et al. 2012). When this responsible person is missing, it could be that some things are missed or stay undecided. Thus, even though three scenarios had, to an extent, the same outcome, there could be differences that are not shown in the graphs.

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13.9 Limitations and Further Research A number of factors that influence an organisation and the learning processes have been left out of consideration, such as the amount of people in an organisation, the relationship for each individual dyad, type of project they are working on, or individual personality traits. Although a model is not representative fully and may not be generalizable to all types of organisations, it provides a useful and relatively simple way to predict general learning pattens. Real life experiments are not suitable for the type of research addressed here, because analysing the differences between different leadership styles in the same situation cannot be done easily by such experiments in reality. Since scenarios, for example, without an active team leader and high level of natural communication could lead to a hostile work environment, real life experiments certainly would not be suited for such research. For further research, differentiations within a scenario could be made. For example, two co-workers have a high level of natural communication between them, but not with another co-worker; for the sake of simplicity, this was not addressed yet. Further research could also look at larger teams, or more layers within a team. Except the research reported here, there is little research linking a leadership style and learning within an organisation. That is something that could be improved upon by further research.

13.10 Appendix: Role Matrices In this section the different role matrices are shown that provide a full specification of the network characteristics defining the adaptive network model in a standardised table format. Here in each role matrix, each state has its row where it is listed which are the impacts on it from that role. Role matrices for connectivity characteristics The connectivity characteristics are specified by role matrices mb and mcw shown in Figs. 13.13 and 13.14. Role matrix mb lists the other states (at the same or lower level) from which the state gets its incoming connections, whereas in role matrix mcw the connection weights are listed for these connections. Nonadaptive connection weights are indicated in mcw (in Fig. 13.14) by a number (in a green shaded cell), but adaptive connection weights are indicated by a reference to the (self-model) state representing the adaptive value (in a peach-red shaded cell). This can be seen for base states X2 –X5 (with self-model states X23 –X27 ), states X7 –X10 (with self-model states X28 –X32 ), X12 –X15 (with self-model states X33 – X37 ), X17 –X20 (with self-model states X38 –X42 ), and X22 (with self-model state X43 ). Moreover, from state X38 –X43 on second-order self-model states X49 –X61 are indicated.

13 Computational Analysis of the Influence of Leadership … Fig. 13.13 Role matrix mb for base connectivity

mb X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17 X18 X19 X20 X21 X22 X23 X24 X25 X26 X27 X28 X29 X30 X31 X32 X33 X34 X35 X36 X37 X38 X39 X40 X41 X42 X43

a_TL b_TL c_TL d_TL e_TL a_D b_D c_D d_D e_D a_M b_M c_M d_M e_M a_O b_O c_O d_O e_O a_F b_F Wa_TL,b_TL Wb_TL,c_TL Wb_TL,d_TL Wc_TL,e_TL Wd_TL,e_TL Wa_D,b_D Wb_D,c_D Wb_D,d_D Wc_D,e_D Wd_D,e_D Wa_M,b_M Wb_M,c_M Wb_M,d_M Wc_M,e_M Wd_M,e_M Wa_O,b_O Wb_O,c_O Wb_O,d_O Wc_O,e_O Wd_O,e_O Wa_F,b_F

349 1 X1 X1 X2 X2 X3 X6 X6 X7 X7 X8 X11 X11 X12 X12 X13 X16 X16 X17 X17 X18 X21 X21 X23 X24 X25 X26 X27 X23 X24 X25 X26 X27 X23 X24 X25 X26 X27 X23 X24 X25 X26 X27 X23

2

3

4

5

X33 X34 X35 X36 X37 X33 X34 X35 X36 X37 X33 X34 X35 X36 X37 X33 X34 X35 X36 X37 X33

X38 X39 X40 X41 X42 X38 X39 X40 X41 X42 X38 X39 X40 X41 X42 X38 X39 X40 X41 X42 X38

X43

X4

X9

X14

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X28 X29 X30 X31 X32 X28 X29 X30 X31 X32 X28 X29 X30 X31 X32 X28 X29 X30 X31 X32 X28

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X43

350 Fig. 13.13 (continued)

D. Bouma et al. X44 X45 X46 X47 X48 X49 X50 X51 X52 X53 X54 X55 X56 X57 X58 X59 X60 X61

F1 F2 F3 CS TLS WWTL,WO WWD,WO WWM,WO WWF,WO WWO,WTL WWO,WD WWO,WM WWTL,WD WWTL,WM WWTL,WF WWD,WM WWD,WF WWM,WF

X44 X45 X46 X47 X48 X49 X50 X51 X52 X53 X54 X55 X56 X57 X58 X59 X60 X61

X44 X44 X45 X45 X45 X45 X46 X46 X46 X47 X47 X47 X47 X47 X47

X48 X48 X48 X48 X48 X48

Role matrices for timing characteristics In Fig. 13.15, the role matrix ms for speed factors is shown, which lists all speed factors. Next to it, the list of initial values can be found. Role matrices for aggregation characteristics The network characteristics for aggregation are defined by the selection of combination functions from the library and values for their parameters. In role matrix mcfw it is specified by weights which state uses which combination function; see Fig. 13.16. In role matrix mcfp (see Fig. 13.17) it is indicated what the parameter values are for the chosen combination functions.

13 Computational Analysis of the Influence of Leadership … Fig. 13.14 Role matrix mcw for connection weights

351

mcw X1

Connection weights a_TL

X2

b_TL

1 X23

X3

c_TL

X24

X4

d_TL

X25

X5

e_TL

X26

X6

a_D

1

X7

b_D

X28

X8

c_D

X29

X9

d_D

X30

X10

e_D

X31

X11

a_M

1

X12

b_M

X33

X13

c_M

X34

X14

d_M

X35

X15

e_M

X36

X16

a_O

1

X17

b_O

X38

X18

c_O

X39

X19

d_O

X40

X20

e_O

X41

X21

a_F

1

X22

b_F Wa_TL,b_TL

X23 X24 X25 X26 X27

1

2

3

4

5

X27

X32

X37

X42

X43 1

X57

X56

X53

X58

Wb_TL,c_TL

1

X57

X56

X53

X58

Wb_TL,d_TL

1

X57

X56

X53

X58

Wc_TL,e_TL

1

X57

X56

X53

X58

Wd_TL,e_TL

1

X57

X56

X53

X58

352 Fig. 13.14 (continued)

D. Bouma et al. X28 X29 X30 X31 X32 X33 X34 X35 X36 X37 X38 X39 X40 X41 X42 X43

Wa_D,b_D

X59

1

X56

X54

X60

Wb_D,c_D

X59

1

X56

X54

X60

Wb_D,d_D

X59

1

X56

X54

X60

Wc_D,e_D

X59

1

X56

X54

X60

Wd_D,e_D

X59

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X54

X60

Wa_M,b_M

X59

X57

1

X55

X61

Wb_M,c_M

X59

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1

X55

X61

Wb_M,d_M

X59

X57

1

X55

X61

Wc_M,e_M

X59

X57

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X55

X61

Wd_M,e_M

X59

X57

1

X55

X61

Wa_O,b_O

X49

X50

X51

1

X52

Wb_O,c_O

X49

X50

X51

1

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Wc_O,e_O

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1

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Wd_O,e_O

X49

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1

X52

Wa_F,b_F

X58

X60

X61

1

X52

F1

1

F2

1

F3

1

CS

1

TLS

1

X49

WWTL,WO

1

X50

WWD,WO

1

X51

WWM,WO

1

X52

1

X53

WWF,WO WWO,WTL

X54

WWO,WD

1

X55

WWO,WM

1

X56

WWTL,WD

1

1

X57

WWTL,WM

1

1

X58

WWTL,WF

1

1

X59

WWD,WM

1

1

X60

WWD,WF

1

1

X61

WWM,WF

1

1

X44 X45 X46 X47 X48

1

13 Computational Analysis of the Influence of Leadership … Fig. 13.15 Role matrix ms for speed factors and initial values iv

353

b_TL

Speed factors 0.5 0.5

Initial Value 1 0

c_TL

0.5

0

X4

d_TL

0.5

0

X5

e_TL

0.5

0

X6

a_D

0.5

1

X7

b_D

0.5

0

X8

c_D

0.5

0

X9

d_D

0.5

0

X10

e_D

0.5

0

X11

a_M

0.5

1

X12

b_M

0.5

0

X13

c_M

0.5

0

X14

d_M

0.5

0

X15

e_M

0.5

0

X16

a_O

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1

X17

b_O

0.5

0

X18

c_O

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X19

d_O

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X20

e_O

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X21

a_F

0.5

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X22

b_F Wa_TL,b_TL

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msv X1

a_TL

X2 X3

X23 X24 X25 X26

0.5

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Wb_TL,c_TL

0.5

0

Wb_TL,d_TL

0.5

0

Wc_TL,e_TL

0.5

0

354 Fig. 13.15 (continued)

D. Bouma et al. Wd_TL,e_TL

0.5

0

Wa_D,b_D

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0

Wb_D,c_D

0.5

1

Wb_D,d_D

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0

Wc_D,e_D

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Wd_D,e_D

0.5

0

Wa_M,b_M

0.5

0

Wb_M,c_M

0.5

0

Wb_M,d_M

0.5

1

Wc_M,e_M

0.5

0

Wd_M,e_M

0.5

1

Wa_O,b_O

0.5

0

Wb_O,c_O

0.5

0

Wb_O,d_O

0.5

0

Wc_O,e_O

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Wa_F,b_F

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F3

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TLS

2/0

0

X49

WWTL,WO

0.1

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WWF,WO WWO,WTL

0.1

0

X54

WWO,WD

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WWO,WM

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WWTL,WD

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WWTL,WM

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WWTL,WF

0.1

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X61

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X27 X28 X29 X30 X31 X32 X33 X34 X35 X36 X37 X38 X39 X40 X41 X42 X43 X44 X45 X46 X47 X48

13 Computational Analysis of the Influence of Leadership … Fig. 13.16 Role matrix mcfw for combination function weights

355

mcfw X1

Combination function weights a_TL

X2

b_TL

1 1

X3

c_TL

1

X4

d_TL

1

X5

e_TL

1

X6

a_D

1

X7

b_D

1

X8

c_D

1

X9

d_D

1

X10

e_D

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X11

a_M

1

X12

b_M

1

X13

c_M

1

X14

d_M

1

X15

e_M

1

X16

a_O

1

X17

b_O

1

X18

c_O

1

X19

d_O

1

X20

e_O

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X21

a_F

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X22

b_F Wa_TL,b_TL

1

X23 X24 X25 X26 X27

alogistic

1

Wb_TL,c_TL

1

Wb_TL,d_TL

1

Wc_TL,e_TL

1

Wd_TL,e_TL

1

steponce

356 Fig. 13.16 (continued)

D. Bouma et al. X28 X29 X30 X31 X32 X33 X34 X35 X36 X37 X38 X39 X40 X41 X42 X43 X44 X45 X46 X47 X48

Wa_D,b_D

1

Wb_D,c_D

1

Wb_D,d_D

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Wc_D,e_D

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Wd_D,e_D

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Wa_M,b_M

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Wb_M,c_M

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Wb_M,d_M

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Wc_M,e_M

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Wd_M,e_M

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Wa_O,b_O

1

Wb_O,c_O

1

Wb_O,d_O

1

Wc_O,e_O

1

Wd_O,e_O

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Wa_F,b_F

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F1

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F3

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CS

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TLS

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X49

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X55

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X58

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13 Computational Analysis of the Influence of Leadership …

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X13

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X14

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X15

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1

X16

a_O

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X17

b_O

5

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X18

c_O

5

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X19

d_O

5

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X20

e_O

5

1

X21

a_F

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b_F Wa_TL,b_TL

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X22 X23 X24 X25 X26 X27 X28 X29 X30 X31

5

1

Wb_TL,c_TL

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1

Wb_TL,d_TL

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1

Wc_TL,e_TL

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1

Wd_TL,e_TL

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1

Wa_D,b_D

5

1

Wb_D,c_D

5

1

Wb_D,d_D

5

1

Wc_D,e_D

5

1

357 steponce

Fig. 13.17 Role matrix mcfp for combination function parameters

steponce

358

D. Bouma et al. X32 X33 X34 X35 X36 X37 X38 X39 X40 X41 X42 X43 X44 X45 X46 X47 X48

Wd_D,e_D

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Wa_M,b_M

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Wa_O,b_O

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Wb_O,c_O

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Wb_O,d_O

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Wa_F,b_F

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F3

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CS

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X52

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X55

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X56

WWTL,WD

5

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X57

WWTL,WM

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X58

WWTL,WF

5

0.5

X59

WWD,WM

5

0.5

X60

WWD,WF

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X61

WWM,WF

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0.5

Fig. 13.17 (continued)

13 Computational Analysis of the Influence of Leadership …

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Part VI

Computational Analysis of the Role of Organisational Culture for Multilevel Organisational Learning

In this part we demonstrate that the self-modeling network modeling approach can be applied to model and evaluate dynamic organisational systems. It uses computational modeling to analyse a variety of contexts and learning mechanisms. It starts by addressing the role of organisational culture as a mechanism influencing multilevel learning flows. This study demonstrates how higher flexibility and discretion in organisational culture result in better mistake management and thus improved organisational learning. It also explores the combined effect of organisational culture and leader’s characteristics on organisational learning. Finally, computational modeling is applied to analyse a more complex scenario of organisational transformational change and its effect on building learning culture. Observations about various interplays and effects of the mechanism are made; they expose that acceptance of mistakes, as a part of learning culture, facilitate transformational and sustainable change.

Chapter 14

Computational Simulation of the Effects of Different Culture Types and Leader Qualities on Mistake Handling and Organisational Learning Natalie Samhan, Jan Treur, Wioleta Kucharska, and Anna Wiewiora Abstract This chapter investigates computationally the following research hypotheses: (1) Higher flexibility and discretion in organisational culture results in better mistake management and thus better organisational learning, (2) Effective organisational learning requires a transformational leader to have both high social and formal status and consistency, and (3) Company culture and leader’s behavior must align for the best learning effects. Computational simulations of the introduced adaptive network were analyzed in different contexts varying in organisation culture and leader characteristics. Statistical analysis results proved to be significant and supported the research hypotheses. Ultimately, this chapter provides insight into how organisations that foster a mistake-tolerant attitude in alignment with the leader can result in significantly better organisational learning on a team and individual level. Keywords Organisational culture · Leader qualities · Mistake handling · Organisational learning

14.1 Introduction Committing mistakes in a professional field is usually perceived as a complete aberration. It is often associated with adverse feelings of guilt, embarrassment, and even lower self-esteem. However, mistakes are an inevitable aspect of an organisation N. Samhan · J. Treur (B) Social AI Group, Vrije Universiteit Amsterdam, Amsterdam, the Netherlands e-mail: [email protected] W. Kucharska Faculty of Management and Economics, Gda´nsk University of Technology, Gda´nsk, Poland e-mail: [email protected] A. Wiewiora QUT Business School, Queensland University of Technology, Brisbane, Australia e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 G. Canbalo˘glu et al. (eds.), Computational Modeling of Multilevel Organisational Learning and Its Control Using Self-modeling Network Models, Studies in Systems, Decision and Control 468, https://doi.org/10.1007/978-3-031-28735-0_14

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whether it acknowledges it or not. Although, the organisation’s conception and reaction to making mistakes can affect its long-term learning and performance (Cannon and Edmondson 2005). Tacit beliefs of individuals regarding committing mistakes are often a by-product of the environment, including the organisation’s culture and leader’s attitudes (Kucharska 2021a). It has been empirically established that mistake tolerance aid organisational learning and as a result its performance (Weinzimmer and Esken 2017). A mistake non-tolerant environment makes it difficult to report mistakes and that often perpetuates the mistake and harms an organisation’s long-term capacity to learn and improve. Whereas a mistake-tolerant environment is warier of long-term repercussions and less concerned about the immediate costs of the mistake. This attitude toward managing mistakes not only develops a healthier psychological response to mistakes but also promotes deliberate experimentation and critical analysis, as opposed to hiding mistakes and trying to move past them swiftly (Cannon and Edmondson 2005). An organisation’s culture, in addition to a leader’s behavior regarding mistake tolerance, is crucial to organisational learning (Kucharska 2021a, b). The idea, however, is not to cultivate an environment that encourages making mistakes, but one that encourages ‘fail intelligently’ to maximize the learning value of mistakes and promote intelligent risk-taking (Weinzimmer and Esken 2017). In essence, this chapter aims to carry out computational simulations to explore the effect on organisational learning twofold: in relation to the organisations’ culture and leader’s behavior, and in relation to mistake management which is influenced by the former. The design of the model is described in Sect. 14.4, several simulations in Sect. 14.5, a statistical analysis of the simulations in Sect. 14.6, and verification of correctness of the model by stationary point analysis in Sect. 14.7.

14.2 Background Literature This section provides background literature revolving around the relevant concepts and acts as a basis for the experimental simulations in the chapter.

14.2.1 Organisational Culture The company culture is a shared mindset or as Hofstede et al. (2010) says a shared “software of the mind”, that strongly determines the perception of company values, employees’ attitudes, beliefs, social norms, and behaviors. Schein (1990) distinguished three fundamental levels of organisational culture consisting of (1) observable artefacts such as physical layout, the dress code, the manner in which people address each other; (2) values such as organisational norms and believes manifesting in people’s behaviors; and (3) basic underlying assumptions, least apparent and based on an organisation’s historical events that determine perceptions, feelings and behaviour. Organisational culture is typically evaluated based on organisational values that organisational members have in common.

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Fig. 14.1 The competing values framework

Cameron and Quinn (2011) identified the key competing company values framework determining company culture (see Fig. 14.1). According to this framework, organisational culture can be derived from a grid of four quadrants that vary in two dimensions. The first-dimension ranges from flexibility and discretion on one end, to stability and control on the other end. This dimension focuses on the distinction of flexibility which values individuality versus stability which values top-down control. The second-dimension ranges from external focus and differentiation on one end, to internal focus and integration on the other end. This dimension addresses whether an organisation values progress within the organisation (internal focus), versus progress in juxtaposition to other organisations or competitors (external focus). This is also sometimes referred to as the external and internal positioning of an organisation respectively. The four types of cultures that arise from these dimensions are clan, adhocracy, hierarchy, and market.

14.2.2 Leadership Qualities Leaders have a powerful influence over the organisation’s environment and indirectly on individuals’ behavior. Given certain leadership qualities, leaders can foster an environment that facilitates multilevel learning and institutionalization of desired behaviors. Leaders who empower their employees manifest better results. Certain leadership practices, such as delegation, coaching, and recognition, are complementary Leadership empowerment behaviors (LEB) and fulfill Lawler’s (1992) four basic conditions of empowerment (Chénard Poirier et al. 2017). All three of these practices

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can encourage employees to more improvement and feedback which can manifest better results. Moreover, delegating tasks to employees can improve task reproduction and also collaboration—team learning. Similarly, coaching behavior guides the employees more and has the same effect as a delegation. Finally, leader recognition empowers employees and improves reinforcement (Chénard Poirier et al. 2017). Furthermore, transformational leaders can contribute significantly to better organisational learning (Kucharska 2021a). Next to professional skills, such attributes as social status and consistency in the behavior of the leader support their transformational power. A leader’s status comprises both social status and formal organisational status. Having both types of status high can enhance the view and attention to the leader and improve vicarious learning. High social status is also important to captivate learners to capture attention to the desired learned behavior. Further, it is important that the leader acts consistently in order to increase the chance of employees memorizing behavior patterns via mirroring (Lawler 1992).

14.2.3 Organisational Learning Organisational learning is a dynamic multi-level cyclical process that has learning flows directed from individual or team level to organisational level and vice versa. There are two learning flows in an organisation: feed forward and feedback directions (Crossan et al. 1999; Wiewiora et al. 2019). Feedback learning is a common method where the learner receives information from the organisation for improving ensuing behaviors in relation to the present performance. Contrastingly, feed-forward learning focuses on the organisation receiving input from the learner or employee to improve future-oriented solutions or options. The multilevel learning theory introduced by Crossan et al. (1999) is an interdependent theory suggesting learning flows are not necessarily linearly, from micro-level individuals to team level—known as mesolevel—to systematic organisational levels—known as macro-level (Wiewiora et al. 2019). The learning from micro and meso levels to macro levels is categorized as feed-forward learning, whereas feedback learning occurs from macro to meso and micro levels, when individuals and teams learn from the organisation. There are numerous of learning theories, but one of the most renowned theories is the social learning theory (Boone et al. 1977). The theory is based on vicarious learning—also known as observational learning—where the individual learns simply by observing and imitating a model person’s behaviors; this process is often referred to as mirroring the model. Vicarious learning has three distinct stages (Winkler 2009). The first stage is the observational phase where the learner requires attention to observe the model in order to memorize the pattern of behaviour—a process referred to as retention. The second stage is the imitation phase where the learner mirrors the model and reproduces the desired behavior, which can be strengthened by reinforcement. Reinforcement is a process that rewards proper reproduction and enhances learning. The final stage is the participation phase where the behavior

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is fully learned. These intricate learning stages can be modeled in an organisational context and adapted according to the existing culture and the behavior of the leader— model. The neurophysiological basis of vicarious learning can be elucidated by understanding mirror neurons and learning processes in the brain. Mirror neuron activations in the brain extend to vicarious activations in the somatosensory cortex which is in the same region mirror neurons are located. The presence of such activations during vicarious learning could be partially explained by the Hebbian learning theory. Hebbian learning comes from Donald Hebb’s theory which provides a neurophysiological account of learning and plasticity (Hebb 1949). The core concept of Hebbian learning emphasizes how one neuron that is continuously and persistently involved in firing a signal to another neuron elicits metabolic changes in one or both neurons. Hebbian learning mainly takes into account the causality of the neuron firing, indicating temporal precedence, but also contingency as the activity of the presynaptic neuron can be indicative of that of the postsynaptic activity (Keysers and Gazzola 2014). The essence of temporal precedence in Hebb’s learning theory can be translated to temporal-causal networks in an organisational context. Based on the existing insights from the organisational culture, leadership and organisational learning literature, we argue that when organisational culture is in alignment with the leader it then manifests presumptions on mistakes, making individuals either try to cover up their mistakes or exploit the learning value and alter the shared mental model of the organisation to learn from it. For example, when cultural values are focused on employee involvement, experimentation, learning from mistakes and favouring change and at the same time when the leader aligns with these values by modeling relevant culturally aligned behaviours, their subordinates are more likely to reveal their shortcomings and learn from them. Conversely, when the culture and the leadership style promote values and behaviours that discourage talking about and sharing mistake, employees are more likely to hide their shortcomings, resulting in not learning. This chapter aims to utilize adaptive network modeling to computationally demonstrate how mistake-tolerant organisations learn better when using mistake management as a source of learning. Ultimately, the chapter explores the effect of culture and leader characteristics on mistake management and individual and team learning. The chapter aims to utilize—in silico—experiments and statistically compare the results to investigate the following proposed research hypotheses: Hypothesis 1: Higher flexibility and discretion in organisational culture results in better mistake management and thus better organisational learning. Hypothesis 2: Effective organisational learning requires a transformational leader to have both high social and formal status and consistency. Hypothesis 3: Company culture and leader’s behavior must align for the best learning effects.

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14.3 Methodology This section delves into more detail about the network modeling approach along with the computational mechanisms behind it, in addition to the motives for the final adaptive network model used to run the simulations.

14.3.1 The Self-modeling Network Modeling Approach Network-oriented modeling is a very common method in academia to approach adaptive and dynamic aspects of causal relations. This method can be used to better understand a myriad of social, cognitive, and biological phenomena. By graphically conceptualizing a complex process, the modeling approach acts as a basis of the conceptualization by representing the dynamic processes without separating or isolating different states. Temporal-causal networks specifically, incorporate the timing of dynamic or cyclical processes based on a continuous-time temporal dimension to time causal effects (Treur 2020a, b, c). Such networks can be represented both conceptually and numerically. Moreover, this network-oriented modeling approach is an appropriate method for modeling a complex phenomenon such as handling mental models in mental processes (Treur and Van Ments 2022) and organisational learning and the roles of different contextual factors, e.g., (Canbalo˘glu et al. 2022, 2023a, b). Organisational learning (Kim 1993; Crossan et al. 1999; Wiewiora et al. 2019) is a non-linear process where causal relations underlying knowledge can change over time. This has been modeled in Canbalo˘glu et al. (2022, 2023a, b) by using network reification or self-modeling introduced in Treur (2020a, b) to obtain an adaptive reified network, also referred to as a self-modeling network (Treur 2020c). The name stems from the fact that network reification enables explicit representation of network characteristics by nodes in the network, which is also called self-modeling. To elaborate, a complex process can be represented conceptually as a base-level network, but to add adaptivity of some of its network characteristics to the model, a higher-order model representing network characteristics can adapt the network structure of the base-level network during the process. This next-higher level in a network for a base-level network is called a first-order self-modeling level. Along the same line, a second-order self-modeling level can be added to make the firstorder self-modeling level model adaptive as well; this enables control of adaptation. These different levels introduce additional complexity to the network which enables context-sensitive adaptation and control of adaptation such as adaptive adaptation speed, connection strength, and other network characteristics at the base level or higher levels. Different context factors can influence higher-level nodes, such that a high extent of context-sensitivity of base processes and also of adaptation processes can be modeled.

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The self-modeling construction can be iterated to create even higher levels of selfmodels (third-order, etc.). Although very few academic studies have used higher than second-order adaptive models (Treur 2020b). In the current chapter, a second-order adaptive self-modeling network approach is used to conduct different simulation experiments (see Sect. 14.4). An illustrative case study in the index is used as inspiration for the experiments which aim to demonstrate the effect of the independent variables: organisational culture and leader’s consistency and status, on the dependent variables: mistake management and organisational learning. A temporal-causal network takes into account the strength of connections, the speed of causality, and the combination of different incoming connections and the way in which they aggregate. Such characteristics are elaborated below. • Connectivity characteristics: connections from a state X to a state Y have a connection weight value, represented by ωX,Y which indicates the strength of the connection. • Timing characteristics: for all states Y, a speed factor represented by ηY indicates how fast the state is changing upon a causal impact. • Aggregation characteristics: for all Y states, a combination function represented by cY (..) is referred to and determines the mathematical way in which the causal impacts from other states combine for state Y. A dedicated software enviroment based on these network characteristics is utilized to generate the simulation output; see Chap. 9 of Treur (2020b) and Treur and Van Ments (2022), Chap. 17. The difference (or differential) equations that are used for simulation purposes and also for analysis of network dynamics incorporate these network characteristics ωX,Y , cY , ηY :     Y (t + ∆t) = Y (t) + ηY cY ω X 1 ,Y X 1 (t), . . . , ω X k ,Y X k (t) − Y (t) ∆t     dY (t)/dt = ηY cY ω X 1 ,Y X 1 (t), . . . , ω X k ,Y X k (t) − Y (t) (14.1) where X 1 , …, X k are the states from which state Y gets incoming base connections. Adaptivity of some of the network characteristics is modeled according to the principle of self-modeling or reification, which means that for each adaptive network characteristic a state is added to the network (called self-model state or reification state) which represents this (adaptive) network characteristic (Treur 2020a). Such states are depicted at a next level (self-model level), where the original network is at a base level. Adaptivity of connections can be modeled by introducing self-model states of the form WX,Y to represent the adaptive weight ωX,Y of the connection from state X to Y; for shortness, such states are also called W-states. Moreover, an adaptive speed factor ηY can be modeled by self-model state HY . This can be done in iteration as well. For example an adaptive speed factor ηW X,Y of weight adaptation state W X,Y can be modeled by a second-order self-model state HW X,Y . A conceptual self-modeling network model was first constructed and then mapped out to different role matrices structuring the network characteristics according to their roles; in them each value refers to characteristics such as connection weights, speed

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Table 14.1 Overview of the different types of role matrices specifying a self-modeling network model Role matrix Description of the network characteristic

Notation

mb

Base matrix: specifies base causal connections in all levels of the model

mcw

Connection weight matrix: submatrix mcwv specifies non-adaptive ωX,Y connection weights and submatrix mcwa specifies adaptive connection weights

mcfw

Combination functions weights matrix: submatrix mcwv specifies non-adaptive function weights and submatrix mcwa specifies adaptive function weights

mcfp

Combination function parameters matrix: submatrix mcfpv specifies πi,k,Y function parameters with non-adaptive parameter values and submatrix mcfpa specifies function parameters with adaptive parameter values

ms

Speed value matrix: submatrix msv specifies nonadaptive speed values ηY and submatrix msa specifies adaptive speed values

iv

Initial values: specifies initial values of all states

γi,Y

factors or combination function parameter values, or a combination function weight. The role matrices input comprises of adaptive and non-adaptive submatrices; an overview of the different types of matrices can be found in Table 14.1. The computing environment used for the software environment is MATLAB and uses 5 different role matrices as input to generate the graphical simulation output. A complete overview of the role matrices used for the final network model can be found in the Appendix Sect. 14.11. The software environment applies Eq. (14.1) for simulation and thereby uses a numbered library of different combination functions to specify the aggregation characteristics of the model. The basic combination functions are represented as a standard format bcf i (p, v), with the allocated list of parameters p and list of values v as seen in Table 14.2. Each index number i in the library refers to one function from more than 65 different mathematical functions that model social contagion, learning, synchrony, correlation, and more (Treur 2020a, b, c). One combination or more combination function can be selected for each state Y; the overall model can contain a number of different functions; see Table 14.2. For each state Y, the software calculates the weighted average of them using combination function weights γ and their parameters π specified in the mcfw and mcfp matrices as such:   cY π1,1,Y , π2,1,Y , . . . , π1,m,Y , π2,m,Y , V1 , . . . , Vk =     γ1,Y bcf1 π1,1,Y , π2,1,Y , V1 , . . . , Vk + · · · + γm,Y bcfm π1,m,Y , π2,m,Y , V1 , . . . , Vk γ1,Y + · · · + γm,Y

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Table 14.2 Overview of combination functions and their parameters selected to model the simulations in this chapter Name

Notation

Formula

Identity

id(V1 , …, Vk )

V1 

Parameters 1

−

1 1+eστ

  1 + e−στ

None p(1) = steepness σ p(2) = threshold τ

Advanced logistic sum

alogisticσ,τ (V1 , …, Vk )

1+e−σ(V1 +···+Vk −τ)

Step-once

steponceα,β (V1 , …,

time t 1 if α≤t≤β else 0

p(1) = start time α p(2) = end time β

max(hebbμ (V1 , V2 , V 3 ), V4 , . . . , V k )

p(1) = persistence factor μ

Vk )

Max Hebbian composition

maxhebbμ (V1 , …, Vk )

with hebbμ (V1 , V2 , V 3 ) = V1 V2 (1 − V3 ) + μ V3

14.3.2 The Conceptual Model and Modeling Decisions Based on the background literature provided, a generalized conceptual model (see Fig. 14.2) was first constructed to form a basis for the final self-modeling network representation used. This section discusses key decisions in the formation of the self-modeling network model. The concepts discussed in the background literature are translated into a computational network model using the software described in Sect. 14.3.1. The basis of this model lies in the variation of culture types of organisations. This notion is captured by modeling context factors that affect the flexibility and focus on ways that align with the different culture types. The focus of the company is discussed in terms of positioning, where internally focused organisations have low positioning and externally focused organisations have high positioning. Each one of the four culture context factors has varying connection weights to the flexibility and positioning, allowing to model different types of cultures without manually altering the values of flexibility and positioning initially. Further, leader traits were considered in relation to the existing culture so that scenarios would not increase in complexity of the possible variations. Table 14.3 details how the context factors, when high, influence the culture and therefore leadership empowerment characteristics and openness in relation to the existing culture. Other leader qualities such as consistency and status were modeled independently of the culture. Consistency was a simple abstraction modeled through one state with the initial value varying in different simulations. Contrastingly, status varies across two dimensions where both social and formal organisational status are considered important in leader behavior. In this model both these concepts were considered as one state, that is stat_L. In scenarios where high status is modeled, the social and

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Fig. 14.2 Abstract conceptual model as a basis for the adaptive network model

Table 14.3 The effect of context factors on culture and dependent leader qualities Flexibility

Positioning

Recognition

Delegation

Openness

C1

High

Low

Mid

Mid

High

C2

Low

High

Low

Low

Mid

C3

High

High

Low

Low

High

C4

Low

Low

Low

Low

Mid

formal organisational status can be determined by the according culture type. An overview of the breakdown of the high-status value is provided in Table 14.4 where the overall status state sums up to 0.8 when high. Whereas when the status is low it is 0.2 and only comprises of formal organisational status. Table 14.4 Contribution of type of status to different culture types when status state is considered high

Culture type

Formal organisational status

Social status

Clan

0.2

0.6

Adhocracy

0.3

0.5

Market

0.4

0.4

Hierarchy

0.6

0.2

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14.3.3 Illustrative Case Study This section elaborates on the illustrative case study provided which utilizes pseudo names to ellucidate the scenario below. John was the CEO of Happy G. Co.—a garden furniture market. Jenny’s father (currently retired) founded Happy G. and employed John as a CEO to help develop the business. John successfully made Happy G. a market leader within the first 5 years of holding this position. He was always a strongly goal-oriented person who organised the company in a way that was working as a “perfect machine”. John always claimed that a good structure of tasks, duties, clear hierarchies, powers, rules, procedures, and strong leadership is key for immediate market-oriented actions. And for a long time, it was. But Jenny—the new successor—noticed that the company began stagnating and stopped developing and improving. For the last eight years, the company has systematically lost the market. Jenny noticed that team is not creative, and employees use old methods of working that do not work in the new business realities. Jenny decided to let John go. She employed Madeline—an experienced, dynamic improvements enthusiast and transformational leader. Soon it became apparent that there is a misalignment between Madeline’s leadership style and company culture. Madeline welcomed participation, employee involvement, and teamwork. But the team existed for years in a strong hierarchy culture characterized by a well-established structure, control, and stability and had trouble adjusting to Madeline’s leadership style. It became apparent to Madeline that the company culture, which currently does not promote reflection and learning, needs changing. The plan was for Madeline to demonstrate desirable behaviors of teamwork, reflection, and sharing ideas for improvement, so the team can begin modeling these behaviors, and eventually unlearn old habits and cement new ways of doing things and the new culture. Madeline presented an engaging presentation of the new strategy and consequently exposed the new pattern of acting. Next, she taught middle managers to do the same and recognize and reward the best followers for gaining their engagement. Madeline noticed that, however, the headquarters of the company exposed a market type of culture—but some subsidiaries, especially those located a long distance from headquarter, reflected quite different types of cultures, e.g., production subsidiary located in a small town exists in a strong hierarchy culture, sales forces located “everywhere” exist in an adhocracy, and design subsidiary located in the most creative city of the country—co-exist as a clan. The most problematic was the introduction of learning culture including components of mistakes acceptance and learning climate) in hierarchy dominated subsidiaries. Critical thinking needed for learning from mistakes was achieved in the clan culture subsidiary. Adhocracy exposing sales forces developed learning climate but faced some problems with reflection. Regarding sales forces, Madeline noticed that the problem with critical reflection was caused by the former head of the division—Mike. So, Mike was replaced by openminded Tim, who quickly noticed the opportunity for development when working

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with new methods. Madeline noticed that all subsidiaries focused on mistakes avoidance, e.g., production, developed slower. Whereas design and salesforces who developed methods of mistake management—achieved the best effects. The headquarter with a market-oriented culture where Johns’ mirroring was the strongest was transformed by Madeline and achieved the full Leader-Company culture alignment.

14.4 The Introduced Adaptive Self-modeling Network Model The final model constructed comprises 81 different states, a complete overview of all 81 states with their according level can be found in Figs. 14.4 (base level, 47 states), 14.5 (first-order self-modeling level, 20 states), and 14.6 (second-order selfmodeling level, 14 states). The second-order adaptive network model is graphically depicted in Fig. 14.3 with the key elements highlighted in Table 14.5. The base model represents two individual mental models along with a leader and a shared mental model, the individuals interact with the leader periodically and learn a set of tasks (a, b, c). The individual and team learning is influenced by the organisational culture and mistake management. The model was also constructed in a way in which context factors facilitate organisational culture change over time, specifically transitions from one culture to another. An overview of the key stages of the designed network are summarized below: Individual mental models: Oval encapsulations in the base plane represent mental models of certain tasks. Individuals A and B have additional inputs from world observation states that can alter their mental model and reproduction of the tasks. These states are a result of observations and mirroring the leader’s mental Table 14.5 Legend for important elements in the adaptive network model Component

Description

Blue nodes

The blue base-level states represent reproduction

Yellow nodes

The yellow weight states represent attention to world observations

Light purple nodes

The green nodes represent the company culture

Dark purple nodes

The dark purple weight states represent attention to leader interactions

Pink nodes

The pink weight states represent retention and learning

Orange nodes

The orange persistence states represent reinforcement

Green nodes

The green nodes represent feed forward and feedback learning

Blue arrows

The blue arrows are upward connections from a lower-level plane

Red arrows

The red arrows are downward adaptive connections from a higher-level plane

Black arrows

The black arrows are connections from and to states on the same plane level

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Fig. 14.3 The second-order adaptive network model

model combined with Hebbian learning which involves the W-states in the middle of the middle plane. Shared mental model: Represented by the parallelogram encapsulation and is formed by taking input indirectly from individual learning of A and B in by connections between W-states in the first-order self-model level (middle) plane: feed forward learning. It occurs by transfer of knowledge from individual learning states (weight states) to shared learning weight states which directly affect the base-level shared mental model. In turn, individuals can learn from a shared mental model by connections between W-states in the opposite direction in the middle plane: feedback learning. Mistake Handling: The dotted oval represents impartial knowledge for task c. This has a negative weight on mistake recognition (mistM1) so that if both b and c task states are high mistake noticing will be low. Mistake management (mistM2) depends on the mistake noticing state and organisational culture. Leader interactions: Two interaction rounds of leader and individuals regarding each task takes place. All interaction states influence the attention of individuals and thus attention to observations states in the first-order self-model level.

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Nr X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17 X18 X19 X20 X21 X22 X23 X24 X25 X26 X27 X28 X29 X30 X31 X32 X33 X34 X35 X36 X37 X38

Notation a_A_WO b_A_WO c_A_WO a_MA b_MA c_MA a_B_WO b_B_WO c_B_WO a_MB b_MB c_MB a_MS b_MS c_MS a_ML b_ML c_ML delg_L stat_L cons_L rec_L att_A att_B int_a_A1 int_b_A1 int_c_A1 int_a_B1 int_b_B1 int_c_B1 int_a_A2 int_b_A2 int_c_A2 int_a_B2 int_b_B2 int_c_B2 open_L flex_C

X39

pos_C

X40 X41 X42 X43 X44 X45 X46 X47

misM1_A misM1_B misM2_A misM2_B context1 context2 context3 context4

Explanation World observation state for task a for indvidual A World observation state for task b for indvidual A World observation state for task c for indvidual A Mental model state for task a for individual A Mental model state for task b for individual A Mental model state for task c for individual A World observation state for task a for indvidual B World observation state for task b for indvidual B World observation state for task c for indvidual B Mental model state for task a for individual B Mental model state for task b for individual B Mental model state for task c for individual B Shared mental model state for task a Shared mental model state for task b Shared mental model state for task c Mental model state for task a for the leader Mental model state for task b for the leader Mental model state for task c for the leader Delegation of tasks state from the leader Formal organisational status and social status of the leader state Consistency in behaviours of the leader state Recognition for working individuals from the leader state Attention state for individual A Attention state for individual B First interaction state regarding task a for individual A and the leader First interaction state regarding task b for individual A and the leader First interaction state regarding task c for individual A and the leader First interaction state regarding task a for individual B and the leader First interaction state regarding task b for individual B and the leader First interaction state regarding task c for individual B and the leader Second interaction state regarding task a for individual A and the leader Second interaction state regarding task b for individual A and the leader Second interaction state regarding task c for individual A and the leader Second interaction state regarding task a for individual B and the leader Second interaction state regarding task b for individual B and the leader Second interaction state regarding task c for individual B and the leader Openness state of the Leader Flexibility state of the company culture Positioning state of the company culture; high positioning represents external focus and low positioning represents internal focus Mistake noticing state for individual A Mistake noticing state for individual B Mistake management state for individual A Mistake management state for individual B First context factor state Second context factor state Third context factor state Fourth context factor state

Fig. 14.4 Base level states of the model

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Notation

X48

Wa_A_WO,a_MA

X49

Wb_A_WO,b_MA

X50

Wc_A_WO,c_MA

X51

Wa_B_WO,a_MB

X52

Wb_B_WO,b_MB

X53

Wc_B_WO,c_MB

X54

Wa_MA, b_MA

X55

Wb_MA,c_MA

X56

Wa_MB,b_MB

X57

Wb_MB,c_MB

X58

Wa_MS,b_MS

X59

Wb_MS,c_MS

X60

Wa_ML,a_MA

X61

Wb_ML,b_MA

X62

Wc_ML,c_MA

X63

Wa_ML,a_MB

X64

Wb_ML,b_MB

X65

Wc_ML,c_MB

X66

Wculture, flex_C

X67

Wculture, pos_C

377

Explanation Weight self-model state influencing the connection between world observations and mental model of individual A for task a Weight self-model state influencing connection between world observations and mental model of individual A for task b Weight self-model state influencing connection between world observations and mental model of individual A for task c Weight self-model state influencing connection between world observations and mental model of individual B for task a Weight self-model state influencing connection between world observations and mental model of individual B for task b Weight self-model state influencing connection between world observations and mental model of individual B for task c Weight self-model state representing retention, influencing connection from mental model of task a to b for individual A Weight self-model state representing retention, influencing connection from mental model of task b to c for individual A Weight self-model state representing retention, influencing connection from mental model of task a to b for individual B Weight self-model state representing retention, influencing connection from mental model of task b to c for individual B Weight self-model state representing shared learning, influencing shared mental model of task a to b Weight self-model state representing shared learning, influencing shared mental model of task b to c Weight self-model state representing attention between leader and individual A for task a Weight self-model state representing attention between leader and individual A for task b Weight self-model state representing attention between leader and individual A for task c Weight self-model state representing attention between leader and individual B for task a Weight self-model state representing attention between leader and individual B for task b Weight self-model state representing attention between leader and individual B for task c Weight self-model state influencing connection between all culture context factors and flexibility state Weight self-model state influencing connection between all culture context factors and positioning state

Fig. 14.5 First-order self-model states of the model

Leader Qualities: All leader qualities (status, consistency, openness, recognition, and delegation) are represented individually. Recognition state in base-level influences persistence of Hebbian learning (in second-order level) as it reproduces the same effect of strengthening learning. Attention: World observations along with interactions affect the base-level attention state. The attention base-level state indirectly influences individual’s mental model by affecting attention first-order level weight states. First-order level weight states comprise attention to leader interactions and world observations. Leader attention weight states are influenced by status and consistency of the leader. Organisational culture: Adaptiveness of culture is modeled by weight factors in first-order plane which are influenced by the context factors. The thick red lines

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Notation

X68

WW fforw

X69

WW fback

X70 X71 X72 X73 X74 X75 X76 X77

context_fforw1 context_fback1 context_fforw2 context_fback2 MWa_MA,b_MA MWb_MA,c_MA MWa_MB,b_MB MWb_MB,c_MB

X78

HWa_MA,b_MA

X79

HWb_MA,c_MA

X80

HWa_MB,b_MB

X81

HWb_MB,c_MB

Explanation Weight self-model state states for the shared learning weight states, influencing feed forward learning Weight self-model state states for the individual learning weight states, influencing feedback learning First round of context state influencing feedforward learning First round of context state influencing feedback learning Second round of context state influencing feedforward learning Second round of context state influencing feedback learning Persistence self-model state influencing individual learning of A for task b Persistence self-model state influencing individual learning of A for task c Persistence self-model state influencing individual learning of B for task b Persistence self-model state influencing individual learning of B for task c Speed factor self-model state influencing speed of individual learning of A for task b Speed factor self-model state influencing speed of individual learning of A for task c Speed factor self-model state influencing speed of individual learning of B for task b Speed factor self-model state influencing speed of individual learning of B for task c

Fig. 14.6 Second-order self-model states of the model

represent four downwards connections, representing influences from each context factor. Individual learning: Hebbian learning in first-order self-model plane takes place by weight states that influence the connections between mental model components in the base-level. The learning quality is also influenced by second-order states as elaborated below. Learning quality: Persistence and speed factors in the second-order self-model plane influence learning forgetfulness and learning rate; lower persistence values mean more forgetfulness. Learning flows: Feed forward and feedback learning control in the second-order self-model plane influences shared and individual weight states respectively in firstlevel self-model plane. They are affected by context states in second-order self-model plane which control timing of different learning flows. Thick pink lines from the WW -feedforward state represent two downwards connections for individual learning weight states. For a full specification of the model by role matrices, see Sect. 14.11. Through variation of settings of the model described above, it was possible to generate 24 different scenarios that model the 4 types of culture with constant factors as a baseline, and for each type of culture, additional simulations will vary in consistency and status of the leader. An overview of all simulated scenarios is highlighted in Table 14.6.

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Table 14.6 Overview of scenarios modeled with varying culture type and leader qualities #

Culture modeled

Context factors

Consistency

Status

1

Clan

High C1

High

High

2

Market

High C2

High

High

3

Adhocracy

High C3

High

High

4

Hierarchy

High C4

High

High

5

Clan

High C1

Low

Low

6

Market

High C2

Low

Low

7

Adhocracy

High C3

Low

Low

8

Hierarchy

High C4

Low

Low

9

Clan

High C1

High

Low

10

Market

High C2

High

Low

11

Adhocracy

High C3

High

Low

12

Hierarchy

High C4

High

Low

13

Clan

High C1

Low

High

14

Market

High C2

Low

High

15

Adhocracy

High C3

Low

High

16

Hierarchy

High C4

Low

High

17

Hierarchy; Adhocracy

Transition of high C4 to C3

High

High

18

Hierarchy; Clan

Transition of high C4 to C1

High

High

19

Market; Clan

Transition of high C2 to C1

High

High

20

Market; Adhocracy

Transition of high C2 to C3

High

High

21

Adhocracy; Hierarchy

Transition of high C3 to C4

High

High

22

Adhocracy; Market

Transition of high C3 to C2

High

High

23

Clan; Hierarchy

Transition of high C1 to C4

High

High

24

Clan; Market

Transition of high C1 to C2

High

High

14.5 Simulation Results This section displays graphs for the simulation results. The graphs display a gradual increasing effect of learning and mistake management increasing as the flexibility of the organisation increases and its positioning decreases. Prior to displaying the effect of culture on mistake management and learning. Prior to displaying the effect of culture on mistake management and learning. Temporal context will be given in terms of the learning flows and interactions. As indicated in Fig. 14.7, there are two rounds of the individual and leader interactions where each is followed by feed forward learning with feedback learning after.

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Interactions

Feedforward learning

Feedback learning

Fig. 14.7 Timeline of learning flows followed by leader interactions with individuals

14.5.1 Comparison for Different Types of Culture and Leadership As seen in Fig. 14.7, interaction time extends from time point 50–150, which is followed by feed forward and feedback learning. The team learning peaks are aligned with the time of feed forward learning. That is because feed forward learning involves learning flows from micro-level (individual) to meso-level (team). Whereas individual learning does not only depend on the timing of feedback learning flows and is consistently higher because individuals can also learn from their environment, i.e., via world observations. Figure 14.8 shows the effect of flexible culture types on mistake acceptance and organisational learning. Figure 14.9 displays the effect of less flexible cultures on the dependent variables when both consistency and status are low. As shown in Figs. 14.10 and 14.11, the same culture types when consistency and status are high display a big impact on individual learning and mistake management. Team learning on the other hand displays a smaller deviation where consistency and status of the leader are high. The most noticeable difference in team learning values was depicted in the hierarchy culture type. In Figs. 14.12 and 14.13 cases are illustrated for clan and adhocracy culture when both consistency and status are low. Further, Fig. 14.14 displays the effect of the culture type on the dependent variables when consistency is low and status is high. These results are identical when status is low and consistency is high. This

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Clan

381

Adhocracy

Team learning

Individual learning

Mistake management

Fig. 14.8 Overview of the effect of culture on dependent variables when consistency and status are high

Hierarchy

Market

Team learning

Individual learning

Mistake management

Fig. 14.9 Overview of effect of culture on dependent variables when consistency and status are low

supports the notion that both status and consistency play an equally important role in organisational learning and mistake tolerance.

14.5.2 Transition from One Type of Culture to Another One Figure 14.15 displays the simulation where hierarchical culture transitions to clan culture. The graph is in line with the expected results as the transition to a culture with more flexibility has a positive correlation on the dependent variables. The hierarchy culture exists from the beginning till time point 450, whereas clan begins from that point on.

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Team learning

Individual learning

Mistake management

Fig. 14.10 Hierarchy culture when both consistency and status are high

Team learning

Individual learning

Fig. 14.11 Market culture when both consistency and status are high

Mistake management

14 Computational Simulation of the Effects of Different Culture Types …

Team learning

Individual learning

Mistake management

Fig. 14.12 Clan culture when both consistency and status are low

Team learning

Individual learning

Mistake management

Fig. 14.13 Adhocracy culture when both consistency and status are low

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Adhocracy

Hierarchy

Market

Team learning

Individual learning

Mistake management

Fig. 14.14 Overview of effect of culture on dependent variables when just one of consistency or status is low

Team learning

Individual learning

Mistake management

Fig. 14.15 Transition from Hierarchy to Clan culture when consistency and status are both high

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14.6 Statistical Analysis Statistical analysis was carried out to compare the 24 scenarios according to the culture type and leader characteristics. The numerical simulation output was measured for the three dependent variables considered: individual learning, team learning, and mistake management. Since the scenarios only vary in culture and leader behavior, the simulations reproduce consistent mistake management, individual and team learning variances. Thus, the simulations were seen as one population that assumes homoscedasticity, that is equal variances among the dependent variables. Moreover, since each simulation is independent of the other simulation its compared to, an independent samples statistical test is used. A Wilcoxon-ranksum nonparametric test, equivalent to Mann Whitney U-test, was utilized. The test considers the summed rank scores to derive a statistical score and a p-value which is considered with a 95% confidence level (α = 0.05). The results were processed using a Python-IDE and an open-source scientific library (SciPy) to carry out the rank-sum test. The graphical output was first stored as excel files that show the state values at each time point (∆t = 0.25). The files were then converted to pandas dataframe split into individual dataframes for each dependent variable, which were then refined into a smaller time frame which excludes the first and last 50 time points in order to ensure significant data points. The scenarios were then compared with each other according to different cultures or the same culture and different leader behavior. A total of 54 comparisons were calculated measuring the statistical difference in individual learning, team learning, and mistake management. All statistical comparisons were significant as the p-value was much lower than the significance level (p-value ≤0.03, where α = 0.05) except for the gray-colored cells which proved to be insignificant differences. Thus, we can reject the null hypotheses as the presence of these non-significant results are still inline and support the research hypotheseses (Fig. 14.16).

14.7 Computational Network Analysis In this section, following Hendrikse et al. (2023) first in Sect. 14.7.1 it is shown how any smooth dynamical system can be modeled by a network representation in a canonical manner and any smooth adaptive dynamical system by a self-modeling network. Next, in Sect. 14.7.2 it is shown how stationary point and equilibrium analysis can be applied for simulations of a self-modeling network and used to verify correctness of such a model. This is illustrated for the four main scenarios for the model introduced in the current chapter.

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Culture types compared Clan Market Clan Adhocracy Clan Hierarchy Clan Clan Clan Clan Clan Clan Market Adhocracy Market Hierarchy Market Market Market Adhocracy Market Market Adhocracy Hierarchy Adhocracy Adhocracy Adhocracy Adhocracy Adhocracy Adhocracy Hierarchy Hierarchy Hierarchy Hierarchy Hierarchy Hierarchy Clan Market Clan Adhocracy Clan Hierarchy Clan Clan Clan Clan Market Adhocracy Market Hierarchy Market Market Market Market Adhocracy Hierarchy Adhocracy Adhocracy Adhocracy Adhocracy Hierarchy Hierarchy Hierarchy Hierarchy Clan Market Clan Adhocracy Clan Hierarchy Clan Clan Market Adhocracy Market Hierarchy Market Market Adhocracy Clan Adhocracy Adhocracy Hierarchy Hierarchy Clan Market Clan Adhocracy Clan Hierarchy Market Adhocracy Market Hierarchy Adhocracy Hierarchy Hierarchy; Hierarchy; Adhocracy Clan Hierarchy; Market; Adhocracy Adhocracy Market; Market; Clan Adhocracy Adhocracy; Adhocracy; Hierarchy Market Adhocracy; Clan; Hierarchy Hierarchy Clan; Clan; Market Hierarchy

Team Learning

Mistake Management

Leader Score P-value HSHC 69.27662 0.0 HSHC 62.25069 0.0 HSHC -51.29402 0.0 HSHC 69.27662 0.0 HSHC 68.75828 0.0 HSHC 68.75828 0.0 HSHC -69.27662 0.0 HSHC -51.29400 0.0 HSHC -55.09626 0.0 HSHC -59.71010 0.0 HSHC -59.71010 0.0 HSHC 56.60092 0.0 HSHC 68.47170 0.0 HSHC 68.79041 0.0 HSHC 68.79041 0.0 HSHC 65.41832 0.0 HSHC 65.20138 0.0 HSHC 65.20138 0.0 LSLC 69.27662 0.0 LSLC 69.05981 0.0 LSLC 69.27662 0.0 LSLC -60.68702 0.0 LSLC -60.68702 0.0 LSLC -66.71987 0.0 LSLC 65.28680 0.0 LSLC 50.37728 0.0 LSLC 50.37728 0.0 LSLC 68.29480 0.0 LSLC 54.44473 0.0 LSLC 54.44473 0.0 LSLC 38.98327 0.0 LSLC 38.98327 0.0 LSHC 69.27662 0.0 LSHC 69.27662 0.0 LSHC 69.27662 0.0 LSHC 0.00000 1.0 LSHC -69.27662 0.0 LSHC 69.27662 0.0 LSHC 0.00000 1.0 LSHC 69.27662 0.0 LSHC 0.00000 1.0 LSHC 0.00000 1.0 HSLC 69.27662 0.0 HSLC 69.27662 0.0 HSLC 69.27662 0.0 HSLC -69.27662 0.0 HSLC 69.27662 0.0 HSLC 69.27662 0.0

Score 4.80910 2.84896 3.72988 3.74788 3.72439 3.72439 -4.79992 -4.16224 -2.15863 -2.11160 -2.11160 3.50283 4.23375 4.23413 4.23413 6.18403 6.18402 6.18402 4.43059 3.83224 6.26334 -2.99761 -2.99761 -4.02528 5.70471 1.68408 1.68408 6.04770 2.45757 2.45757 2.30323 2.30323 4.48061 3.84604 6.27496 0.00000 -4.02593 5.70433 0.00000 6.04651 0.00000 0.00000 4.48061 3.84604 6.27496 -4.02593 5.70433 6.04651

P-value 1.52 10-06 0.00439 0.00019 0.00018 0.00020 0.00020 1.59 10-06 3.15 10-05 0.03088 0.03472 0.03472 0.00046 2.30 10-05 2.29 10-05 2.29 10-05 6.25 10-10 6.25 10-10 6.25 10-10 9.40 10-06 0.00013 3.77 10-10 0.00272 0.00272 5.69 10-05 1.17 10-08 0.09217 0.09217 1.47 10-09 0.01399 0.01399 0.02127 0.02127 7.44 10-06 0.00012 3.50 10-10 1.00 5.68 10-05 1.17 10-08 1.00 1.48 10-09 1.00 1.00 7.44 10-06 0.00012 3.50 10-10 5.68 10-05 1.17 10-08 1.48 10-09

Score 69.27662 69.27662 69.27662 69.27662 68.91859 68.91859 69.27662 -51.73025 -69.27662 -69.27662 -69.27662 69.27662 69.27662 69.27662 69.27662 67.28492 68.07295 68.07295 69.27662 69.27662 69.27662 -67.64447 -67.64447 -69.27662 69.27662 69.27662 69.27662 69.27662 69.27662 69.27662 69.27662 38.98327 69.27662 69.27662 69.27662 0.00000 -69.27662 69.27662 0.00000 69.27662 0.00000 0.00000 69.27662 69.27662 69.27662 -69.27662 69.27662 69.27662

P-value 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 1.0 0.0 1.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0

HSHC -13.92681 4.35 10-44

0.70973

0.47787

-17.03181

4.77 10-65

HSHC 22.80623 3.98 10-115

1.69005

0.09102

1.55944

0.11889202

-35

0.73567

0.46193

16.93995

2.28 10-64

HSHC 13.75686 4.63 10-43

0.96089

0.33661

-20.73143

1.80 10-95

HSHC -33.90828 5.03 10-252

0.99430

0.32008

-17.24027

1.32 10-66

HSHC -10.32306 5.54 10-25

0.72952

0.46569

16.49104

4.26 10-61

HSHC 12.43436 1.70 10

Fig. 14.16 Statistical analysis results

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14.7.1 The Canonical Self-modeling Network Representation of an Adaptive Dynamical System It is common to represent dynamical systems in a mathematical format, see Ashby (1960, pp. 241–252). Such dynamical systems comprise of a finite set of states, also referred to as state variables X 1 , …, X n , where the changes of the states over time are defined via functions X 1 (t), …, X n (t) of time t. As further elucidated in Port and van Gelder (1995), a dynamical system is a statedetermined system which means that they can be described by a rule of evolution that expresses how, for each time point t the future value of each state X i at time t + s uniquely depends on s and on X 1 (t), …, X n (t). This can be described via n functions F i (X 1 , …, X n , s) for each X i in the following manner (see also Ashby 1960, pp. 243–244): X i (t + s) = Fi (X 1 (t), . . . , X n (t), s) for s > 0

(14.2)

Note that a transitivity rule holds for s = s' + s'' with s' , s'' > 0; this can be derived as follows.      X i t + s ' + s '' = Fi X 1 (t), . . . , X n (t), s ' + s ''          X i t + s ' + s '' = Fi X 1 t + s ' , . . . , X n t + s ' , s ''

(14.3)

Since within the latter equation for all j it holds     X j t + s ' = F j X 1 (t), . . . , X n (t), s ' it can be derived          X i t + s ' + s '' = Fi F1 X 1 (t), . . . , X n (t), s ' , . . . , Fn X 1 (t), . . . , X n (t), s ' , s ''

(14.4) Therefore,      Fi X 1 (t), . . . , X n (t), s ' + s '' = X i t + s ' + s ''    = X i t + s ' + s ''       = Fi F1 X 1 (t), . . . , X n (t), s ' , . . . , Fn X 1 (t), . . . , X n (t), s ' , s ''

(14.5)

So, the following transitivity rule is obtained for any state-determined system:         Fi X 1 (t), . . . , X n (t), s ' + s '' = Fi F1 X 1 (t), . . . , X n (t), s ' , . . . , Fn X 1 (t), . . . , X n (t), s ' , s ''

(14.6)

This is a reformulation in a slightly different format of Theorem 19/8 in Ashby (1960, p. 244).

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A dynamical system is referred to as smooth if the functions F i and the X i are continuously differentiable. It turns out that any smooth dynamical system can be represented in a canonical network representation. Here the canonical temporalcausal network representation of it is defined by ω X j ,X i , c X i , η X i for all i and j with c X i (V1 , . . . , Vn ) = Vi + [∂ Fi (V1 , . . . , Vn , s)/∂s]s=0 ω X j ,X i = 1 for all i and j η X i = 1 for all i

(14.7)

As described by Eq. (14.1) in Sect. 14.3.1, this network representation has dynamics induced by the following canonical differential equations.     dX i (t)/dt = η X i c X i ω X 1 ,X i X 1 (t), . . . , ω X n ,X i X n (t) − X i (t)

(14.8)

This canonical transformation is described by the following theorems. Theorem 14.1 Any smooth dynamical system can be formalized in a canonical manner by a temporal-causal network model called its canonical network representation. Conversely, any temporal-causal network model is a dynamical system model. Proof of Theorem 14.1 Suppose such a smooth dynamical system is given. Consider Eq. (14.2) where the functions F i are continuously differentiable. By continuity, in the particular case of s = 0 it holds X i (t) = Fi (X 1 (t), . . . , X n (t), 0)

(14.9)

Now assume s > 0. Subtracting (14.9) from (14.2) and dividing the results by s provides: 

 X j (t + s) − X i (t) /s = [Fi (X 1 (t), . . . , X n (t), s) − F(X 1 (t), . . . , X n (t), 0)]/s (14.10)

When the limit for s > 0 very small, approaching 0 is taken, the left-hand side becomes dX i (t)/dt and the right-hand side [∂ Fi (X 1 (t), . . . , X n (t), s)/∂s]s=0 It follows that dX i (t)/dt = [∂ Fi (X 1 (t), . . . , X n (t), s)/∂s]s=0

(14.11)

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Now define the function gi (V 1 , …, V n ) by gi (V1 , . . . , Vn ) = Vi + [∂ Fi (V1 , . . . , Vn , s)/∂s]s=0

(14.12)

Then it holds dX i (t)/dt = [∂ Fi (X 1 (t), . . . , X n (t), s)/∂s]s=0 = gi (X 1 (t), . . . , X n (t)) − X i (t)

(14.13)

From this it immediately follows that     dX i (t)/dt = η X i c X i ω X 1 ,X i X 1 (t), . . . , ω X n ,X i X n (t) − X i (t)

(14.14)

with η X i = 1, c X i = gi for all i, and ω X j ,X i = 1 for all i and j. This shows that any given smooth dynamical system can be formalised in a canonical manner in temporal-causal network format. ∎ Furthermore, applying the above to both a base dynamical system and the dynamical system for its adaptation model will yield a self-modeling network representation of any smooth adaptive dynamical system. For more details, see Hendrikse et al. (2023). Theorem 14.2 Any adaptive smooth dynamical system model can be transformed in a canonical manner into a self-modeling network model called its canonical selfmodeling network representation. Conversely, any self-modeling network model is an adaptive dynamical system model. These also apply to higher-order adaptive dynamical systems in relation to higher-order self-modeling networks.

14.7.2 Analysis of Stationary Points and Equilibria This network-oriented perspective has been applied to perform computational network analysis of the model’s dynamics, in particular stationary points for the model presented in this chapter. Generally, there are certain characteristics that are often considered for equilibrium analysis of dynamical systems. These following types of properties are elaborated below. Let Y be a network state • Y has a stationary point at t if dY (t)/dt = 0. • The network model is in equilibrium at t if every state Y of the model has a stationary point at t. More specifically, criteria in terms of the network characteristics ωX,Y , cY , ηY for network model dynamics can be considered. Let Y be a state and X 1 , …, X k the states connected toward Y. For nonzero speed factors ηY the following criteria in terms of network characteristics for connectivity and aggregation apply; here aggimpact Y (t) = cY (ω X 1 ,Y X 1 (t), . . . , ω X k ,Y X k (t)):

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• Y has a stationary point at t ⇔ aggimpact Y (t) = Y (t). • The network model is in equilibrium a t ⇔ aggimpact Y (t) = Y (t) for every state Y. These criteria for a network showing a stationary point or an equilibrium (assuming nonzero speed factors) depends on both the connections weights ωX,Y used for connectivity and on the combination function cY used for aggregation. Note that in a self-modeling network, these criteria can be applied to both base states and the self-model states. In the latter case they can be used for equilibrium analysis of learning processes. By analysis through verifying these criteria for a sample of states and time points in one or more example simulation scenarios, evidence can be obtained that the implemented network model is correct compared to its design specifications. Such an analysis was caried out for four scenarios varying in organizational culture. For each of the four scenarios, the dependent variables were analyzed at four different time stamps, accumulating in samples of twelve timepoints each. Note that the characteristics of each scenario (i.e., high/low status or consistency) are irrelevant since the equilibrium analysis concerns the correctness of the actual model in alignment with the connection weights and aggregation functions, rather than the states themselves. Tables 14.7, 14.8, 14.9, and 14.10 summarize the results of the equilibrium analysis for each scenario. All results show significantly low deviation values across all dependent variables, strengthening evidence for the correctness of the model. In general deviation values lower than 0.001 are considered significant, resulting in statistically significant small deviation values across all states and time points in the chosen sample. Table 14.7 Computational network analysis for the Ahhocry culture scenario Adhocracy culture—high status and consistency Description

State X i

Time point t

Value X i (t)

aggimpactXi (t)

Deviation

Feed forward learning

X 58

300

0.999857

0.999920605

−6.4 10–5

Feed forward learning

X 58

232.75

0.999857

0.999920605

6.39 10–5

Feed forward learning

X 58

632

0.999857

0.999920605

6.39 10–5

Feed forward learning

X 58

700

0.999857

0.999920605

6.38 10–5

Feedback learning

X 54

800

0.993147

0.993505591

−0.00036

Feedback learning

X 54

413

0.993147

0.993505591

0.000358

Feedback learning

X 54

378

0.993147

0.993505591

0.000358

Feedback learning

X 54

535

0.994144

0.994501374

0.000357

Mistake management

X 43

170

0.67673

0.676526867

0.000204

Mistake management

X 43

535

0.656852

0.656851618

−8.6 10–7

Mistake management

X 43

645.5

0.669349

0.669351519

2.82 10–6

Mistake management

X 43

320

0.669442

0.669440371

−1.7 10–6

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Table 14.8 Computational network analysis for the clan culture scenario Clan culture—low status and consistency Description

State X i

Time point t

Value X i (t)

aggimpactXi (t)

Deviation

Feed forward learning

X 58

271.5

0.001443

0.00145265

−9.3 10–6

Feed forward learning

X 58

699.75

0.0015

0.001509123

8.84 10–6

Feed forward learning

X 58

287.25

0.001415

0.999920605

0.001425

Feed forward learning

X 58

295.75

0.001401

0.001410928

9.65 10–6

Feedback learning

X 54

884.75

0.008941

0.008966782

−2.6 10–5

Feedback learning

X 54

437.75

0.010329

0.010499964

0.000171

Feedback learning

X 54

247.75

0.010333

0.010342074

8.67 10–6

Feedback learning

X 54

452

0.008883

0.008912124

2.93 10–5

Mistake management

X 43

844.5

0.754167

0.754166676

7.04 10–9

Mistake management

X 43

395

0.754167

0.754166649

−6.7 10–9

Mistake management

X 43

659

0.754169

0.754169342

−3.7 10–8

Mistake management

X 43

435.75

0.754166

0.754166466

−4.7 10–9

Table 14.9 Computational network analysis for the market culture scenario Market culture—high consistency and low status Description

State X i

Time point t

Value X i (t)

aggimpactXi (t)

Feed forward learning

X 58

300

0.000837

0.001088447

Deviation −0.00025

Feed forward learning

X 58

224

0.000844

0.001089107

0.000245

Feed forward learning

X 58

620

0.000844

0.001089072

0.000245

Feed forward learning

X 58

699

0.000844

0.001089112

0.000245

Feedback learning

X 54

210

0.005989

0.006365808

−0.00038

Feedback learning

X 54

107.5

0.008257

0.008771557

0.000515

Feedback learning

X 54

429

0.005989

0.006365727

0.000376

Feedback learning

X 54

604

0.00599

0.006365971

0.000376

Mistake management

X 43

610

0.360204

0.36020375

9.12 10–10

Mistake management

X 43

766

0.360204

0.360203747

8.33 10–12

Mistake management

X 43

508

0.360067

0.360066992

2.87 10–9

Mistake management

X 43

372

0.360204

0.360203747

2.39 10–12

14.8 Discussion This chapter uses material from Samhan et al. (2022). The dynamics of the introduced adaptive network model has been verified on correctness in Sect. 14.7 for four different simulations by stationary point analysis. Moreover, according to the simulation results and statistical analysis, it is clear that culture in accordance with certain transformational leadership qualities plays a role in mistake acceptance and organisational learning. The simulations provide a clear visual indicator of the effect on

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Table 14.10 Computational network analysis for the hierarchy culture scenario Hierarchy culture—low consistency and high status Description

State X i

Time point t

Value X i (t)

aggimpactXi (t)

Deviation

Feed forward learning

X 58

300

0.001128

0.001455381

−0.00033

Feed forward learning

X 58

224

0.001128

0.001455423

0.000327

Feed forward learning

X 58

625

0.001128

0.00145542

0.000327

Feed forward learning

X 58

700

0.001128

0.001455381

0.000327

Feedback learning

X 54

843

0.007925

0.008303202

−0.00038

Feedback learning

X 54

115

0.010988

0.011507428

0.000519

Feedback learning

X 54

240

0.007925

0.008303225

0.000379

Feedback learning

X 54

520

0.010989

0.011508014

0.000519

Mistake management

X 43

40

0.155733

0.155733492

−2.3 10–7

Mistake management

X 43

104

0.155655

0.155654508

−8.6 10–8

Mistake management

X 43

350

0.15573

0.155729809

−9.3 10–15

Mistake management

X 43

656

0.15573

0.155729809

−1.1 10–11

the dependent variables: individual learning, team learning, and mistake acceptance. But they also demonstrate significant statistical results from each other. The statistical analysis in Sect. 14.6 aimed to provide statistical significance in simulation comparisons to support the research hypotheses: 1. Higher flexibility and discretion in organisational culture results in better mistake management and thus better organisational learning 2. Effective organisational learning requires a transformational leader to have both high social and formal status and consistency. 3. Company culture and leader’s behavior must align for the best learning effects. Twelve of the non-statistically significant results are in accordance with the second hypothesis. These non-significant values show that alternating low consistency or status when the other is high is not significantly different from each other; as one of them being low demonstrates the same effect as the other being low. Lack of high consistency or status hinder the imitation phase making the retention much lower in such scenarios. In that regard there is limited learning from the leader and only team learning and learning from world observations. This supports that for optimal results both consistency and status require to be high. Further, this aligns not only with the second hypothesis but also the third hypothesis as having a culture with high flexibility and discretion and high transformational leadership qualities, such as consistency and status, achieves the best results in terms of organisational learning. Finally, all statistically significant results (non-gray cells) support the first hypothesis as higher flexibility always resulted in better individual learning and mistake management. Notably, team learning did not result in statistically significant differences. There are two instances, besides culture transitioning scenarios, in which team learning had insignificant difference (p-value ≥ 0.05). This can be because team learning values are completely dependent on the incoming connections from individual learning values. Thus, when individual learning is significantly high, team learning values will consistently result in the same pattern displaying higher values

14 Computational Simulation of the Effects of Different Culture Types …

393

than individual learning. This pattern, however, was not evident in all culture simulations. Hierarchy with low status or consistency, for instance, resulted in significantly low level of individual learning which was not enough to surpass the threshold to increase team learning level more.

14.9 Limitations and Future Research As evident from this chapter and the field of Management Science, organisational studies suffer from ample factors to account for. Leadership, for instance, has multiple different behavior frameworks to consider. This chapter solely investigates mistake tolerance and organisational learning while varying consistency and status of the leader, where other leadership behaviors are aligned and dependent on the organisational culture. The increasingly complex scenario combinations limit the possibility to explore the effect of leadership practices independent of the culture. Future research can isolate the causality of leadership practices with culture and forecast different scenarios. For instance, future research can further explore whether the organisation size resembling a large company or SMEs (Small and medium-sized enterprises) play a role in mistake tolerance and organisational learning. Further, some studies have shown that discrepancies in exposure level or uneven implementation of LEB practices can cause a negative effect in relation to individual behavior empowerment (Chénard Poirier et al. 2017). Future research can also further explore the effect of leadership practices with different frameworks of effective leadership in relation to culture. For example, the model can include states taking account of the Leadership Practices Inventory (LPI) developed by Kouzes and Posner (2012). In addition, research can also explore if adaptation of mistake acceptance would result in having a curvilinear relation with organisational learning. That is, if mistake tolerance was extremely high would that affect organisational learning negatively or not have an influence at some point? There are numerous possibilities to explore more intricate organisational contexts while utilizing a computational self-modeling network environment.

14.10 Conclusion In conclusion, the chapter aimed to investigate the following research hypotheses: 1. Higher flexibility and discretion in organisational culture results in better mistake management and thus better organisational learning 2. Effective organisational learning requires a transformational leader to have both high social and formal status and consistency. 3. Company culture and leader’s behavior must align for the best learning effects. Computational simulations of the adaptive network were analyzed in different contexts varying in organisation culture and leader characteristics. Statistical analysis results proved to be significant and supported the research hypotheses.

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Ultimately, this chapter provides insight into how flexible organisations that foster a mistake-tolerant attitude in alignment with the leader, can result in significantly better organisational learning on a team and individual level.

14.11 Appendix: The Role Matrices Specification of the Model In Fig. 14.17 and further, the different role matrices are shown that define a full specification of the the adaptive network model in a standardised table format. In each role matrix, each state has its row where it is listed which are the impacts on it from that role. Role matrices for connectivity characteristics The connectivity characteristics are specified by role matrices mb and mcw shown in Figs. 14.17 and 14.18. Role matrix mb each lists the other states (at the same or lower level) from which the state addressed by that row gets its incoming connections, while in role matrix mcw the connection weights are listed for these connections. In mcw, nonadaptive connection weights are indicated (in Fig. 14.18) by a number (in a green shaded cell) and adaptive connection weights are indicated by a reference to the (self-model) state representing the adaptive value (in a peach-red shaded cell). In Fig. 14.20 this can be seen at the base level rows for states X4 to X6 , X10 to X12 , X14 to X15 , X38 to X39 , Similarly, at the first-order self-model level this can be seen for states X54 to X59 . Role matrices for aggregation characteristics The network characteristics for aggregation are defined by the selection of combination functions from the library and values for their parameters. In role matrix mcfw it is specified by weights which state uses which combination function; see Fig. 14.19. In role matrix mcfp (see Fig. 14.20) it is indicated what the parameter values are for the chosen combination functions. Role matrices for timing characteristics In Fig. 14.21, the role matrix ms for speed factors is shown. This lists all speed factors. Also for ms some entries are adaptive: the speed factors of states X54 to X57 are represented by (second-order) self-model states. Finally, the list of initial values can be found in Fig. 14.22.

14 Computational Simulation of the Effects of Different Culture Types … mb 1 2 3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17 X18 X19 X20 X21 X22 X23 X24 X25 X26 X27 X28 X29 X30 X31 X32 X33 X34 X35 X36 X37 X38 X39 X40 X41

base connectivity a_A_WO b_A_WO c_A_WO a_MA b_MA c_MA a_B_WO b_B_WO c_B_WO a_MB b_MB c_MB a_MS b_MS c_MS a_ML b_ML c_ML delg_L stat_L cons_L rec_L att_A att_B int_a_A1 int_b_A1 int_c_A1 int_a_B1 int_b_B1 int_c_B1 int_a_A2 int_b_A2 int_c_A2 int_a_B2 int_b_B2 int_c_B2 open_L flex_C pos_C misM1_A misM1_B

Fig. 14.17 Role matrix mb

1 X1 X1 X2 X1 X2 X3 X7 X7 X8 X7 X8 X9 X19 X13 X14 X16 X16 X17 X38 X20 X21 X38 X1 X7 X25 X26 X27 X28 X29 X30 X31 X32 X33 X34 X35 X36 X38 X44 X44 X5 X11

2

3

X16 X4 X5

X19 X17 X18

X16 X10 X11

X19 X17 X18

395

4

5

6

7

8

9

X26 X29

X27 X30

X31 X34

X32 X35

X33 X36

X39

X39 X2 X8

X3 X9

X25 X28

X39 X45 X45 X6 X12

X46 X46 X38 X38

X47 X47 X39 X39

396

N. Samhan et al. X42 X43 X44 X45 X46 X47 X48 X49 X50 X51 X52 X53 X54 X55 X56 X57 X58 X59 X60 X61 X62 X63 X64 X65 X66 X67 X68 X69 X70 X71 X72 X73 X74 X75 X76 X77 X78 X79 X80 X81

misM2_A misM2_B context1 context2 context3 context4 Wa_A_WO,a_MA Wb_A_WO,b_MA Wc_A_WO,c_MA Wa_B_WO,a_MB Wb_B_WO,b_MB Wc_B_WO,c_MB Wa_MA, b_MA Wb_MA,c_MA Wa_MB,b_MB Wb_MB,c_MB Wa_MS,b_MS Wb_MS,c_MS Wa_ML,a_MA Wb_ML,b_MA Wc_ML,c_MA Wa_ML,a_MB Wb_ML,b_MB Wc_ML,c_MB Wculture, flex_C Wculture, pos_C WW fforw WW fback context_fforw1 context_fback1 context_fforw2 context_fback2 MWa_MA,b_MA MWb_MA,c_MA MWa_MB,b_MB MWb_MB,c_MB HWa_MA,b_MA HWb_MA,c_MA HWa_MB,b_MB HWb_MB,c_MB

Fig. 14.17 (continued)

X38 X38 X44 X45 X46 X47 X23 X23 X23 X24 X24 X24 X4 X5 X10 X11 X54 X55 X21 X21 X21 X21 X21 X21 X44 X44 X70 X71 X70 X71 X72 X73 X22 X22 X22 X22 X4 X5 X10 X11

X39 X39

X40 X41

X5 X6 X11 X12 X56 X57 X20 X20 X20 X20 X20 X20 X45 X45 X72 X73

X54 X55 X56 X57 X58 X59

X58 X42 X58 X43

X46 X46

X47 X47

X54 X55 X56 X57 X5 X6 X11 X12

X44 X44 X44 X44 X54 X55 X56 X57

X45 X45 X45 X45

X59 X59

X46 X46 X46 X46

X47 X47 X47 X47

14 Computational Simulation of the Effects of Different Culture Types … mcw X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17 X18 X19 X20 X21 X22 X23 X24 X25 X26 X27 X28 X29 X30 X31 X32 X33 X34 X35 X36 X37 X38 X39 X40

connection weights a_A_WO b_A_WO c_A_WO a_MA b_MA c_MA a_B_WO b_B_WO c_B_WO a_MB b_MB c_MB a_MS b_MS c_MS a_ML b_ML c_ML delg_L stat_L cons_L rec_L att_A att_B int_a_A1 int_b_A1 int_c_A1 int_a_B1 int_b_B1 int_c_B1 int_a_A2 int_b_A2 int_c_A2 int_a_B2 int_b_B2 int_c_B2 open_L flex_C pos_C misM1_A

Fig. 14.18 Role matrix mcw

1 1 1 1 X48 X49 X50 1 1 1 X51 X49 X53 1 X58 X59 1 1 1 0.9 1 1 0.9 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X66 X67 1

2

3

X60 X54 X55

0.7 X61 X62

X63 X56 X57

0.7 X64 X65

397

4

5

6

7

8

9

1 1

1 1

1 1

1 1

1 1

-0.1

-0.1 1 1

1 1

1 1

1 X66 X67 -1

X66 X67 1

X66 X67 1

398

N. Samhan et al. X40 X41 X42 X43 X44 X45 X46 X47 X48 X49 X50 X51 X52 X53 X54 X55 X56 X57 X58 X59 X60 X61 X62 X63 X64 X65 X66 X67 X68 X69 X70 X71 X72 X73 X74 X75 X76 X77 X78 X79 X80 X81

misM1_A misM1_B misM2_A misM2_B context1 context2 context3 context4 Wa_A_WO,a_MA Wb_A_WO,b_MA Wc_A_WO,c_MA Wa_B_WO,a_MB Wb_B_WO,b_MB Wc_B_WO,c_MB Wa_MA, b_MA Wb_MA,c_MA Wa_MB,b_MB Wb_MB,c_MB Wa_MS,b_MS Wb_MS,c_MS Wa_ML,a_MA Wb_ML,b_MA Wc_ML,c_MA Wa_ML,a_MB Wb_ML,b_MB Wc_ML,c_MB Wculture, flex_C Wculture, pos_C WW fforw WW fback context_fforw1 context_fback1 context_fforw2 context_fback2 MWa_MA,b_MA MWb_MA,c_MA MWa_MB,b_MB MWb_MB,c_MB HWa_MA,b_MA HWb_MA,c_MA HWa_MB,b_MB HWb_MB,c_MB

Fig. 14.18 (continued)

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X68 X68 0.65 0.65 0.65 0.65 0.65 0.65 1.5 0.1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

-1 -1 1 1

1 1 1 1

1 1

1 1 1 1 X68 X68 0.65 0.65 0.65 0.65 0.65 0.65 0.1 0.7 1 1

1 1 1 1 0.8 0.8

X69 1 X69 1

0.5 0.5

0.45 0.45

1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1

1 1 1 1

X69 X69

1 1 1 1

1 1 1 1

14 Computational Simulation of the Effects of Different Culture Types … Fig. 14.19 Role matrix mcfw

mcfw X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17 X18 X19 X20 X21 X22 X23 X24 X25 X26 X27 X28 X29 X30 X31 X32 X33 X34 X35 X36 X37 X38 X39 X40

combination function weights a_A_WO b_A_WO c_A_WO a_MA b_MA c_MA a_B_WO b_B_WO c_B_WO a_MB b_MB c_MB a_MS b_MS c_MS a_ML b_ML c_ML delg_L stat_L cons_L rec_L att_A att_B int_a_A1 int_b_A1 int_c_A1 int_a_B1 int_b_B1 int_c_B1 int_a_A2 int_b_A2 int_c_A2 int_a_B2 int_b_B2 int_c_B2 open_L flex_C pos_C misM1_A

1

399

2

3

4

5

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

400 Fig. 14.19 (continued)

N. Samhan et al. X41 X42 X43 X44 X45 X46 X47 X48 X49 X50 X51 X52 X53 X54 X55 X56 X57 X58 X59 X60 X61 X62 X63 X64 X65 X66 X67 X68 X69 X70 X71 X72 X73 X74 X75 X76 X77 X78 X79 X80 X81

misM1_B misM2_A misM2_B context1 context2 context3 context4 Wa_A_WO,a_MA Wb_A_WO,b_MA Wc_A_WO,c_MA Wa_B_WO,a_MB Wb_B_WO,b_MB Wc_B_WO,c_MB Wa_MA, b_MA Wb_MA,c_MA Wa_MB,b_MB Wb_MB,c_MB Wa_MS,b_MS Wb_MS,c_MS Wa_ML,a_MA Wb_ML,b_MA Wc_ML,c_MA Wa_ML,a_MB Wb_ML,b_MB Wc_ML,c_MB Wculture, flex_C Wculture, pos_C WW fforw WW fback context_fforw1 context_fback1 context_fforw2 context_fback2 MWa_MA,b_MA MWb_MA,c_MA MWa_MB,b_MB MWb_MB,c_MB HWa_MA,b_MA HWb_MA,c_MA HWa_MB,b_MB HWb_MB,c_MB

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

14 Computational Simulation of the Effects of Different Culture Types …

mcfp X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17 X18 X19 X20 X21 X22 X23 X24 X25 X26 X27 X28 X29 X30 X31 X32 X33 X34 X35 X36 X37 X38 X39 X40

combination function parameter values a_A_WO b_A_WO c_A_WO a_MA b_MA c_MA a_B_WO b_B_WO c_B_WO a_MB b_MB c_MB a_MS b_MS c_MS a_ML b_ML c_ML delg_L stat_L cons_L rec_L att_A att_B int_a_A1 int_b_A1 int_c_A1 int_a_B1 int_b_B1 int_c_B1 int_a_A2 int_b_A2 int_c_A2 int_a_B2 int_b_B2 int_c_B2 open_L flex_C pos_C misM1_A

Fig. 14.20 Role matrix mcfp

401

id

alogistic

maxhebb

stepmod

steponce

1

2

3

4

5

5 5 5

1.1 1.5 1.5

5 5 5 5 5 5

1.1 1.5 1.5 1 1.5 1.5

5 5 5

0.3 0.3 0.7

5 5 5 5

1.5 0.7 2.7 2.7 50 50 50 50 50 50 450 450 450 450 450 450

5 5 5 5

0.5 0.5 0.5 0.5

150 150 150 150 150 150 550 550 550 550 550 550

402

N. Samhan et al. X41 X42 X43 X44 X45 X46 X47 X48 X49 X50

misM1_B misM2_A misM2_B context1 context2 context3 context4 Wa_A_WO,a_MA Wb_A_WO,b_MA Wc_A_WO,c_MA

5 5 5

5 5 5

1.5 1.5 1.5

X51 X52 X53 X54 X55 X56 X57 X58 X59 X60 X61 X62 X63 X64 X65 X66 X67 X68 X69 X70 X71 X72 X73 X74 X75 X76 X77 X78 X79 X80 X81

Wa_B_WO,a_MB Wb_B_WO,b_MB Wc_B_WO,c_MB Wa_MA, b_MA Wb_MA,c_MA Wa_MB,b_MB Wb_MB,c_MB Wa_MS,b_MS Wb_MS,c_MS Wa_ML,a_MA Wb_ML,b_MA Wc_ML,c_MA Wa_ML,a_MB Wb_ML,b_MB Wc_ML,c_MB Wculture, flex_C Wculture, pos_C WW fforw WW fback context_fforw1 context_fback1 context_fforw2 context_fback2 MWa_MA,b_MA MWb_MA,c_MA MWa_MB,b_MB MWb_MB,c_MB HWa_MA,b_MA HWb_MA,c_MA HWa_MB,b_MB HWb_MB,c_MB

5 5 5

1.5 1.5 1.5

Fig. 14.20 (continued)

0.5 1.6 1.6 0 0 0 0

900 900 900 900

200 300 600 700

300 400 700 800

X74 X75 X76 X77 5 5 5 5 5 5 5 5 5 5 5 5

5 5 5 5 5 5 5 5

0.85 0.85 0.7 0.7 0.7 0.7 0.7 0.7 0.5 0.5 0.5 0.5

0.8 0.8 0.8 0.8 0.5 0.5 0.5 0.5

14 Computational Simulation of the Effects of Different Culture Types … Fig. 14.21 Role matrix ms

ms X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17 X18 X19 X20 X21 X22 X23 X24 X25 X26 X27 X28 X29 X30 X31 X32 X33 X34 X35 X36 X37 X38 X39 X40 X41

403 speed factors a_A_WO b_A_WO c_A_WO a_MA b_MA c_MA a_B_WO b_B_WO c_B_WO a_MB b_MB c_MB a_MS b_MS c_MS a_ML b_ML c_ML delg_L stat_L cons_L rec_L att_A att_B int_a_A1 int_b_A1 int_c_A1 int_a_B1 int_b_B1 int_c_B1 int_a_A2 int_b_A2 int_c_A2 int_a_B2 int_b_B2 int_c_B2 open_L flex_C pos_C misM1_A misM1_B

1 0 0 0 0 0.5 0.5 0 0 0 0 0.5 0.5 0 0 0 0 0.5 0.5 0.5 0 0 0.5 0.8 0.8 2 2 2 2 2 2 2 2 2 2 2 2 0.5 0.5 0.5 0.6 0.6

404 Fig. 14.21 (continued)

N. Samhan et al. X42 X43 X44 X45 X46 X47 X48 X49 X50 X51 X52 X53 X54 X55 X56 X57 X58 X59 X60 X61 X62 X63 X64

misM2_A misM2_B context1 context2 context3 context4 Wa_A_WO,a_MA Wb_A_WO,b_MA Wc_A_WO,c_MA Wa_B_WO,a_MB Wb_B_WO,b_MB Wc_B_WO,c_MB Wa_MA, b_MA Wb_MA,c_MA Wa_MB,b_MB Wb_MB,c_MB Wa_MS,b_MS Wb_MS,c_MS Wa_ML,a_MA Wb_ML,b_MA Wc_ML,c_MA Wa_ML,a_MB Wb_ML,b_MB

0.8 0.8 1 1 1 1 0.5 0.5 0.5 0.5 0.5 0.5 X78 X79 X80 X81 0.5 0.5 0.5 0.5 0.5 0.5 0.5

X65 X66 X67 X68 X69 X70 X71 X72 X73 X74 X75 X76 X77 X78 X79 X80 X81

Wc_ML,c_MB Wculture, flex_C Wculture, pos_C WW fforw WW fback context_fforw1 context_fback1 context_fforw2 context_fback2 MWa_MA,b_MA MWb_MA,c_MA MWa_MB,b_MB MWb_MB,c_MB HWa_MA,b_MA HWb_MA,c_MA HWa_MB,b_MB HWb_MB,c_MB

0.5 0.5 0.5 0.5 0.5 1 1 1 1 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

14 Computational Simulation of the Effects of Different Culture Types … Fig. 14.22 The initial values matrix iv

iv X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17 X18 X19 X20 X21 X22 X23 X24 X25 X26 X27 X28 X29 X30 X31 X32 X33 X34 X35 X36 X37 X38 X39 X40

405 initial values a_A_WO b_A_WO c_A_WO a_MA b_MA c_MA a_B_WO b_B_WO c_B_WO a_MB b_MB c_MB a_MS b_MS c_MS a_ML b_ML c_ML delg_L stat_L cons_L rec_L att_A att_B int_a_A1 int_b_A1 int_c_A1 int_a_B1 int_b_B1 int_c_B1 int_a_A2 int_b_A2 int_c_A2 int_a_B2 int_b_B2 int_c_B2 open_L flex_C pos_C misM1_A

1 0.7 0.7 0.7 0.7 0 0 0.7 0.7 0.7 0.7 0 0 0 0 0 0.7 0 0 1 0.8 0.2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.2 0 0 0

406 Fig. 14.22 (continued)

N. Samhan et al. X41 X42 X43 X44 X45 X46 X47 X48 X49 X50 X51 X52 X53 X54 X55 X56 X57 X58 X59 X60 X61 X62 X63 X64 X65 X66 X67 X68 X69 X70 X71 X72 X73 X74 X75 X76 X77 X78 X79 X80 X81

misM1_B misM2_A misM2_B context1 context2 context3 context4 Wa_A_WO,a_MA Wb_A_WO,b_MA Wc_A_WO,c_MA Wa_B_WO,a_MB Wb_B_WO,b_MB Wc_B_WO,c_MB Wa_MA, b_MA Wb_MA,c_MA Wa_MB,b_MB Wb_MB,c_MB Wa_MS,b_MS Wb_MS,c_MS Wa_ML,a_MA Wb_ML,b_MA Wc_ML,c_MA Wa_ML,a_MB Wb_ML,b_MB Wc_ML,c_MB Wculture, flex_C Wculture, pos_C WW fforw WW fback context_fforw1 context_fback1 context_fforw2 context_fback2 MWa_MA,b_MA MWb_MA,c_MA MWa_MB,b_MB MWb_MB,c_MB HWa_MA,b_MA HWb_MA,c_MA HWa_MB,b_MB HWb_MB,c_MB

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

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Treur, J.: Network-Oriented Modeling for Adaptive Networks: Designing Higher-Order Adaptive Biological, Mental and Social Network Models. Springer Nature (2020b) Treur, J.: Modeling multi-order adaptive processes by self-modeling networks (keynote speech). In: Tallón-Ballesteros, A.J., Chen, C.-H. (eds.) Proceedings of the 2nd International Conference on Machine Learning and Intelligent Systems, MLIS ’20. Frontiers in Artificial Intelligence and Applications, vol. 332, pp. 206–217. IOS Press (2020c) Treur, J., Van Ments, L. (eds.): Mental Models and Their Dynamics, Adaptation, and Control: A Self-Modeling Network Modeling Approach. Springer Nature, Cham (2022) Weinzimmer, L.G., Esken, C.A.: Learning from mistakes: how mistake tolerance positively affects organisational learning and performance. J. Appl. Behav. Sci. 53(3), 322–348 (2017). https:// doi.org/10.1177/0021886316688658 Wiewiora, A., Smidt, M., Chang, A.: The “how” of multilevel learning dynamics: a systematic literature review exploring how mechanisms bridge learning between individuals, teams/projects and the organisation. Eur. Manag. Rev. 16(1), 93–115 (2019) Winkler, I.: Social learning theory of leadership. Contemporary Leadership Theories: Enhancing the Understanding of the Complexity, Subjectivity and Dynamic of Leadership, 85–91. (2009)

Chapter 15

Computational Analysis of Transformational Organisational Change with Focus on Organisational Culture and Organisational Learning: An Adaptive Dynamical Systems Modeling Approach Lars Rass, Jan Treur, Wioleta Kucharska, and Anna Wiewiora Abstract Transformative Organisational Change becomes more and more significant both practically and academically, especially in the context of organisational culture and learning. However computational modeling and formalization of organisational change and learning processes are still largely unexplored. This chapter aims to provide an adaptive network model of transformative organisational change and translate a selection of organisational learning and change processes into computationally modeled processes. Additionally, it sets out to connect the dynamic systems view of organisations to self-modeling network models. The creation of the model and the implemented mechanisms of organisational processes are based on extrapolations of an extensive literature study and grounded in related work in this field, and then applied to a specified hospital-related case scenario in the context of safety culture. The model was evaluated by running several simulations and variations thereof. The results of these were investigated by qualitative analysis and comparison to expected emergent behaviour based on related available academic literature. The simulations performed confirmed the occurrence of an organisational transformational change towards a constant learning culture by offering repeated and effective

L. Rass School of Business and Economics, Vrije Universiteit Amsterdam, Amsterdam, Netherlands e-mail: [email protected] L. Rass · J. Treur (B) Social AI Group, Vrije Universiteit Amsterdam, Amsterdam, Netherlands e-mail: [email protected] W. Kucharska Faculty of Management and Economics, Gda´nsk University of Technology, Gda´nsk, Poland e-mail: [email protected] A. Wiewiora QUT Business School, Queensland University of Technology, Brisbane, Australia e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 G. Canbalo˘glu et al. (eds.), Computational Modeling of Multilevel Organisational Learning and Its Control Using Self-modeling Network Models, Studies in Systems, Decision and Control 468, https://doi.org/10.1007/978-3-031-28735-0_15

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learning and changes to organisational processes. Observations about various interplays and effects of the mechanism have been made, and they exposed that acceptance of mistakes as a part of learning culture facilitates transformational change and may foster sustainable change in the long run.. Further, the model confirmed that the self-modeling network model approach applies to a dynamic systems view of organisations and a systems perspective of organisational change. The created model offers the basis for the further creation of self-modeling network models within the field of transformative organisational change and the translated mechanisms of this model can further be extracted and reused in a forthcoming academic exploration of this field. Keywords Transformational change · Organisational culture · Organisational learning · Safety culture

15.1 Introduction Organisational culture plays an important role in organisations’ success and failures (Johnson et al. 2016), as organisational culture offers employees a framework they can apply to reality, which helps them to evaluate what is of significance for the organisation and themselves, and what is irrelevant to the organisation (Łukasik 2018). Therefore often, to be successful in a change of a strategy, e.g., towards more sustainability first, the change in organisational culture is often inevitable (Kucharska and Bedford 2021). Organisational culture is a priority nowadays especially of importance of its constant improvement in the context of Health Care, as Covid 19 is putting further pressure on public health care systems (Ojogiwa and Qwabe 2021). The constant learning culture of the healthcare organisations supports their innovation performance thanks to human capital development (Kucharska 2021). Furthermore, communication and cooperation patterns between employees directly impact care for patients, such demanding circumstances lead to lower quality patient outcomes (Johnson et al. 2016). Patient safety is naturally the healthcare system’s priority, hence many of the healthcare organisations have deeply embedded safety-oriented cultures. To prevent healthcare safety-related harms, the Institute of Medicine (IOM) recommends a culture of safety, understood as a constant improvement of patient care. In this context, the concept of healthcare safety is closely related to constant learning culture composed of such components as learning climate and mistakes acceptance as a natural part of a constant learning process (Kucharska and Bedford 2020; Kucharska 2021). Especially in the context of hospitals or patient care, it is understandable that admitting mistakes regarding one’s work is difficult, both from an emotional as well as a legal standpoint. However, as studies have shown, the establishment of an organisational culture in which reporting of mistakes and errors is encouraged and instead of punishment or shame the focus is shifted towards a

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learning process, not only improves patient care but also improves the overall work environment and safety of healthcare workers (Clark 2002). To better study the mechanisms of how we can facilitate and encourage such cultural change, considering organisations as complex adaptive systems in which organisational processes are dependent on the interactions of independent individuals (Hazy and Silberstang 2009) offer an interesting starting point for academic work. Precisely, they exposed that organisational change happens when specific microenactments are composed to reframe an organisation’s capabilities and competencies. In this context in the space between the research concerning organisational culture transitions on the one hand and, formalized modeling and network sciences, on the other hand; there exists a void in research about computational modeling of organisational cultural change processes. Although much research has been done on the topic of organisational culture change (e.g., Maes and Van Hootegem 2019) and the mechanisms and conditions facilitating it, and a little academic attention has been given to a formalization of these mechanisms and conditions into a multilevel computational model. So, this study focuses on it. While some formalization exists concerning organisational change in general, e.g. the work by Hazy and Silberstang (2009), or work by (Canbalo˘glu et al. 2022a, 2023a) regarding organisational learning, especially in the field of cultural change within an organisation is largely unexplored; see also Canbalo˘glu et al. (2023b), Chaps. 6 and 7 (this volume). Further current simulations regarding cultural change have mainly focused on cultural change happening in response to a crisis, when employees perform crisis tasks (Beech et al. 2012), rather than examining conditions and mechanisms facilitating persistent cultural change within an organisation. The field of “safety culture” within the context of the healthcare domain has gained rising attention (Halligan and Zecevic 2011) substantiating academic interest in further exploration and experimentation. Additionally, in the broader context, management scholars have a keen interest in searching and uncovering conditions enabling lasting adoption of sustainability-related practices (Haack et al. 2021), including safety culture as both aim to preserve resources and enable sustainable delivery of services. Nevertheless, while some computational models in relation to safety culture in other domains exist (Sharpanskykh and Stroeve 2011), formal modeling and simulation studies in the domain of health care are still quite under-presented in academic research. In contrast, research regarding complex adaptive temporal-causal networks, which are the basis of many simulation studies, has been extensive and is documented to be transferable to a large number of different domains (Treur, 2016, 2020). Therefore, an interesting research opportunity arises in connecting the fields of transformational change in the context of organisational culture and learning with computational modeling to create a (Multilevel) Computational Model of Transformative Organisational Cultural Change. Next, in Sect. 15.2 the methodology used is briefly explained including the adaptive dynamical systems modeling approach based on self-modeling networks and in Sect. 15.3 background literature is discussed. After this, in Sect. 15.4 the dynamical system model is introduced and in Sect. 15.5 simulation results are presented. Finally, Sect. 15.6 is a discussion section and Sect. 15.7 provides an appendix with the full specification of the model by role matrices.

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15.2 Methodology This chapter aims to close the void in research and inter-disciplinary computational scientific work that exists within the field of transformative organisational cultural change (in the context of organisational learning) by creating computational mechanisms and algorithms based on real-world processes. More specifically the goal of this chapter is, to collect information on cultural change and organisational learning processes within organisations, analyse the underlying mechanisms and translate them into computational models. Both to create a formalization of the process in form of a computational model, as well as using simulations, based on this model, to examine and signify the influence of different factors on cultural change and organisational learning.

15.2.1 Research Logic and Philosophy As the precise academic situation of the topic of this chapter is still under-researched (Sandberg and Alvesson 2011) within the bigger context of organisational transitions and cultural change, this chapter’s research logic will be based on an inductive approach, following a “bottom-up” strategy. As described in Cresswell (2007) this translates into collecting and organising information from different sources, building themes and abstractions of the found concepts and organising these towards a general conclusion. To be more precise a “Grounded Theory” research approach is used, as the aim of this chapter is to create a new “theory”, or in the context of computational modeling a new “model”, aiming to explain and exemplify the underlying mechanisms and conditions that enable sustained and transformative cultural change. As this research aims to explore an underrepresented academic field and examines real-world processes as its basis for theory building, it naturally falls into an ontological research philosophy. More precisely it follows an interpretive/constructivist philosophy combining various sources and perspectives, to better understand the phenomenon of sustained cultural change.

15.2.2 Research Basis (Information Collection and Analysis) As this research aims to build a new computational model of transformative cultural change processes within organisations, and the methodological fit of research is significantly influenced by prior related work (Edmondson and McManus 2007), the collection of information will follow the academic standard within the field. Examples can be found in Canbalo˘glu et al. (2022a, 2023a, b) and Treur (2020).

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The information collection will be mostly based on a narrative literature review (Tranfield et al. 2003) collecting the current state of theory and knowledge within the field of transformational change, cultural change and adjacent concepts. The concepts to be included in the theoretical background of the model will be addressed by their most important and relevant prior studies, and (causal) links between concepts will be enriched and justified by relevant publications. The analysis will be a conceptualization of found common themes, mechanisms and interplays and a subsequent translation of these into a computational causal network model based on connections and behaviour derived from the available literature. The model will be conceptualized around a case study situated within a medical institution in the context of safety and learning culture. Data is then generated from the (numerical) simulations created by the usage of the model. The data found in this phase will be used for additional analysis, based on a qualitative analysis of the results of the simulation, based on a comparison with previously found data or information (background literature) and other empirical findings in the context of the research.

15.2.3 The Self-modeling Network Modeling Approach The adaptive computational causal network model that this chapter aims to create will be based on the computational modeling approach described by Treur (2020) and contextualized in Treur (2021a). This approach focuses on adaptive self-modeling network models, which are characterized by ● the connections between nodes X and Y of the network, also called states with activation values X(t) and Y (t) over time ● the weights ωX,Y of these connections ● the aggregation functions cY of the nodes Y ● the timing of the nodes in the model by speed factors ηY In more detail, it works as follows: State and Connectivity Characteristics The basis of the model consists of interconnected nodes representing real-world concepts translated into a computational context which’s connections to other states represent causal relations between the real-world concepts. The connections between the states are further defined by their weights ωX,Y which determines the strength of influence the value of one note has on another. As we are creating an adaptive network, some connections’ weight will be determined by another (self-model) node as explained below.

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Aggregation Characteristics Each node or state within a network model can have multiple incoming connections providing input which needs to be aggregated to determine the numerical value of the destination node’s state. The effect on the destination node is determined by the chosen combination function cY (..) which will calculate the aggregated impact on the node based on the single impacts ωX,Y X(t) for the state activation values X(t) and the weights ωX,Y of the connections. Timing Characteristics Each state Y ’s timing or rate of change is further determined by its speed factor ηY which determines how fast it reacts to the incoming influences. In adaptive network models, this speed factor can be controlled by another (self-modeling) state as well as being static. These characteristics are used to formalise and define the internal processes of the computational network model. Emergent from this formalisation an introduction of adaptive characteristics to the computational model is possible by making use of the concept of first- or higher-order self-models. Self-models Adaptive characteristics of the networks are introduced by using self-model states added as nodes to the network, representing not a real-world concept or relation, but an internal representation of adaptive circumstances to the model’s processes. As two specific cases, the speed factors and the weights adaptiveness of a connection can be represented by such self-model (also called reification) states. The naming convention for the adaptive speed factor representation state is HY and for the adaptive connection weight representation state WX,Y . Similarly, it is possible to also change the characteristics of the chosen combination functions by self-modeling states. The following related difference equations consolidate the characteristics of the network ωX,Y , cY (..), ηY into an effect in a standard numerical format: Y (t + ∆t) = Y (t) + ηY [cY (ω X 1 ,Y X 1 (t), . . . , ω X k ,Y X k (t)) − Y (t)]∆t

(15.1)

Here the Y represents the state, X i the states with incoming connections for Y, ωX,Y the weight or degree of effect of the specific connection, ηY the rate of change to the destination state and cY (..) the aggregation function used. The computational formalization of a selection of most of the more than 65 often applied mathematical functions can be found in Chap. 9 of Treur (2020) in the form of a provided combination function library. Each of the described functions have different use cases and need to be carefully chosen for each new computational model, based on the best fit for the formalization

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and modeling of the underlying real-world context. These functions enable a declarative design of network models on basis of mathematical definitions and calculations. An introduction to the different combination functions used in the created model of the current chapter is given: The identity combination function id(..) transfers the source node’s values directly to the receiving node and can only be used on states with only 1 incoming connection. It is further sometimes used to maintain a node’s numerical value by a connection to itself, to represent a persistent activation of the node with no decay of its numerical value. The formal definition is as follows: id(V ) = V

(15.2)

The advanced logistic sum combination function alogisticσ,τ (V 1 , …, V k ) combines multiple incoming effects on the node by applying a logistic sum function. It is characterised by the excitability threshold parameter τ and the steepness parameter σ. The formal definition is as follows: [ alogistic σ,τ (V1 , . . . , Vk ) =

1 1 + e−σ(V1 +···+Vk −τ)

−

] 1 (1 + e−στ ) (15.3) 1 + eστ

The steponce combination function steponceα,β (…) is used to model changing context factors that are considered for the model and its environment. It is defined by two parameters α determining the start time of activation and β determining the end time of activation. The mathematical definition is as follows: 1 i f time t is between α and β, else 0

(15.4)

Per the academic standards of the field, the created adaptive network model will be specified in role matrices, a standardized table format further explained in detail in Treur (2020); see also the Appendix Sect. 15.7 of this chapter. Theoretical research described in (Treur 2021b) and (Hendrikse et al. 2023) has shown by mathematical analysis that any smooth adaptive dynamical system has a canonical representation as a self-modeling network. Therefore, it is expected that this modeling approach will turn out to be a suitable choice in practice as well. The simulation will then be performed based on the above-given specifications, by use of a dedicated software environment in the form of a provided MatLab script, to be found in Chap. 9 of Treur (2020). Running the script will result in the values of each state over time being calculated based on the dynamics between the states leading to emergent behaviours that will constitute the simulation and its results. The generated data from this simulation will then be exported, visualized and further investigated.

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15.3 Theory—Background Literature 15.3.1 General Concepts A systems model of organisational change While organisational change can be facilitated through different means and can be examined with the help of various theories, the position of this chapter suggests a focus on a holistic and system-based theory. This can be found in the systems model of organisational change proposed by Maes and Van Hootegem (2019) which proposes to view organisational change not as a linear process but as a multidimensional mechanism. In the proposed model organisational change is dependent on 4 key elements of organisational context (namely strategy, structure, people and culture) which are influenced by individual and team effects propagated during change, as well as on the interdependencies between the organisation and its external environment which are influenced by organisational effects originating from change within the organisation (Maes and Van Hootegem 2019). In this understanding organisational change can be viewed as an emergent sub-system or behaviour within the systems model of an organisation in contrast to being an external process applied. However, as already suggested by the model and confirmed by further research it is of significant importance that all business units of an organisation should be involved in a (cultural) change effort (Ojogiwa and Qwabe 2021) and that change needs to be facilitated by the participation of all levels operational levels, but especially by leaders, e.g. executives and managers (Łukasik 2018; Ojogiwa and Qwabe 2021). High-Level Leadership support is a key necessity and driving force for sustained (cultural) change (Johnson et al. 2016; Wijethilake et al. 2021; Willis et al. 2016) as culture is best established and conveyed by leaders (Schein 2010). Further, it is of importance that existing assumptions within an organisational system are critically questioned and replaced through a learning process by all of its participants (individuals, teams and organisations) (Mascarenhas 2019). Organisational Culture Organisational Culture is one of the most integral parts of an organisation (Ojogiwa and Qwabe 2021). It not only significantly shapes the decision-making processes and behaviours of its members (Farla et al. 2012; Johnson et al. 2016; Ojogiwa and Qwabe 2021), but can also, in the case of a strong and good organisational culture, positively influence efficiency, performance, productivity and morale (Łukasik 2018; Ojogiwa and Qwabe 2021). The culture of an organisation is thereby mainly shaped by its members’ shared values, norms and assumptions about reality (Schein, 2010; Johnson et al. 2016; Wijethilake et al. 2021; Willis et al. 2016), but is understood to be more than just the sum of shared elements. Predominantly organisational culture shows emergent

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characteristics and a feed-forward and feedback loop from and back to the organisation’s members while further also being shaped by the past, symbols and rituals of the organisation (Łukasik 2018). In other words, organisational culture could be understood as a shared coherent framework (between employees) supporting the trouble-free operation of an organisation, while also shaping organisational and human behaviour through shared values and norms (Łukasik 2018). This framework can as well be applied by the employees to identify possibilities and risks from changes within the company (Łukasik 2018). Culture Change As already demonstrated in the introduction organisational culture plays a major role in the transformation of organisations, as organisational change is significantly influenced by organisational culture (Wijethilake et al. 2021). This influence has been largely underestimated, which can in some cases lead to transitions failing due to organisational culture being left unmodified (Ojogiwa and Qwabe 2021; Wijethilake et al. 2021). Further, organisational culture change is notoriously difficult to achieve (Johnson et al. 2016; Łukasik 2018) and can be a long-lasting multi-year effort (Limwichitr et al. 2015), as the internalisation of new organisational values takes time (Łukasik 2018). Nonetheless, theoretical models regarding sustained cultural change have been developed and refined. These models usually entail a three-step approach toward organisational cultural change, beginning with “unfreezing”, the breaking with old behaviours and the fostering of awareness that change is needed. Following that, the “change or transformation state” takes place, in which processes and behaviours are experimented with and transformed. It is of importance in this stage to motivate people to use/internalize newly found processes and values. Lastly, the “freezing” stage takes place in which new behaviours and values are locked in Johnson et al. (2016), Lewin (1951), Weick and Quinn (1999). Cultural change can further be propagated through many ways, e.g., changing of organisational structures, different recruitment tactics, the establishment of new company guidelines, coaching, change of leadership(-style) etc. (Łukasik 2018). It is recommended to use multiple approaches concurrently as this seems to be most effective in creating sustained cultural change (Johnson et al. 2016). Constant Learning Culture Vital parts of organisational change are the organisational as well as individual learning processes that facilitate the adaption of internal organisational processes. While learning by individuals is often encouraged in organisations and widespread knowledge collaboration would be highly beneficial to the organisations, organisations can be unable to take advantage of this benefit with an underdeveloped or flawed learning culture. Therefore, organisations should aim to propagate and establish a constant learning culture within. Constant learning culture aims to provide an environment for sustained learning possibilities on both the personal and the organisational level by improving

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on two distinct building blocks for a constant learning culture and can be considered a practical implementation of critical thinking on an organisational level (Kucharska and Bedford 2020). Firstly, a positive learning climate needs to be established that supports selfdevelopment and growth as well as organisational development and growth. A shared knowledge culture and emphasis on collaboration here can positively influence learning culture, for example encouraging employees to take responsibility for learning and prioritizing heightened and honest communication (Rebelo and Gomes 2011). This can further be facilitated by encouraging the personal development of the employees and encouraging creative and innovative solution-seeking (Kucharska and Bedford 2020). Equally important, a culture of mistake acceptance needs to be fostered, as an acknowledgement of mistakes is a necessary predecessor of true learning (Senge 2006). Mistakes are necessary learning opportunities that will improve the overall processes over time rather than damaging them, by allowing people to leave their comfort zones and innovate on their processes (Rebelo and Gomes 2011). This can be promoted by encouragement towards a public declaration of mistakes to change the organisational attitude towards mistakes. However to ensure truthful reporting of mistakes, punishment when hidden mistakes are uncovered, might be necessary. Further mistakes, their origins and consequences should be reflected upon internally or discussed in a team or with a superior to formulate lessons learned and adjust one’s conceptions (Kucharska and Bedford 2020).

15.3.2 Transforming Organisational Culture and Processes Enabling Change In the first step of organisational cultural change, employees must be motivated to identify the current culture as a problem to create a basis for effective cultural change (Johnson et al. 2016; Ojogiwa and Qwabe 2021). It is vital in this phase that employees are aware of the importance of the change, as the commitment of all members (employees) of the organisation is necessary (Łukasik 2018), as change needs to be on both individual and group levels (Limwichitr et al. 2015). Nonetheless, initial employee resistance can arise (Limwichitr et al. 2015; Ojogiwa and Qwabe 2021; Wijethilake et al. 2021). This resistance to cultural change can stem from a perceived threat to an individual’s status, identification and doubt in their professional work (Willis et al. 2016). While in a system perspective, transition processes are emergent of the interplay of various actors pursuing their interests, the overall direction is usually driven and propagated by actors with a larger plan/vision (leaders) (Farla et al. 2012). Leadership’s commitment and positive intent can significantly increase motivation and empowerment toward change in employees (Hornstein 2015; Wijethilake et al.

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2021) It is further important that organisational change is not just delegated to lowerlevel employees by executives and managers, as transformation is reached by full engagement of and direction by the leadership (Łukasik 2018). In short, this can be summarised as a transformational leader, identifying a need for change, creating and advertising a new vision and engaging their employees through inspirational influence (Burns 1978), to establish the rationale for change that is needed to initiate the change process within the organisation (Maes and Van Hootegem 2019). Transforming Organisational Processes and Culture In the following “transformation” phase of the process, the actual organisational transformational change occurs. This transformational change is characterised by the reshaping of strategies and behaviours as well as a shift of values and culture (Anderson and Anderson 2002). Here the major challenge is the change of the underlying assumptions deriving from the old company culture (Limwichitr et al. 2015). It is usually facilitated by continuous training sessions and workshops (Johnson et al. 2016; Wijethilake et al. 2021). The phase is further defined by a continuous feedback loop that exists between the behaviour of members of an organisation and the organisation itself, especially concerning shared assumptions (Łukasik 2018). In the systems perspective, groups of individuals implicitly negotiate “programmes of action” to coordinate their actions and individual communicative events concerning sense-making/giving of individual agents can converge into a collective aim or programme (Hazy and Silberstang 2009). The resulting actions by different individual actors, which can influence or reinforce, other actors’ actions, then add together to create specific dynamics at the system level of complex systems (Farla et al. 2012). If a critical mass of adaption is reached on a local level an overall organisational transformation (change of system dynamics) can occur (Hazy and Silberstang 2009). These system-level transformation process modifications then feedback and influence individual actors’ perceived actions and strategies (Johnson et al. 2016). This feedback loop back to the staff during the change phase can increase new behaviour retention as positive feedback, in form of other employees transforming their tasks, can encourage employees to sustain changes (Hazy and Silberstang 2009; Johnson et al. 2016).

15.3.3 Learning Mechanisms To facilitate a possible change of the prevalent (system-level) mechanisms and relations between the different actors and groups within the organisation adaptation of the processes needs to be possible. This adaptation or modification can take place through various processes, however, in this study, we will focus on specific forms of learning, specifically multilevel organisational learning, dyad learning and learning from mistakes.

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Feedback and Feed Forward learning in Multilevel Organisational Learning Organisational change is a dynamic and complex process based on interactions and propagation of information between the different levels of the organisation. It can be divided into 2 main processes, feed forward learning, in which information and processes get propagated towards higher organisational levels, and feedback learning where changes on the organisational or team level get propagated back towards lower levels of the organisation (Crossan et al. 1999). This type of learning is suggesting the existence of individual and shared mental models existing on the different levels of the organisation. The individual will have their own representation of specific assumptions, be it a value or a task, in their personal mental model. Such mental models can be used to describe specific tasks that are performed within an organisation, but other mental models can describe the patterns and assumptions underlying the organisational culture. The mental models of multiple individuals can then when aggregated create shared mental models on a team or group level. The aggregation of group-level mental models then is the basis for organisational-level mental representations, which represent the abstract understanding or established guidelines of a specific process or value of the whole organisation (Canbalo˘glu et al. 2022b; Crossan et al. 1999). A formalization of this type of feed forward and feedback learning recently has been made in Canbalo˘glu et al. (2022a) and (Canbalo˘glu et al. 2023a), and conceptualizes the process in 4 elements the formation of mental models on the individual level, the transfer from the individual level to the organisational level through the creation of shared mental models, the maintenance and improvement of the mental model of organisational level and the backpropagation of organisational share mental models and knowledge to the individual incorporating these into their mental model (Canbalo˘glu et al. 2022a, 2023a). Dyad Learning and Learning from Mistakes Organisational learning however does not only happen on higher levels of abstraction but also takes place through the practice of coaching and mentoring. This form of learning is characterised by experienced people within an organisation, directly teaching a task or the understanding of a process to less experienced people (Wiewiora et al. 2020). In this dyad learning mechanism, the mental models of the participating actors directly influence the opposing mental models, either in only one direction or in both directions, depending on the situation. This form of learning further often takes place in the form of training sessions or discussions of previous work, allowing a reflection on one’s assumptions and a transfer of individual and organisational level knowledge (Canbalo˘glu et al. 2022a), which offers a great opportunity to combine dyad learning in form of mentoring with the practice of learning from mistakes. In an organisational environment that fosters the acceptance of mistakes learning from these can be facilitated and offers great value by helping the organisation change and adapt more efficiently (Kucharska 2021; Kucharska and Bedford 2020). To allow this learning to happen, one needs to acknowledge that a mistake was made (Senge

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2006) and encourage an understanding that mistakes are part of human learning that allows us to restructure our processes, learn and adapt to change. The acceptance and openness about mistakes is the first step and initiator for a scanning and interpretation of a mistake, or the suspected decision causing it (Mangels et al. 2006), which enables us to transform mistakes into newly acquired knowledge on individual and organisational levels (Kucharska and Bedford 2020). This process however could not take place if mistakes are hidden, necessitating error reporting as an important step to enable learning from mistakes (Mohsin et al. 2019). Further positive or negative incentives, e.g. mandatory workshop attendance if a hidden error gets uncovered, might need to be considered to ensure sufficient levels of error reporting. In the context of modeling this learning computationally or algorithmically these findings suggest a procedure containing multiple steps to be followed orderly to ensure learning from mistakes: 1. Observation or identification of a mistake occurring 2. Investigation if mistake got hidden by the causing actor a. If a mistake was hidden positive incentives, e.g. workshops might be necessary 3. Open declaration of mistake 4. Analysis or Interpretation of mistake a. Either by self-reflection b. discussion with team members c. feedback from more experienced people 5. Incorporation of lessons into individual or organisational knowledge A proposed computational modeling of this process can be found in part of the mechanisms of the presented computational model following.

15.4 Designing the Dynamical Systems Model 15.4.1 Research Focus Given the wide scope of academic research into transformational organisational change, organisational culture and organisational learning mechanisms, a focus on specific aspects needs to be established. Therefore, the created model and case scenario will concentrate on the following aspects of the previously established research: ● Confirming if the explored dynamic systems view of organisations (Farla et al. 2012; Hazy and Silberstang 2009) can be translated into the self-modeling network modeling approach from Treur (2020).

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● Verifying if a shift in learning culture happens towards a constant learning culture (Kucharska 2021). ● Exploring organisational learning mechanisms’ effects and their effectiveness in correcting inaccurate mental models or organisational processes, in particular for: – Feedback and Feed forward learning on both organisational and team levels (Crossan et al. 1999) – Learning from Mistakes (Kucharska and Bedford 2020) and Dyad Learning (Canbalo˘glu et al. 2021) – Leadership inspired/instructed (Łukasik 2018) organisational culture change incentives e.g. workshops (Johnson et al. 2016; Wijethilake et al. 2021) or change of organisational structures (restructuring of teams)

15.4.2 Description of a Case To translate the findings from the academic literature into a coherent, dependable and practical model we will base the model on an applied case within the context of a medical institution, incorporating the found mechanisms into the greater context of the case. To achieve this, we will employ the use of multi-level self-models within the model to create a second-order adaptive network model of the initiation and adaption phases of transformative organisational cultural change. The theoretical case the model is based on is created and confirmed by the collaboration of researchers from different disciplines (Wioleta Kucharska and Anna Wiewiora from Management and Business Science, Jan Treur from AI and Network Science) and is described as follows: (1) Edward—an authentic transformational leader is focused on organisational constant improvement to secure a high level of performance (patient care). He wants to achieve it by creating a learning culture in which employees learn from each other. (2) Edward believed that learning from mistakes is one of the best ways of creating a sustainable learning culture, as the acceptance of mistakes is a source of precious lessons and creates a better learning climate. It doesn’t mean Edward tolerated the attitude of negligence. Edwards’ intention was the avoidance of hiding mistakes. In his opinion hiding mistakes made harms patients and stopped learning. So, he was looking for a solution to keep high standards of healthcare. (3) Edward implemented a set of organisational routines supporting his new strategy focused on the intellectual capital increase thanks to constant learning culture implementation (A) Edward introduced monthly obligatory meetings in which a senior staff was asked to present their own “precious mistakes made” in his/her career that gave him/her precious lessons and young doctors follow this practice (creation of shared knowledge).

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(B) To the existing practice of discussing the most interesting, often successful cases, the presenting person obligatory also needed to add the presentation of “his/her recent lesson from a mistake.” (dissemination of knowledge within the organisation). (C) Edward introduced the principle that employees change shift teams every month to reduce focus on social experience and replace employees’ focus on patients, learning and better dissemination of knowledge. (D) Edward introduced the obligatory registration of mistakes, admitting to them openly and proactively. After each shift, the most valuable lessons learned, from the mistakes that happened during the shift, were immediately discussed with the shift staff (experienced doctor) to correct misunderstandings and learn from mistakes. (E) If someone was caught hiding their mistakes, they have to attend an afterhours training and pay for it themselves. This should incentivise the doctors to not hide mistakes anymore and be proactive about them.

15.4.3 The Designed Dynamical Systems Model Considering the case described above, an abstract approximation in the form of a computational dynamical systems model is created. It is greatly based on how organisational and individual learning mechanisms controlled by the organisational culture influence the mental model representations, illustrated for a simple 3-step healthcare-related task, on the individual, team and organisational level. This 3-step task is used as an abstraction and could be replaced by any task in which it is of utmost importance that step 1 is followed by step 2 being followed by step 3. This model deals with repairing a faulty mental representation of said task, which would lead to a young doctor, skipping one of these steps. The designed computational network model created on this basis is depicted in 3D according to three levels in Fig. 15.1. For an extensive explanation of the different states, an overview can be found in Figs. 15.2, 15.3 and 15.4 for the three levels, respectively. The base level (the pink lower plane in Fig. 15.1) is the undermost level. It represents the mental models of the aforementioned 3-step process of different entities within different organisational levels (individual, group, organisation) of an organisation (Canbalo˘glu et al. 2022a, 2023a, b). The 3 states in each mental model, e.g. Y1T1, Y1T2, and Y1T3, represent as aforementioned an understanding of a 3-step healthcare-related task, that needs to be followed in succession. However, as visible by the connections between the states, it can be possible for the mental models to be faulty, which would lead to Task 2 getting skipped. In this case, Task 1 would have a strong connection to Task 3 and would not trigger Task 2. Further, the base level depicts mental models on different levels of the organisation, namely:

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Fig. 15.1 Graphical representation of the connectivity of the second-order adaptive network model: base-level mental states and mental models; the first-order self-model level for representations of weights of mental model connections (W-states) and inter mental model connections (connections between W-states); the second-order self-model for organisational/individual learning control mechanisms and supporting internal mechanisms

● Young 1–4 Four young doctors’ understanding of the task. Each doctor can have a different understanding and therefore different mental model of the task ● Team 1–2 The shared understanding of the task within a team by a shared mental model. Two shift teams exist in this model, each consisting of 2 young doctors.

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State Y1T1 Y1T2 Y1T3 Y2T1 Y2T2 Y2T3 Y3T1 Y3T2 Y3T3 Y4T1 Y4T2 Y4T3 Team1T1 Team1T2 Team1T3 Team2T1 Team2T2 Team2T3 ET1 ET2 ET3 OrgT1 OrgT2 OrgT3 WST1 WST2 WST3

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Explanation Individual mental model state for Young Doctor 1 for task 1 Individual mental model state for Young Doctor 1 for task 2 Individual mental model state for Young Doctor 1 for task 3 Individual mental model state for Young Doctor 2 for task 1 Individual mental model state for Young Doctor 2 for task 2 Individual mental model state for Young Doctor 2 for task 3 Individual mental model state for Young Doctor 3 for task 1 Individual mental model state for Young Doctor 3 for task 2 Individual mental model state for Young Doctor 3 for task 3 Individual mental model state for Young Doctor 4 for task 1 Individual mental model state for Young Doctor 4 for task 1 Individual mental model state for Young Doctor 4 for task 1 Shared mental model state for Team 1 for task 1 Shared mental model state for Team 1 for task 2 Shared mental model state for Team 1 for task 3 Shared mental model state for Team 2 for task 1 Shared mental model state for Team 2 for task 2 Shared mental model state for Team 2 for task 3 Individual mental model state for Experienced Doctor for task 1 Individual mental model state for Experienced Doctor for task 2 Individual mental model state for Experienced Doctor for task 3 Shared mental model state for Organisation for task 1 Shared mental model state for Organisation for task 2 Shared mental model state for Organisation for task 3 Task 1 executed in the world Task 2 executed in the world Task 3 executed in the world

Fig. 15.2 Base level states of the introduced adaptive network model

● Experienced An experienced doctor who will act as the supervisor of the young doctors. His mental model, given his experience, is next to a perfect representation of the task. ● Organisation The understanding of the task on the organisational level ● WST 1–3 The world states, the states representing the actual real-world tasks occurring. These are the states in which the error detection mechanism detects mistakes. Above the base level, the first-order self-model level (blue middle plane in Fig. 15.1) reflects the adaptiveness of the mental models of the base plane. This plane is characterised by the W-states, grouped in triads in this model, which represent the adaptive weights for the connectivity between the states of the mental models of the different entities of the organisation (young doctors, experienced doctor, teams, organisation). There further exist same-level connections between some of the W-states, providing the possibility for either feed forward learning, feedback learning

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State WY1T1,Y1T2

Explanation First-order self-model W-state for weight of the connection from Task 1 to Task 2 within the individual mental model of Young Doctor 1 WY1T2,Y1T3 Y1 mental model connection weight W-state from task 1 to 2 WY1T1,Y1T3 Y1 mental model connection weight W-state from task 1 to 3 WY2T1,Y1T2 Y2 mental model connection weight W-state from task 1 to 2 W Y2T2,Y1T3 Y2 mental model connection weight W-state from task 2 to 3 W Y2T1,Y1T3 Y2 mental model connection weight W-state from task 1 to 3 W Y3T1,Y3T2 Y3 mental model connection weight W-state from task 1 to 2 W Y3T2,Y3T3 Y3 mental model connection weight W-state from task 2 to 3 W Y3T1,Y3T3 Y3 mental model connection weight W-state from task 1 to 3 W Y4T1,Y4T2 Y4 mental model connection weight W-state from task 1 to 2 W Y4T2,Y4T3 Y4 mental model connection weight W-state from task 2 to 3 W Y4T1,Y4T3 Y4 mental model connection weight W-state from task 1 to 3 WTeam1T1, Team1T2 Team 1 mental model connection weight W-state from task 1 to 2 WTeam1T2, Team1T3 Team 1 mental model connection weight W-state from task 2 to 3 WTeam1T1, Team1T3 Team 1 mental model connection weight W-state from task 1 to 3 WTeam2T1, Team2T2 Team 2 mental model connection weight W-state from task 1 to 2 WTeam2T2, Team2T3 Team 2 mental model connection weight W-state from task 2 to 3 WTeam2T1, Team2T3 Team 2 mental model connection weight W-state from task 1 to 3 WET1, ET2 Experienced Doctor mental model connection weight W-state from task 1 to 2 WET2, ET3 Experienced Doctor mental model connection weight W-state from task 2 to 3 WET1, ET3 Experienced Doctor mental model connection weight W-state from task 1 to 3 WOrgT1, OrgT2 Organisational mental model connection weight W-state from task 1 to 2 WOrgT2, OrgT3 Organisational mental model connection weight W-state from task 2 to 3 WOrgT1, OrgT3 Organisational mental model connection weight W-state from task 1 to 3 error_occurs Error detection control state error_proactive State representing error registration supervisor_reflection State representing triggering of supervisor reflection

Fig. 15.3 First-order self-model states of the introduced adaptive network model

(Canbalo˘glu et al. 2022a, 2023a, b), dyad learning (e.g., cooperation, mentoring) (Wiewiora et al. 2020) or learning from mistakes (Kucharska 2021; Kucharska and Bedford 2020). These connections either enable the creation of new shared mental models, the adaptation of shared or individual models or the correction of faulty mental models. The further states in this plane are parts of some of the learning or detection mechanisms otherwise depicted in the uppermost plane. The “error_occurs” state detects if a mistake happens in the real-world task (world states). The “error_proactive” state, determines if the mistake that happened gets registered/openly proclaimed. The “supervisor_reflection” state gets triggered as a result of the young doctor being proactive about an error and triggers the “Learning from Mistakes” mechanism. In the second-order self-model level (purple upper plane in Fig. 15.1), some context-sensitive control mechanisms necessary for the learning mechanisms, are

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Explanation Speed state for Young Doctor 1 first-order self-model W-states Speed state for Young Doctor 2, 3, 4 firstHYoung2-3-4 order self-model W-states Speed state for Experienced Doctor firstHExpert order self-model W-states Speed state for Team first-order self-model HTeam W-states Speed state for Organisation first-order HOrg self-model W-states Context state triggering workshop context_transformational_hiding_error_workshop mechanism Detection state triggering a workshop if control_workshop_trigger non-registration of mistake is detected Connection weight from error_occurs to WWerror_occurs, error_proactive error_proactive Connection weight from Experienced WWE, Y1 Doctors to Young Doctors 1 W-states context_transformational_monhtly_ Context state triggering monthly meeting meeting_sharing feedforward learning Connection weight for feedforward WWFeedforward learning (team => org W-states) Connection weight for feedforward WWE_Feedforward learning (experienced => org W-states) context_transformational_monhtly_ Context state triggering monthly meeting meeting_discussion feedback learning Connection weight for feedback learning WWFeedback (org => team W-states) control_change_of_teams Context state triggering shuffling of teams Threshold state for T1 => T3 W-states of TYoungT1T3 Young Doctors maintain_threshold Internal support state to maintain threshold context_transformational_daily_ Context state triggering daily meeting meeting_sharing feedforward learning Connection weight for feedforward WWteam_Feedforward learning (young => team W-states) Connection weight for feedforward WWteam_E_Feedforward learning (experienced => team W-states) context_transformational_daily_ Context state triggering daily meeting meeting_discussion feedback learning Connection weight for feedback learning WWteam_feedback (team => young W-states) day_one_sharing Context state triggering day 1 sharing day_two_sharing Context state triggering day 2 sharing day_three_sharing Context state triggering day 3 sharing day_one_discussion Context state triggering day 1 discussion day_two_discussion Context state triggering day 2 discussion day_three_discussion Context state triggering day 3 discussion HYoung1

Fig. 15.4 Second-order self-model states of the introduced adaptive network model

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situated. For a better understanding of the model, each mechanism’s states are highlighted according to the mechanisms they belong to: ● The yellow highlighted states depict the mistake registration mechanism, as well as a control state detecting nonregistered mistakes, which triggers the mechanisms (after-hours training) taken by the organisation to incentivise the young doctors not to hide mistakes. If a mistake gets registered by the doctor this last incentivising mechanism is not triggered. The context of the transformational leader establishing the mistake management system is depicted in a state there as well (Kucharska 2021). ● The orange highlighted states, portray the triggering and implementation of the “Learning from Mistakes” mechanism. Here the “supervisor_reflection” state triggers the analysis and discussion of the mistake. This analysis and discussion take place in form of dyad learning or mentorship by the experienced doctor toward the young doctor (Mangels et al. 2006). ● The green highlighted states represent the daily shift closing meetings and their triggering by context states. These meetings are divided into 2 different phases. – First is the sharing phase, representing the sharing of mistakes and experiences during the previous shift. This triggers feedforward learning, which creates or adapts shared mental models on the team level. It is the first step in organisational learning. – Secondly, the discussion phase gets triggered, in which the lessons learned from that mistake are formulated. This leads to learning and adjustments of understanding on the individual (young doctors level), which is modeled by feedback learning and represent the dissemination of knowledge ● The purple highlighted states relate to the monthly meetings in which experienced and young doctors share and discuss their most important learning experiences and mistakes of the past. Here, the sharing phase triggers feedforward learning to create a shared organisational-level mental model. In the discussion phase, the knowledge is then passed down all the organisational levels, leading to adjustments of the mental models and their corresponding weights. ● The red highlighted states model the influence of young doctors changing or shuffling their teams. The increased focus of the doctors on work is represented here by a change in some of their threshold states. This change in thresholds for some of their states enables them to be more open to learning from each other via the shared mental models. ● The turquoise highlighted states are part of an internal control mechanism, that controls some of the model’s behaviours, and ensures the simulations run correctly and smoothly. Overall the model aims at conceptualizing and modeling transformational organisational change, in the context of learning from mistakes and a change in organisational culture. A culture in which mistakes aren’t shared and hidden is transformed into a culture with an emphasis on constant learning, safety culture and collaboration. This is facilitated by several changes in the existing organisational processes or by added

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mechanisms, which enable and create a critical reflection on all organisational levels (individual, team, organisational).

15.5 Simulation Results This section will discuss the simulation results of the model that was created based on the aforementioned case and described in the previous section.

15.5.1 Full Scenario In Fig. 15.5 a full scenario with all its states is shown. Figure 15.6 shows highlighted W-states for learnt connections of Young Doctor 1. The simulation starts with the visible formation of the mental models of the Young Doctors 1 to 4 (Y1–Y4) and Expert (E) from Time 0 to 50. At around 100 the transformational leader puts mistake registration and disciplinary workshops in place (context_transformational_hiding_error_disincentivizing), aiming to increase the chance of the young doctor to be proactive about (registering) his mistake. This triggers the activation of the ‘Learning from Mistakes’ mechanism which takes place between 100 and 300. Following the modeling of 3 days and the respective daily closing shift meeting are modeled. This phase begins at 350 and finishes around 250. Each day’s closing shift meeting is signified by 2 different sub-phases, the sharing of mistakes of that day modeled by feedforward learning leading to the creation or adaption of shared team mental models, as well as the discussion of said mistake and the takeaway lesson learned from it, which is modeled by feedback learning and the adaption of the young doctors’ mental model representations. At around 1300 the “change of teams” is modeled, which has a direct influence on the young doctors’ thresholds TYoungT1T3 by increasing the said threshold, therefore increasing their ability to focus on their work and enable better learning. From 1500 to 1600 the first phase of the monthly shift meeting takes place, with every doctor recapping the last month and sharing their most precious mistake made in their career. In this phase, a shared organisational level mental model is created, via feedforward learning, based on the lower-level organisation mental models. From 1700 till 1800 the second phase of the monthly meetings takes place, in which the mistakes are discussed, and the lessons learned from said mistakes are disseminated within the organisation via feedback learning and the adaption of lower-level mental models. Overall, we can observe in the results of the simulations that the changes made to the prevailing organisational processes, led to a shift in learning culture enabling and triggering constant learning opportunities and incentives for the employees,

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Fig. 15.5 Simulation graph showing a full overview of the scenario and all states

which results in corrected mental models representing a correct understanding of the succession of task on all organisational levels.

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Fig. 15.6 Simulation graph showing a full overview of the scenario and all states with WY1T1,Y1T3 and WY1T1,Y1T2 highlighted

15.5.2 Learning from Mistakes As observable in Fig. 15.7, the learning from mistakes in this simulation starts with the transformational leader enabling the mistake/error registration and workshops, at around 100.

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Fig. 15.7 Simulation graph showing “learning from mistakes” phase of simulation and related states

Although already before this activation the observation state “error_occurs” gets activated by the world states, as WST2 is too low and doesn’t get fully activated, signifying that an error in the process occurs. Theoretically, if the young doctor is proactive about his mistake and registered it, the state “error_proactive” would be activated as well. However, at the beginning of the simulation, the young doctor doesn’t register his mistake and hides them. This is registered by the “control_workshop_trigger” state around 130, which activates a correction mechanism by making the young doctor attend a workshop on error handling which leads to an increase in them being proactive about their mistake and registering it at around 150 (by increasing Werror_occurs, error_proactive ) (Kucharska 2021). Registering the mistake and with this the doctor openly admitting to his mistake is the first important step in this process as it enables them to analyse and learn from the mistake, confirming and approximating behaviour that was validated in previous studies (Senge 2006). The registration of the mistake activates the analysis and reflection phase of this process, by activating the “supervisor_reflection” state at 175, which triggers the dyad learning and mentorship learning between the experienced doctor (E) and the young doctor (Y1). This corrects the young doctor’s understanding of the task, by influencing the weights that create his mental model representation (WY1T1,Y1T2 ; WY1T2,Y1T3 ; WY1T1,Y1T3 ), as visible between 150 and 225. After this learning has taken place, and the mental model of the young doctor is corrected, the real-world state WST2 gets activated to the necessary extent, which signals that the mistake

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doesn’t occur anymore. This confirms literature findings in which a reflection upon mistakes leads to correct knowledge representation (Kucharska and Bedford 2020). If no mistake is occurring anymore the “learning from mistakes” mechanism shuts itself down, without outside influence. However, if the mental representation of the young doctor would be incorrect again, the mechanism would be triggered again via the world states.

15.5.3 Daily Shift Reflections Next in the simulation, the modeling of 3 days of shift closing reflections takes place, as shown in Fig. 15.8. Each day’s reflection starts with the sharing of the mistakes that have happened and a recap of the last shift (feedforward learning), here at 350, 650 and 950, followed by a formulation of lessons learned (feedback learning), here at 500, 800 and 1100. As evident by the highlighted red line showing the value for WY3T1,Y3T2 (the mental connection for the third young doctor between tasks 1 and 2) the daily shift meetings positively influence and adapt the young doctors’ mental representations towards a more correct understanding of the task. While in the beginning, he did not believe in Task 2 following Task 1, with only a value for this connection of 0.2, he does believe in this connection after 3 days of end-of-shift reflections, shown by the connection value now being around 0.9. This is expected behaviour when referencing it with the found literature, as it proves that learning from mistakes in a context of a constant learning culture enabling organisational learning, proves effective (Canbalo˘glu et al. 2021, 2023a; Kucharska 2021; Kucharska and Bedford 2020). If we observe the shift meeting closer, by focusing, e.g., on the second shift closing meeting we can observe some further behaviour. As Fig. 15.9 shows, the division of the process into 2 subphases is clear. First, between 650 and 725, the sharing part of the meeting takes place. Here it is visible how the shared mental models on the team level are formulated further. After they were already established to an extent in the first shift meeting the second shift meeting increases the clarity of the team levels’ mental representation. Once the first phase of the meetings, the sharing has finished, slightly later the second phase of the meetings gets triggered. This phase starts at 800 and extends until 900. It is characterized by a team reflection happening and the formulation of lessons learned that are then disseminated to the doctors who adapt their mental representations based on the lesson, evident for example by the red highlighted line representing the mental representation of the connection’s strength between task 1 and 2 of Young Doctor 3. This process of the formulation of shared mental models and their subsequent influence on the lower-level mental models is known as feed forward and feedback learning as defined by Crossan et al. (1999), and functions as expected and theorized in other related work (Canbalo˘glu et al. 2022a, 2022b, 2023a).

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Fig. 15.8 Simulation graph showing complete ‘Daily Shifts reflection’ Phase of simulation and all states

15.5.4 Monthly Shift Reflections and Change of Teams The next phase of the simulation is characterised by the occurrence of the monthly organisational meeting, in which the whole organisation and all doctors meet up. It is necessary to mention that previous to this meeting at the time of 1300 the “changing of teams” occurred. The simulation tries to approximate the effects of a shuffling

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Fig. 15.9 Simulation graph showing ‘2nd Daily Shifts reflection’ of simulation and all states

of the teams of the young doctors, which directs their focus away from socializing back to their work, by adapting their thresholds to learning. As visible in Fig. 15.1 at 1300 this is modeled by an increase in the adaptive threshold of the young doctors represented by TYoungT1T3 . Following this, the monthly meeting begins to take place at 1500, characterized by the formation of an organisational level shared mental model) via propagation and aggregation of their specific weight states. This represents the doctors, especially also the experienced doctors sharing their most precious mistakes made in their career.

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At the time of 1700, the second part of this process commences in which the panel discusses the cases, and integrates the lessons learned from the “precious” mistakes shared by the doctors. This leads to organisational learning throughout all organisational levels in the form of feedback learning. As expected, this results in a correction of the mental models on the different organisational levels. An example can be seen in the red highlighted line in the right part of Fig. 15.10 which shows how young doctor 3 unlearns the wrong association between task 1 and task 3 (WY3T1,Y3T2 ), visible by the decrease of its value from around 0.7 to 0.2. (Canbalo˘glu et al. 2022a; Crossan et al. 1999).

Fig. 15.10 Simulation graphs showing the ‘Feedforward and Feedback Learning’ phase of the simulation and all states

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Fig. 15.10 (continued)

15.5.5 Scenario Variations To observe some of the influences that the different mechanisms have in interconnection to the overall simulation 2 variations to the scenario were implemented. First, we wanted to observe what difference a change of teams made to the dissemination of lessons learned within the process of organisational learning in form of feedforward and feedback learning. The result of this change can be seen in Fig. 15.11. Here especially the red highlighted line is again of interest. It represents the same state highlighted in Fig. 15.12 and shows a significantly less pronounced learning effect than previously. We can

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observe that the increased threshold for the young doctors had a significant influence on their ability to correct their mental models as a previous decrease of the strength of the wrong connection of tasks by 0.5 points is now reduced to only a correction by 0.2 points. Proving that a change of teams and the subsequently increased focus by the doctors on their work has significant effects. Another variation that was made to the simulation was the deactivation of the ‘learning form mistake’ mechanism, to observe the difference it made for young

Fig. 15.11 Simulation graphs showing the ‘Feedback Learning’ phase of simulation and all states with the variation of no change of teams being triggered

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Fig. 15.12 Simulation graph showing a full overview of the scenario and all states without triggering of ‘Learning From Mistakes’ mechanism

doctor 1 to have them learn from their mistakes at the beginning of the simulation. In Fig. 15.12 the overview of the simulation is shown in which no learning from mistakes has occurred. Highlighted in the figure in red is the state WY1T1,Y1T3 representing the connection that skips a task, leading to a mistake, and in purple/pink WY1T1,Y1T2 which represents the correct succession of task after task 1. As observable in Fig. 15.6, the values for both highlighted lines are quickly reaching close to their ideal values. For WY1T1,Y1T3 that is reaching a value of 0,

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representing complete disbelief in the wrong succession of tasks and for WY1T1,Y1T2 that is reaching close to 1, representing a correct understanding of the succession of tasks. In contrast to that in Fig. 15.12 it is visible that the correction of the mental representation of the succession of tasks does not occur to the same extent. For WY1T1,Y1T3 for example we can observe that the correction only happens significantly when the monthly meeting and with that full organisational learning occurs. For WY1T1,Y1T2 while we still see a correction to the same extent as in Fig. 15.6 happens, without the learning from mistakes, in the beginning, this learning effect required the full time and mechanisms of the simulation. These observations conclude that learning from mistakes is a powerful mechanism in the correction of faulty mental models, and has a significant influence, but also that the further organisational learning mechanisms are equally powerful in ushering adaptation and correction of mental representation in individuals.

15.6 Discussion This chapter was based on material from (Rass et al. 2023). The goal of this research was to further explore the field of transformational change, in the context of organisational learning and culture by computational modeling of organisational and individual processes. This specifically realizes itself in the objective to create an adaptive multi-order self-modeling network model that conceptualizes and approximates transformative organisational cultural change. The implemented mechanisms of organisational processes were based on an extensive literature study and grounded in related work in this field (Canbalo˘glu et al. 2022a), creating the described computational model of this study.

15.6.1 Evaluation of the Computational Model for the Research Focus To confirm the validity of the created computational model, a scenario and variations to it were created, enabling us to compare the models’ emergent behaviours. To further substantiate the model, the results of the variations of the scenario got compared to the base scenario, to gain knowledge about possible network effects (is there a better way to say something like “observe interplays and isolations of the mechanisms” again). Overall, the simulations are in line with the academic findings and show expected emergent behaviour. The variations of the base simulation further enabled us to observe interplays and isolations of the mechanisms. As previously established the study and model took specific research focus on certain theories, which were considered of importance to be explored within the limitations of this research.

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We observed and confirmed for the model that learning from mistakes is a powerful tool for individual learning (Kucharska and Bedford 2020) and that leadership instructed (Łukasik 2018) change in organisational structures (restructuring/shuffling teams) resulted in an increased focus on work, significantly influencing individuals’ ability to adapt their mental models. We could further confirm that organisational culture change incentives (Johnson et al. 2016; Wijethilake et al. 2021), were effective in changing the personal mistake handling of individuals. Overall, the model as well demonstrates a cultural shift towards a constant learning culture, verifiable by many and interacting learning opportunities occurring. Additionally, we recognized that successful organisational learning via feed forward and feedback learning as described by (Crossan et al. (1999), can (at least in some contexts) necessitate a monthly meeting with full organisational sharing, reflection and learning, to allow for a significant correction of the mental model (Canbalo˘glu et al. 2023a), suggesting the occurrence of unexplored network effects within the model. Further, the simulations show that the daily shift reflections have a constant and robust positive impact on the correction of the mental models, suggesting this tool as the most reliable mechanism to choose. Lastly, the model and its results further confirm that the self-modeling approach by Treur (2020) is a suitable approach to formalize the systems model of organisational change (Maes and Van Hootegem 2019) and the proposed dynamic systems view of organisations (Farla et al. 2012; Hazy and Silberstang 2009). In addition, this has validated previous more theoretical research (Treur 2021b; Hendrikse et al. 2023) showing by mathematical analysis that any smooth adaptive dynamical system can be modeled as a self-modeling network.

15.6.2 Practical Implications This study’s results and observations suggest a few different practical implications concerning transformative organisational change initiatives. The simulations clearly show that a combined approach of all mechanisms is the most effective option given arising interplay and network effects, suggesting that real-world initiatives should as well employ numerous mechanisms at the same time. Further, it seems that daily reflections are the most powerful organisational learning tool in correcting wrong knowledge offering a reason for managers to prioritize this instrument. However, it should be noted that learning from mistakes enabled better and more effective learning during the daily reflections, suggesting their use in tandem. Lastly, the simulations delivered strong results concerning the effect of increased organisational learning by diverging the focus back to work implicating these as an important catalysator in organisational learning that managers should acknowledge.

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15.6.3 Theoretical Implications This research offers a theoretical and computational expansion to the academic field of transformative organisational change by creating a functional scenariobound model of organisational change and translating organisational processes into computational approximations. This study, therefore, suggests an advancement of the field of transformative organisational change into the field of computational modeling and simulations. It would further be highly interesting and fitting to expand Canbalo˘glu et al. (2022a, 2023b) research into organisational learning toward organisational transformation processes in general, in which this chapter would situate itself, as a starting point for further research.

15.6.4 Future Research and Limitations Nonetheless, the presented computational model and study are not without limitations. Although it reflects some transformative organisational change mechanisms and variables, many further mechanisms and with those possible hidden interactions and emergent behaviour are still missing. A further advanced model could e.g. also integrate observational learning for the task-observing doctor, or could integrate counterfactual thinking as a learning and decision mechanism as proposed in Bhalwankar and Treur (2022). While the proposed model is scenario-specific the translated mechanisms of this model can be extracted and reused in other related models. Therefore, future research suggests itself in an extension of the proposed model as well as in the creation of a library of computationally translated transformative organisational change mechanisms. This would enable a rapid extension of research in the field of self-modeling and adaptive computational modeling of transformative organisational change.

15.7 Appendix: Role Matrices In this section, the full specification of the dynamical model is provided by the role matrices for the different types of network characteristics, see Figs. 15.13, 15.14, 15.15, 15.16, 15.17, 15.18, 15.19, 15.20, 15.21, 15.22, 15.23, 15.24, 15.25, 15.26 and 15.27.

15 Computational Analysis of Transformational Organisational Change … Fig. 15.13 Base connectivity for the base level states

Fig. 15.14 Base connectivity for the first-order self-model states

mb X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17 X18 X19 X20 X21 X22 X23 X24 X25 X26 X27

base connectivity Y1T1 Y1T2 Y1T3 Y2T1 Y2T2 Y2T3 Y3T1 Y3T2 Y3T3 Y4T1 Y4T2 Y4T3 Team1T1 Team1T2 Team1T3 Team2T1 Team2T2 Team2T3 ET1 ET2 ET3 OrgT1 OrgT2 OrgT3 WST1 WST2 WST3

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base connectivity WY1T1,Y1T2 WY1T2,Y1T3 WY1T1,Y1T3 WY2T1,Y1T2 W Y2T2,Y1T3 W Y2T1,Y1T3 W Y3T1,Y3T2 W Y3T2,Y3T3 W Y3T1,Y3T3 W Y4T1,Y4T2 W Y4T2,Y4T3 W Y4T1,Y4T3 WTeam1T1, Team1T2 WTeam1T2, Team1T3 WTeam1T1, Team1T3 WTeam2T1, Team2T2 WTeam2T2, Team2T3 WTeam2T1, Team2T3 WET1, ET2 WET2, ET3 WET1, ET3 WOrgT1, OrgT2 WOrgT2, OrgT3 WOrgT1, OrgT3 error_occurs error_proactive supervisor_reflection

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connection weights WY1T1,Y1T2 WY1T2,Y1T3 WY1T1,Y1T3 WY2T1,Y1T2 W Y2T2,Y1T3 W Y2T1,Y1T3 W Y3T1,Y3T2 W Y3T2,Y3T3 W Y3T1,Y3T3 W Y4T1,Y4T2 W Y4T2,Y4T3 W Y4T1,Y4T3 WTeam1T1, Team1T2 WTeam1T2, Team1T3 WTeam1T1, Team1T3 WTeam2T1, Team2T2 WTeam2T2, Team2T3 WTeam2T1, Team2T3 WET1, ET2 WET2, ET3 WET1, ET3 WOrgT1, OrgT2 WOrgT2, OrgT3 WOrgT1, OrgT3 error_occurs error_proactive supervisor_reflection

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Fig. 15.20 Combination function weights for the first-order self-model states

L. Rass et al. mcfw combination function weights X1 Y1T1 X2 Y1T2 X3 Y1T3 X4 Y2T1 X5 Y2T2 X6 Y2T3 X7 Y3T1 X8 Y3T2 X9 Y3T3 X10 Y4T1 X11 Y4T2 X12 Y4T3 X13 Team1T1 X14 Team1T2 X15 Team1T3 X16 Team2T1 X17 Team2T2 X18 Team2T3 X19 ET1 X20 ET2 X21 ET3 X22 OrgT1 X23 OrgT2 X24 OrgT3 X25 WST1 X26 WST2 X27 WST3 mcfw combination function weights X28 WY1T1,Y1T2 X29 WY1T2,Y1T3 X30 WY1T1,Y1T3 X31 WY2T1,Y1T2 X32 W Y2T2,Y1T3 X33 W Y2T1,Y1T3 X34 W Y3T1,Y3T2 X35 W Y3T2,Y3T3 X36 W Y3T1,Y3T3 X37 W Y4T1,Y4T2 X38 W Y4T2,Y4T3 X39 W Y4T1,Y4T3 X40 WTeam1T1, Team1T2 X41 WTeam1T2, Team1T3 X42 WTeam1T1, Team1T3 X43 WTeam2T1, Team2T2 X44 WTeam2T2, Team2T3 X45 WTeam2T1, Team2T3 X46 WET1, ET2 X47 WET2, ET3 X48 WET1, ET3 X49 WOrgT1, OrgT2 X50 WOrgT2, OrgT3 X51 WOrgT1, OrgT3 X52 error_occurs X53 error_proactive X54 supervisor_reflection

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Fig. 15.23 Combination function parameters for the first-order self-model states mcfp combination function parameters

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Fig. 15.24 Combination function parameters for the second-order self-model states

15 Computational Analysis of Transformational Organisational Change … ms iv

Fig. 15.25 Speed factors and initial values for the base level states

Fig. 15.26 Speed factors and initial values for the first-order self-model states

X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17 X18 X19 X20 X21 X22 X23 X24 X25 X26 X27

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1 speed factors WY1T1,Y1T2 X55 WY1T2,Y1T3 X55 WY1T1,Y1T3 X55 WY2T1,Y1T2 X56 W Y2T2,Y1T3 X56 W Y2T1,Y1T3 X56 W Y3T1,Y3T2 X56 W Y3T2,Y3T3 X56 W Y3T1,Y3T3 X56 W Y4T1,Y4T2 X56 W Y4T2,Y4T3 X56 W Y4T1,Y4T3 X56 WTeam1T1, Team1T2 X58 WTeam1T2, Team1T3 X58 WTeam1T1, Team1T3 X58 WTeam2T1, Team2T2 X58 WTeam2T2, Team2T3 X58 WTeam2T1, Team2T3 X58 WET1, ET2 X57 WET2, ET3 X57 WET1, ET3 X57 WOrgT1, OrgT2 X59 WOrgT2, OrgT3 X59 WOrgT1, OrgT3 X59 error_occurs 1 error_proactive 1 supervisor_reflection 1

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HYoung1 HYoung2-3-4 HExpert HTeam HOrg context_transformational_hiding_error_workshop control_workshop_trigger WWerror occurs, error proactive WWE, Y1 context_transformational_monhtly_meeting_sharing WWFeedforward WWE Feedforward context_transformational_monhtly_meeting_discussion WWFeedback control_change_of_teams TYoungT1T3 maintain_threshold context_transformational_daily_meeting_sharing WWteam Feedforward WWteam E Feedforward context_transformational_daily_meeting_discussion WWteam feedback day_one_sharing day_two_sharing day_three_sharing day_one_discussion day_two_discussion day_three_discussion

1 speed factors 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

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Fig. 15.27 Speed factors and initial values for the second-order self-model states

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Part VII

Mathematical Analysis for Network Models and Organisation Learning

This part addresses some further mathematical analysis behind the developed models. First, a conceptual background of computational modeling of dynamical systems is discussed. Results on the generality for adaptive network models are presented: it is shown how every smooth adaptive dynamic system can be modeled in a canonical manner by an adaptive self-modeling network. Moreover, it is discussed how equilibrium analysis can be done for adaptive network models, taking into account their connectivity structure and properties of the aggregation used. Next, it is shown how equilibrium analysis can be done for organisational learning models, such as those presented in Part III, illustrated for specific properties of the aggregation of mental models to obtain shared team and organisation mental models. In particular, the feed forward learning is analysed and how team and individual mental models can be learnt from shared organisation mental models by feedback learning.

Chapter 16

Modeling and Analysis of Adaptive Dynamical Systems via Their Canonical Self-modeling Network Representation Jan Treur

Abstract In this chapter, first it is shown how any (smooth) adaptive dynamical system can be modeled in a unique, canonical way as a self-modeling network model. In this way, any adaptive dynamical system has its canonical representation as a selfmodeling network model and can be analysed based on this canonical representation. This is applied in particular to perform equilibrium analysis for adaptive dynamical systems. Addressing equilibrium analysis for a self-modeling network model can relate to any of its network characteristics, such as its connectivity characteristics and aggregation characteristics. For aggregation characteristics, it is shown how, in contrast to often held beliefs, certain classes of nonlinear functions used for aggregation in network models enable equilibrium analysis of the emerging dynamics within the network like linear functions do. For connectivity characteristics, it is shown by introducing a form of stratification how specifically for acyclic networks the equilibrium values of all nodes can be directly computed (by the functions used to specify aggregation) from the equilibrium values of the (independent) nodes without incoming connections. Moreover, for any type of (cyclic) connectivity, by introducing a form of stratification for the network’s strongly connected components, similar equilibrium analysis results can be obtained relating equilibrium values in any component to equilibrium values in (independent) components without incoming connections. Keywords Adaptive dynamical system · Equilibrium analysis · Self-modeling network model

J. Treur (B) Social AI Group, Department of Computer Science, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 G. Canbalo˘glu et al. (eds.), Computational Modeling of Multilevel Organisational Learning and Its Control Using Self-modeling Network Models, Studies in Systems, Decision and Control 468, https://doi.org/10.1007/978-3-031-28735-0_16

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16.1 Introduction Self-modeling network models provide a widely applicable modeling approach for adaptive dynamical systems. This chapter introduces a canonical way to model any smooth adaptive dynamical system in a unique manner by a self-modeling network model, which shows that self-modeling network models provide a generic manner to model any smooth adaptive dynamical system. In this way it is shown that any adaptive dynamical system has a canonical representation as a self-modeling network defined by network characteristics such as connectivity, aggregation and timing characteristics. The network concepts of this canonical representation of an adaptive dynamical system provide useful tools for formal analysis of the dynamics of the adaptive dynamical system addressed. With this idea in mind, in the second part of this chapter, equilibrium analysis of self-modeling network models is addressed. Dynamics in network models are described by node states that change over time (for example, for individuals’ opinions, intentions, emotions, beliefs, …). Such dynamics depend on network characteristics for the connectivity between nodes, the aggregation of impacts from different nodes on a given node, and the timing of the node activation updates, e.g., Treur (2020b). For example, whether within a well-connected group in the end a common opinion, intention, emotion or belief is reached (a common value for all node states) depends on all these network characteristics. Sometimes silent assumptions are made about the aggregation and timing characteristics. For timing characteristics, often it is silently assumed that the nodes are updated in a synchronous manner, although in application domains this assumption is usually not fulfilled. For aggregation, in social network models usually linear functions are applied, which means that it is often not investigated how a variation of this choice of aggregation would affect the dynamics. In this chapter, a more diverse landscape is explored which is not limited by the fixed conditions on connectivity, aggregation or timing as are so often imposed. For connectivity, both acyclic and cyclic networks are considered here, and for cyclic networks both strongly connected networks and networks that are not strongly connected. For aggregation, both networks with linear and nonlinear aggregation are considered and for networks with nonlinear aggregation, networks with logistic aggregation are addressed but also networks with other forms of nonlinear aggregation that can be analysed similarly to how networks with linear aggregation can be analysed. Finally, for timing both synchronous and asynchronous timing are covered. The often-occurring use of linear functions for aggregation for social network models may be based on a more general belief that dynamical system models can be analysed better for linear functions than for nonlinear functions. Although there may be some truth in this if specifically logistic nonlinear functions are compared to linear functions, in the current chapter it is shown that such a belief is not correct in general. It is shown that also classes of nonlinear functions exist that enable good analysis possibilities when it comes to the emerging dynamics within a network model. Such classes and the dynamics they enable are analysed here in some depth, thereby among

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others not using any conditions on the connectivity but instead exploiting for any network its structure of strongly connected components (Bloem et al. 2006; Fleischer et al. 2000; Harary et al. 1965; Łacki 2013; Wijs et al. 2016). In Chap. 17 of this volume (Canbalo˘glu et al. 2023), as application domain in particular, the domain of multilevel organisational learning is addressed. It is shown how the equilibrium analysis methods addressed in the current chapter can be applied to adaptive self-modeling network models for multilevel organisational learning. Predictions are obtained on the eventually achieved learning results in terms of the mental models learnt. In the current chapter, in Sect. 16.2 the basics of the modeling and analysis approach used from Treur (2020b) are briefly introduced. In Sect. 16.3 it is shown that for the nonadaptive case this network-oriented modeling approach is equivalent to any smooth dynamical systems modeling approach (Theorem 16.1 and Corollary 16.1), and in Sect. 16.4 that for the adaptive case using self-modeling networks it is equivalent to any adaptive dynamical systems approach (Theorem 16.2 and Corollary 16.2). In Sects. 16.5, 16.6 and 16.7 a number of other mathematically proven results are presented on equilibrium analysis of network models. These results cover some variations concerning connectivity, aggregation and timing. Section 16.6 addresses equilibrium analysis for a specific condition on connectivity and no condition on aggregation or timing: the case of acyclic networks. It does so by introducing a form of stratification for acyclic networks, thus obtaining Theorem 16.3 and Corollary 16.3, which indeed do not require any condition on the functions used for aggregation or on the timing. In Sect. 16.7, equilibrium analysis is addressed for some specific conditions on aggregation and no conditions on connectivity and timing. In this case, following Treur (2020a) the general connectivity structure is analysed in some more depth by taking into account the strongly connected components of a network with their mutual connections and the condensation graph based on them, which is always acyclic, e.g., Harary et al. (1965). By introducing a stratification of this condensation graph similar to the stratification that is introduced in Sect. 16.6 for acyclic networks, results are obtained that are to a certain extent similar to the results for acyclic networks: Theorem 16.4 and Corollaries 16.4 and 16.5. In contrast to Sect. 16.6, these results do assume some conditions on the aggregation: the functions for aggregation have to be strictly monotonic, scalar-free and normalised. Finally, Sect. 16.8 is a discussion.

16.2 Modeling Dynamics and Adaptation by Self-modeling Networks In this section, the underlying network-oriented modeling approach used is briefly discussed and in relation to this the basic concepts used for equilibrium analysis. Following Treur (2020b), a temporal-causal network model is specified by the

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following types of network characteristics (here X and Y denote nodes of the network, also called states, which have state values X(t) and Y (t) over time t): • Connectivity characteristics. Connections from a state X to a state Y and weights ωX,Y for them. • Aggregation characteristics. For any state Y, some combination function cY (V 1 , …, V k ) defines the aggregation that is applied to the single impacts Vi = ω X i ,Y X i (t) on Y from its incoming connections from states X 1 , …, X k . • Timing characteristics. Each state Y has a speed factor ηY defining how fast it changes. The following canonical difference equation used for simulation and analysis purposes incorporates these network characteristics ωX,Y , cY , ηY in a numerical format: Y (t + ∆t) = Y (t) + ηY [aggimpact Y (t) − Y (t)]∆t

(16.1)

where aggimpact Y (t) = cY (ω X 1 ,Y X 1 (t), . . . , ω X k ,Y X k (t)) for any state Y and X 1 to X k are the states from which Y gets its incoming connections. This is equivalent to the differential equation dY (t)/dt = ηY [aggimpact Y (t) − Y (t)]∆t This expresses the general principle that network dynamics is implied (or entailed) by the network’s structure characteristics. A combination function is called normalised in a network model if the aggregated impact is 1 if all state values in it are 1, i.e., if cY (ω X 1 ,Y , . . . , ω X k ,Y ) = 1 for all Y The timing characteristics specified by speed factors ηY enable to model more realistic processes for which not all states change in a synchronous manner. Network models that do not possess this option are less flexible as they silently impose synchronous processing as an artefact. The aggregation characteristics specified by the choice of combination functions cY and their parameters provide another form of flexibility to fit better to specific realistic applications. Also in this case, network models that do not possess such an option are less flexible and silently impose artefacts that may make them fit less to specific applications. For example, for aggregation in social networks often only linear functions are used for aggregation. The above concepts enable to design network models and their dynamics in a declarative manner, based on mathematically defined functions and relations. Realistic network models are usually adaptive: often some of their network characteristics change over time. By using self-modeling networks (or network reification), a similar network-oriented conceptualisation can also be applied to adaptive networks

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to obtain a declarative description using mathematically defined functions and relations for them as well; see Treur (2020b). This works through the addition of new states to the network (called self-model states or reification states) which represent network characteristics by network states. If such self-model states are dynamic, they describe adaptive network characteristics. In a graphical 3D-format (e.g., see Sect. 16.7), such self-model states are depicted at a next level (self-model level or reification level), where the original network is at a base level. As an example, the weight ωX,Y of a connection from state X to state Y can be represented (at a next reification level) by a self-model state named WX,Y . During processing based on the canonical difference Eq. (16.1), the value of this state WX,Y is used as the connection weight ωX,Y it represents. Similarly, all other network characteristics from ωX,Y , cY (..), ηY can be made adaptive by including self-model states for them. As a selfmodeling network model is also a temporal-causal network model itself, as has been shown in Treur (2020b, Chap. 10), this self-modeling construction can easily be applied iteratively to obtain multiple self-model levels. This self-modeling network construction can provide higher-order adaptive network models, and has turned out quite useful to model, for example, plasticity and metaplasticity in the form of a second-order adaptive mental network with three levels, one base level and a first-order self-model level for adaptation of connections and a second-order self-model level for control over such adaptation; e.g., Treur (2020b, Chap. 4). Recently, a three-level self-modeling network architecture has also been adopted to successfully model adaptation of internal mental models and its control (Treur and Van Ments 2022) and to model organisational learning and its control (Canbalo˘glu et al. 2023). For the latter, see also Sect. 16.7.

16.3 Dynamical Systems and Their Canonical Network Representation Dynamical systems are usually specified in mathematical formats; see Ashby (1960 pp. 241–252) for some historical details. In the first place a finite set of states (or state variables) X 1 , …, X n is assumed describing how the system changes over time via functions X 1 (t), …, X n (t) of time t. As discussed in Port and van Gelder (1995) and Ashby (1960), a dynamical system is a state-determined system which can be formalized in a numerical manner by a relation (rule of evolution) that expresses how for each time point t the future value of each state X i at time t + s uniquely depends on s and on X 1 (t), …, X n (t). Therefore, a dynamical system can be described via n functions F i (X 1 , …, X n , s) for each X i in the following manner (see also Hendrikse et al. (2023)): X i (t + s) = Fi (X 1 (t), . . . , X n (t), s) for s ≥ 0

(16.2)

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If these functions F i and X i are continuously differentiable, we call the dynamical system smooth. Suppose such a smooth dynamical system is given. It turns out that it can always be described in a canonical manner by a temporal-causal network model; the argument is as follows. Consider (16.2) where the functions F i are continuously differentiable. In the particular case of s = 0 it holds X i (t) = Fi (X 1 (t), . . . , X n (t), 0)

(16.3)

Now assume s > 0. Subtracting (16.3) from (16.2) and dividing by s provides: [X i (t + s) − X i (t)]/s = [Fi (X 1 (t), . . . , X n (t), s) − Fi (X 1 (t), . . . , X n (t), 0)]/s (16.4) When the limit for s very small, approaching 0 is taken, it follows that   ∂ F i (X 1 (t), . . . , X n (t), s) d X i (t) = dt ∂s s=0

(16.5)

Now define the function gi (V 1 , …, V n ) by  gi (V1 , . . . , Vn ) = Vi +

∂ F i (V1 , . . . , Vn , s) ∂s

 (16.6) s=0

Then it holds   ∂ F i (X 1 (t), . . . , X n (t), s) d X i (t) = = gi (X 1 (t), . . . , X n (t)) − X i (t) dt ∂s s=0 (16.7) From this it immediately follows that d X i (t) = η X i [c X i (ω X 1 ,X i X 1 (t), . . . , ω X n ,X i X n (t)) − X i (t)] dt

(16.8)

with η X i = 1 and c X i = gi for all i and ω X j ,X i = 1 for all i and j. This shows that any given smooth dynamical system can be formalised in a canonical manner in temporal-causal network format. Definition 16.1 (canonical network representation of a smooth dynamical system) Let any smooth dynamical system be given by X i (t + s) = Fi (X 1 (t), . . . , X n (t), s) for s ≥ 0 for i = 1, . . . , n where the functions F i are continuously differentiable. Then the canonical temporalcausal network representation of it is defined by

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ω X j ,X i , c X i , η X i for all i and j with ω X j ,X i = 1 for all i and j   ∂ Fi (V1 , . . . , Vn , s) for all i c X i (V1 , . . . , Vn ) = Vi + ∂s s=0 η X i = 1 for all i This network representation has dynamics induced by the following canonical differential equations d X i (t) = η X i [c X i (ω X 1 ,X i X 1 (t), . . . , ω X n ,X i X n (t)) − X i (t)] dt Therefore, the following theorem is obtained: Theorem 16.1 (the canonical network representation of a smooth dynamical system) Any smooth dynamical system can be formalised in a canonical manner by a temporal-causal network model called its canonical network representation. Conversely, any temporal-causal network model is a dynamical system model. ∎ Note that the temporal-causal network model described by (16.7) as constructed in the above argument is fully connected, as ω X j ,X i = 1 for all i and j. As a corollary from Theorem 16.1 the following well-known result immediately follows. Corollary 16.1 (from smooth dynamical system to first-order differential equations) Any smooth dynamical system can be formalised as a system of first-order differential equations. ∎ The latter result was proven in a different way in Ashby (1960, pp. 241–252). For more details on the approach in the current and next section, see (Hendrikse et al. 2023).

16.4 Adaptive Dynamical Systems and Their Canonical Self-modeling Network Representation In this section, it is shown how the approach described in Sect. 16.3 can be extended to obtain a transformation of an adaptive dynamical system into a self-modeling network model. Adaptive dynamical systems are usually modeled by two levels of dynamical systems (see Fig. 16.1) where the higher level dynamical system models the dynamics of the parameters Pi,j of the lower level dynamical system (the lower level component in Fig. 16.1) that describes the dynamics of variables X i , for example by

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Fig. 16.1 Architecture of an adaptive dynamical system

Adaptation dynamical system Values Xi

Parameter values Pi,j

Base dynamical system

X i (t + s) = Fi (Pi.1 , . . . , Pi,k , X 1 (t), . . . , X n (t), s) for s ≥ 0

(16.9)

In addition, for the dynamics of the Pi,j there will also be a dynamical system (the upper level component in Fig. 16.1): Pi, j (t + s) = G i, j (P1.1 (t), . . . , Pn,k (t), X 1 (t), . . . , X n (t), s) for s ≥ 0

(16.10)

By applying the argument from Sect. 16.3 to both levels, a self-modeling network is obtained covering the entire adaptive dynamical system. d X i (t) X 1 (t), . . . , ω X n ,X i X n (t)) − X i (t)] (16.11) = η X [c X i (ω Pi,1 ,X i Pi,1 (t), . . . , ω Pi,k ,X i Pi,k (t), ω i X 1 ,X i dt d P i, j (t) = η P [c Pi, j (ω Pi,1 ,Pi, j Pi,1 (t), . . . , ω Pi,k ,Pi, j Pi,k (t), ω X 1 ,Pi, j X 1 (t), . . . , ω X n ,Pi, j X n (t)) − Pi, j (t)] i, j dt

(16.12)

where all η and ω are 1. Definition 16.2 (canonical self-modeling network representation of a smooth adaptive dynamical system) Let any smooth adaptive dynamical system be given by X i (t + s) = Fi (Pi.1 , . . . , Pi,k , X 1 (t), . . . , X n (t), s) for s ≥ 0, i = 1, . . . , n Pi, j (t + s) = G i, j (P1.1 (t), . . . , Pn,k (t), X 1 (t), . . . , X n (t), s) for s ≥ 0, j = 1, . . . , k

where the functions F i and Pi,j are continuously differentiable. Then the canonical self-modeling network representation of it is defined by characteristics ω, c, η where all ω and η are 1 and 

c X i Wi,1 , . . . , Wi,k , V1 , . . . , Vn

c Pi, j







  ∂ F i Wi,1 , . . . , Wi,k , V1 , . . . , Vn , s = Vi + ∂s







for all i

s=0

∂G i Wi,1 , . . . , Wi,k , V1 , . . . , Vn , s Wi,1 , . . . , Wi,k , V1 , . . . , Vn = Wi, j + ∂s

 s=0

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This self-modeling network representation has dynamics induced by the following canonical differential equations d X i (t) X 1 (t), . . . , ω X n ,X i X n (t)) − X i (t)] = η X [c X i (ω Pi,1 ,X i Pi,1 (t), . . . , ω Pi,k ,X i Pi,k (t), ω i X 1 ,X i dt d P i, j (t) = η P [c Pi, j (ω Pi,1 ,Pi, j Pi,1 (t), . . . , ω Pi,k ,Pi, j Pi,k (t), ω X 1 ,Pi, j X 1 (t), . . . , ω X n ,Pi, j X n (t)) − Pi, j (t)] i, j dt

Thus, the following theorem is obtained (for more details, see Hendrikse et al. (2023)): Theorem 16.2 (the canonical self-modeling network representation of an adaptive dynamical system) Any adaptive smooth dynamical system model can be transformed in a canonical manner into a self-modeling network model called its canonical self-modeling network representation. Conversely, any self-modeling network model is an adaptive dynamical system model. These also apply to higher-order adaptive dynamical systems in relation to higher-order self-modeling networks. ∎ As a corollary it now follows that any adaptive dynamical system can be described by first-order differential equations: Corollary 16.2 (from a smooth adaptive dynamical system to first-order differential equations) Any smooth adaptive dynamical system can be formalised as a system of first-order differential equations. ∎

16.5 Basic Concepts for Equilibrium Analysis of Dynamic and Adaptive Networks The following types of properties are often considered for equilibrium analysis of dynamical systems in general. Definition 16.3 (stationary point, increasing, decreasing, equilibrium) Let Y be a network state • • • •

Y has a stationary point at t if dYdt(t) = 0 Y is increasing at t if dYdt(t) > 0 Y is decreasing at t if dYdt(t) < 0 The network model is in equilibrium at t if every state Y of the model has a stationary point at t.

For network models, the following criteria in terms of the network characteristics ωX,Y , cY , ηY can be derived from the generic difference Eq. (16.1); see also Treur (2016, 2018):

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Criteria for network model dynamics Let Y be a state and X 1 , …, X k the states connected toward Y. For nonzero speed factors ηY the following criteria in terms of network  characteristics for connectivity  and aggregation apply; here aggimpact Y (t) = cY ω X 1 ,Y X 1 (t), . . . , ω X k ,Y X k (t) : • • • •

Y has a stationary point at t Y is increasing at t Y is decreasing at t The network model is in equilibrium at t

⇔ ⇔ ⇔ ⇔

aggimpact Y (t) = Y (t) aggimpact Y (t) > Y (t) aggimpact Y (t) < Y (t) aggimpact Y (t) = Y (t) for every Y

The above criteria for a network being in an equilibrium (assuming nonzero speed factors) depend both on the connections weights ωX,Y used for connectivity and on the combination function cY used for aggregation. Note that in a self-modeling network, these criteria can be applied not only to base states but also to self-model states. In the latter case they can be used for equilibrium analysis of learning processes, as will be illustrated for organisational learning in Sect. 16.7. Other applications of this type of analysis of network dynamics can be found in (Canbalo˘glu et al. 2023), Chapter 6 (Sect. 6.6), Chapter 14 (Sect. 14.7), Chapter 8 (Sect. 8.6), and Chapter 17 (Sects. 17.3–17.7) (this volume). In subsequent sections the equilibrium analysis is addressed not at the level of specific network structures and implied dynamics but at a more abstract level of properties of network structures and properties of dynamics implied by them. More specifically, in the remainder of this chapter, it will be analysed how the criteria relate certain properties of the connectivity characteristics and aggregation characteristics: • For connectivity characteristics: how the criteria relate to properties of paths based on connections, such as – whether the network is acyclic or cyclic – for cyclic networks, the way in which the network is composed of its strongly connected components (the condensation graph of the network) • For aggregation characteristics: how the criteria relate to properties of the combination functions defining the network’s aggregation, such as – monotonicity – being scalar-free – comparison relations between combination functions These properties will not only apply to linear functions but also to a wider class of functions extending the class of linear functions beyond the border with the class of nonlinear functions. Exploring nonlinear functions in this class and how some of them still may relate to linear functions is one of the main aims of the current chapter.

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16.6 Equilibrium Analysis for Acyclic Networks In the current section a relatively simple case will be addressed where a condition on the connectivity in the network (but no conditions on aggregation in the network) is considered: the case of acyclic networks.

16.6.1 Stratification for Acyclic Networks A relatively simple but still very useful structure that can be added to any acyclic graph or network is the following form of stratification. Definition 16.4 (stratification for an acyclic graph or network) For an acyclic graph or network, stratification levels 0, 1,.. are (inductively) assigned to the nodes such that the following hold: • For a node Y without incoming connections from other nodes: level(Y ) = 0 • For a node Y with incoming connections from nodes X 1 , . . . , X k : level(Y ) = 1 + maxi (level(X i )) A simple example of an acyclic network with 7 states is shown in Fig. 16.2. Based on their connectivity, the four indicated stratification levels are obtained. Note that for each state Y, the longest path from any level 0 state to Y determines its stratification level. For example, in Fig. 16.2 state X6 has level 2 since its longest path from any level 0 state is from X2 via X5 , and X7 has level 3 since its longest path from a level 0 state is from X2 via X5 and X6 .

16.6.2 Using Stratification for Equilibrium Analysis of Acyclic Networks Stratification is a useful instrument to analyse equilibria of acyclic networks; the following theorem can easily be obtained. It shows how for acyclic networks equilibrium values of states (with nonzero speed factor) for all levels i > 0 depend on equilibrium values of states at a lower level < i. This dependency across levels can directly be expressed by a mathematical function expression using the network characteristics for connectivity (the connection weights ωX,Y ) and aggregation (the combination functions cY (…)); see Sect. 16.11 for proofs of all results in this chapter. Theorem 16.3 (relating equilibrium values for an acyclic network from different stratification levels) Suppose a network is acyclic and all states with incoming connections from other states have nonzero speed factors. Then the following hold.

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X1 X5 X2

X3 X6

X7

X4

Level 0

Level 1

Level 2

Level 3

Fig. 16.2 Example acyclic network with connectivity that induces the indicated stratification levels

(a) In any equilibrium for each state Y of any stratification level i > 0, the equilibrium value Y depends by some mathematical function on the equilibrium values X of states X of level < i. (b) More specifically, in any equilibrium for any state Y of stratification level i > 0, its equilibrium value Y can be determined from equilibrium values Xj of states X j at lower levels < i by: ∎ Y = cY (ω X 1 ,Y X1 , . . . , ω X k ,Y Xk ) By iterating the dependency relations across stratification levels described in Theorem 16.3, the equilibrium values of all states from all levels can be related to equilibrium values of states at level 0. This dependency can be described again by a mathematical function expression using the network characteristics for connectivity (the connection weights ωX,Y ) and aggregation (the combination functions cY (…)). This is expressed in Corollary 16.3. Corollary 16.3 (relating all equilibrium values for an acyclic network to those of the level 0 states) Suppose a network is acyclic and all states with incoming connections from other states have nonzero speed factors. Then the following hold. (a) By applying Theorem 16.1(b) iteratively according to the stratification levels, in a straightforward manner for each state Y of the network, a mathematical expression can be obtained showing how its equilibrium value depends on the equilibrium values of states of level 0. (b) The mathematical expression in a) defines a mathematical function for Y in terms of the equilibrium values X of some states X of level 0 with as parameters connectivity and aggregation characteristics ω Z 1 ,Z 2 and cZ (..) of the network relating to states Z, Z 1 , Z 2 on the paths from the involved level 0 states X to state

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Y . This mathematical function essentially is based on an iterated composition of combination functions of the states on the paths to Y in the network, nested according to the (inverse) branching structure of these paths to Y. ∎ Note that although the mathematical functions to describe the dependencies for equilibrium values still can be expressed directly based on the connectivity and aggregation characteristics ωX,Y and cY (…) of the network, in Corollary 16.3 they get a more complex, nested structure. First, for the example acyclic network of Fig. 16.2 (assuming the combination function max), by Theorem 16.3 the following relations between the equilibrium values of states at stratification levels 0 to 4 are obtained (here the Xi are the equilibrium values of states Xi ): Level 3 equilibrium value X7 : dependence on Level 1 and 2 equilibrium values X5 and X6 X7 = max(X5 , X6 ) Level 2 equilibrium value X6 : dependence on Level 0 and Level 1 equilibrium values X3 , X4 , and X5 X6 = max(X3 , X4 , X5 ) Level 1 equilibrium value X5 : dependence on Level 0 equilibrium values X5 = max(X1 , X2 ) Next, applying the iteration indicated in Corollary 16.3, this leads to the following functions for how the equilibrium values for the level 2 and 3 states X6 and X7 depend on the ones of the level 0 states: X6 = max(X3 , X4 , X5 ) = max(X3 , X4 , max(X1 , X2 )) X7 = max(X5 , X6 ) = max(max(X1 , X2 ), max(X3 , X4 , X5 )) = max(max(X1 , X2 ), max(X3 , X4 , max(X1 , X2 ))) = max(X1 , ..., X4 )

Note that these are indeed nested combination functions according to the paths in the network to X6 and X7 . This illustrates how in an acyclic network, the equilibrium values of all states of the entire network are determined by the equilibrium values of the level 0 states. In Chap. 17 of this volume (Canbalo˘glu et al. 2023), other examples of expressions of nested combination functions as indicated in Corollary 16.3 will be shown for the application to a network model for organisational learning.

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Note also that for realistic domains, networks are often not acyclic: usually they include at least some cycles or even many of them. Then the above Theorem 16.3 and Corollary 16.3 are not applicable to the network as a whole. However, even for such cyclic networks, sometimes it can be useful to consider subnetworks that still are acyclic and apply the above Theorem 16.3 and Corollary 16.3 to them. As an example, this will be illustrated for the application to organisational learning addressed in Chap. 17 of this volume (Canbalo˘glu et al. 2023). Moreover, following Treur (2020a) in Sect. 16.7 it will be shown how the approach based on stratification applied for Theorem 16.3 and Corollary 16.3 to the nodes of the (acyclic) network can also be applied not to the nodes but to (the condensation graph of) the strongly connected components of any network. In that section, some further results are obtained for networks with any type of (possibly cyclic) connectivity. The results there also show relations between equilibrium values of states from different stratification levels (and with the states at level 0) and in that sense are to a certain extent similar to those of Theorem 16.3 and Corollary 16.3 but much more general.

16.7 Equilibrium Analysis for Any Network by Its Strongly Connected Components In this section an equilibrium analysis approach is discussed that considers how the network is composed of its strongly connected components. It is sometimes believed that for dynamical models the borderline between linear and nonlinear functions is also the borderline between well-analyzable behavior and less wellanalyzable behavior. In contrast to this, it has been found that this borderline between well-analyzable behavior and less well-analyzable behavior lies somewhere within the domain of nonlinear functions: between one class (called monotonic scalar-free functions) covering both linear and nonlinear functions and another subclass of the class of nonlinear functions not satisfying these. More specifically, whether or not combination functions are scalar-free is an important factor determining whether or not by social contagion all members of a well-connected social network converge to the same level of emotion, opinion, information, belief, intention, or any other mental or physical state; e.g., Treur (2020b, Chaps. 11 and 12). The class of scalar-free functions includes all linear functions but also includes a number of types of nonlinear functions, such as the weighted Euclidean functions and weighted geometric functions (as will be defined below). In this section some further analysis is made of scalar-free functions, thereby also using a weakened variant of them called weakly scalar-free functions. The definitions are as follows. Definition 16.5 (weakly scalar-free and scalar-free functions) Consider functions f : R k → R and θ : R → R for some subset R ⊆ R which is R or R>0 . (a) A function f : R k → R is called weakly scalar-free for function θ if for all

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V1 , . . . , Vk ∈ R and all α ∈ R it holds f (αV1 , . . . , αVk ) = θ(α) f (V1 , . . . , Vk )

(b) A function f : R k → R is called scalar-free if for all V1 , . . . , Vk ∈ R and all α ∈ R it holds f (αV 1 , . . . , αV k ) = α f (V1 , . . . , Vk )

16.7.1 Introducing Stratification for the Strongly Connected Components of a Network As an illustration, consider the example of a mental network model with connectivity depicted in Fig. 16.3. This is a mental network model for how a person is sensing (sensor state sss ) a stimulus s in the world (word state wss ), represents this (representation state srss ), and is triggered to prepare (preparation state psa ) and perform (execution state esa ) action a, after evaluation of the predicted (predicted effect representation state srse ) effect e of this action. In simulations it can be seen that because of a constant value a of stimulus wss all state values are increasing until they reach an equilibrium value a as well. The question then is whether these observations based on one or more simulation experiments agree with a mathematical equilibrium analysis. In the current section a general perspective is followed, and theorems are discussed that have been found based on the network’s strongly connected components described in Treur (2020a). The perspective is based on the notion of (strongly connected) component of a network; this is a maximal subnetwork C such that every node within C can be reached from every other node via a path following the direction of the connections; e.g., (Bloem et al. 2006; Fleischer et al. 2000; Harary et al. 1965; Łacki 2013; Wijs et al. 2016). From this literature, it is known that these components partition the set of nodes in disjoint subsets and the connections between them induce a socalled condensation graph with the components as nodes which is always acyclic. In Fig. 16.4 these components are shown for the example network: C1 to C5 . In Treur (2020a) the notion of stratification was introduced for the condensation graph based on this a partition of a network so that each component gets a level (or stratum) assigned; see Sect. 16.3 for a more precise definition of this notion of

Fig. 16.3 Connectivity of the example network model

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Fig. 16.4 Stratified strongly connected components for the example network model

stratification of an acyclic network or graph in general. In this case the stratification levels are 0 to 4 as indicated in Fig. 16.4.

16.7.2 Using the Stratification to Relate Equilibrium Values for Different Components Based on the levels defined by this notion of stratification, a few general theorems and corollaria have been found and proven and presented in Treur (2020a); see also Treur (2020b, Chaps. 12 and 15). For aggregation these are not limited to linear functions and for connectivity no condition at all is demanded; some of these results are the following. Theorem 16.4 (relating equilibrium values of states in components at different levels) If the following aggregation conditions are fulfilled • The combination functions are normalised, scalar-free and strictly increasing then in an achieved equilibrium the following hold: (a) In any level 0 component C • All states in C have the same equilibrium value V • This V is between the highest and lowest initial value of the states within C (b) If for any level i > 0 component C the components C 1 ,…, C k are the strongly connected components from which C gets an incoming connection, then • The equilibrium values of the states in C are between the highest and lowest equilibrium values of the states in C 1 ,…, C k • If all states in C 1 ,…, C k have the same equilibrium value V , then also all states in C have this same equilibrium value V ∎ Corollary 16.4 (dependence of all equilibrium values on the values in level 0 components) If the following aggregation conditions are fulfilled

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• The combination functions are normalised, scalar-free and strictly increasing then in an achieved equilibrium: (a) The equilibrium values of all states in the network • are between the highest and lowest equilibrium values of the states in the level 0 components • are between the highest and lowest initial values of the states in the level 0 components (b) If all states in all level 0 components C have the same equilibrium value V, then all states of the whole network have that same equilibrium value V ∎ For the special case of a strongly connected network (consisting of one component), this implies: Corollary 16.5 (strongly connected networks) If the following connectivity and aggregation conditions are fulfilled. • The network is strongly connected • The combination functions are normalised, scalar-free and strictly increasing then in an achieved equilibrium: • All states have the same equilibrium value V • This equilibrium value V is between the highest and lowest initial values of the states ∎ Given that in the example network model there is only one level 0 component with constant value a, by Theorem 16.4 or Corollary 16.4 above it can be concluded that all states will have equilibrium value a, as long as the aggregation conditions are fulfilled. Note that in an acyclic network, each state forms a (singleton) strongly connected component. Applying Theorem 16.4 and its corollaries to this special case will again provide Theorem 16.1 and Corollary 16.1 from Sect. 16.3. That shows that the above results generalise the results from Sect. 16.3.

16.8 Discussion In this chapter, mathematical analysis was addressed for network models. The material mainly comes from Treur (2018, 2020a, 2021), Canbalo˘glu and Treur (2022). The first type of analysis addressed shows that any smooth adaptive dynamical system has a canonical representation by a self-modeling network. Furthermore, equilibrium analysis was addressed, both for acyclic and cyclic networks, in the latter case making use of the network’s strongly connected components (Bloem et al. 2006; Fleischer et al. 2000; Harary et al. 1965; Łacki 2013; Wijs et al. 2016). The intended

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application here is on organisational learning and computational network models for it. See for this application Chap. 17 of this volume (Canbalo˘glu et al. 2023).

References Ashby, W.R.: Design for a Brain. Chapman and Hall, London (2nd extended edition) (1960). Bloem, R., Gabow, H.N., Somenzi, F.: An algorithm for strongly connected component analysis in n log n symbolic steps. Form. Methods Syst. Des. 28, 37–56 (2006) Canbalo˘glu, G., Treur, J.: Equilibrium analysis for linear and non-linear aggregation in network models: applied to mental model aggregation in multilevel organizational learning. J. Inf. Telecommun. 6(3), 289–340 (2022) Canbalo˘glu, G., Treur, J., Wiewiora, A. (eds.): Computational Modeling of Multilevel Organisational Learning and Its Control Using Self-Modeling Network Models (this volume). Springer Nature (2023) Fleischer, L.K., Hendrickson, B., Pınar, A.: On identifying strongly connected components in parallel. In: Rolim J. (ed.) Parallel and Distributed Processing. IPDPS 2000. Lecture Notes in Computer Science, vol. 1800, pp. 505–511. Springer (2000) Harary, F., Norman, R.Z., Cartwright, D.: Structural Models: An Introduction to the Theory of Directed Graphs. Wiley, New York (1965) Hendrikse, S.C.F., Treur, J., Koole, S.L.: Modeling emerging interpersonal synchrony and its related adaptive short-term affiliation and long-term bonding: a second-order multi-adaptive neural agent model. Int. J. Neural Syst. (2023). https://doi.org/10.1142/S0129065723500387 Łacki, J.: Improved deterministic algorithms for decremental reachability and strongly connected components. ACM Trans. Algorithms 9(3), (2013). Article 27 Port, R.F., van Gelder, T.: Mind as Motion: Explorations in the Dynamics of Cognition. MIT Press, Cambridge, MA (1995) Treur, J.: Verification of temporal-causal network models by mathematical analysis. Vietnam J. Comput. Sci. 3, 207–221 (2016) Treur, J.: Relating emerging network behaviour to network structure. In: Proc. of the 7th International Conference on Complex Networks and their Applications, ComplexNetworks’18, vol. 1. Studies in Computational Intelligence, vol. 812, pp. 619–634. Springer Publishers (2018). Treur, J.: Analysis of a network’s asymptotic behaviour via its structure involving its strongly connected components. Network Science 8(S1), S82–S109 (2020a) Treur, J.: Network-Oriented Modeling for Adaptive Networks: Designing Higher-Order Adaptive Biological, Mental and Social Network Models. Springer Nature Publishers (2020b) Treur, J., Van Ments, L. (eds.): Mental Models and Their Dynamics, Adaptation, and Control: A Self-modeling Network Modeling Approach. Springer Nature (2022) Treur, J.: On the dynamics and adaptivity of mental processes: relating adaptive dynamical systems and self-modeling network models by mathematical analysis. Cogn. Syst. Res. 70, 93–100 (2021) Wijs, A., Katoen, J.P., Bošnacki, D.: Efficient GPU algorithms for parallel decomposition of graphs into strongly connected and maximal end components. Form. Methods Syst. Des. 48, 274–300 (2016)

Chapter 17

Equilibrium Analysis for Multilevel Organisational Learning Models Gülay Canbalo˘glu and Jan Treur

Abstract In this chapter, equilibrium analysis for network models is addressed and applied to a network model of multilevel organisational learning. Equilibrium analysis can consider both properties of aggregation characteristics and properties of connectivity characteristics of a network. For connectivity characteristics, it is shown by introducing a form of stratification how for acyclic networks the equilibrium values of all nodes can be directly computed (by any functions used for aggregation) from those of the (independent) nodes without incoming connections. Moreover, by introducing a form of stratification for the network’s strongly connected components, it is also shown for any type of connectivity, similar equilibrium analysis results can be obtained relating equilibrium values in any component to equilibrium values in (independent) components without incoming connections. For aggregation characteristics, it is shown how certain classes of nonlinear functions used for aggregation in network models enable equilibrium analysis of the emerging dynamics within the network like linear functions do. All these results are illustrated by applying them to an example network model for organisational learning. Keywords Equilibrium analysis · Multilevel organisational learning

G. Canbalo˘glu · J. Treur (B) Social AI Group, Department of Computer Science, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands e-mail: [email protected] G. Canbalo˘glu e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 G. Canbalo˘glu et al. (eds.), Computational Modeling of Multilevel Organisational Learning and Its Control Using Self-modeling Network Models, Studies in Systems, Decision and Control 468, https://doi.org/10.1007/978-3-031-28735-0_17

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17.1 Introduction Equilibrium analysis for the dynamics in network models depends on network characteristics for the connectivity between nodes, the aggregation of impacts from different nodes on a given node, and the timing of the node activations, e.g., (Treur, 2020b). In (Canbalo˘glu et al. 2023b), Ch 16 (this volume), it was shown how equilibrium analysis for network models can be performed and also how this can be used for equilibrium analysis for any adaptive dynamical system. In this chapter, such analysis for the domain of multilevel organisational learning is addressed (Crossan et al. 1999; Kim, 1993; Wiewiora et al. 2020, 2019). It is shown how equilibrium analysis methods can be applied to adaptive self-modeling network models for multilevel organisational learning (Canbalo˘glu et al. 2022, 2023d, 2023a; Canbalo˘glu and Treur 2022). Predictions are obtained on the eventually achieved learning results in terms of the mental models learnt. In this chapter, in Sect. 17.2 the basics of the modeling and analysis approach used from (Treur, 2020b) are briefly introduced. In Sects. 17.3, 17.4, 17.5 and 17.6 a few mathematically proven results are presented on equilibrium analysis of network models; all proofs can be found in the Appendix of (Canbalo˘glu and Treur 2022). These results cover many variations concerning connectivity, aggregation, and timing. In particular, these results address both linear and nonlinear types of aggregation. Section 17.3 addresses equilibrium analysis for a specific condition on connectivity (and no condition on aggregation or timing), namely the case of acyclic networks. It does so by introducing a form of stratification for acyclic networks, thus obtaining Theorem 17.1 and Corollary 17.1, which indeed do not require any condition on the functions used for aggregation or on the timing. In Sect. 17.4, equilibrium analysis is addressed for some specific conditions on aggregation (and no conditions on connectivity and timing). Some (comparative equilibrium analysis) results are obtained for cases of monotonicity of functions used for aggregation and comparison relations between a few often-considered specific types of such functions (scaled sum, Euclidean, geometric, logistic, minimum and maximum functions); here in addition to a number of propositions for different cases, Theorem 17.2 and Corollaries 17.2 and 17.3 are obtained. Section 17.5 addresses another condition on aggregation (and again no condition on connectivity or timing); it in addition focuses on the role of being scalar-free for the functions used for aggregation, leading to results for the more general class of monotonic and scalar-free functions formulated as Theorem 17.3. In Sect. 17.6, again only conditions on aggregation are considered and no conditions on connectivity or timing. Following (Treur 2020a) the general connectivity structure is analysed in some more depth by considering the strongly connected components of a network with their mutual connections and the condensation graph based on them, which is always acyclic, e.g., (Harary et al. 1965). By introducing a stratification of this condensation graph similar to the stratification that is introduced in Sect. 17.3 for acyclic networks, results are obtained that are to a certain extent similar to the results for acyclic networks: Theorem 17.4 and Corollaries 17.4 and

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17.5. In contrast to Sect. 17.3, these results do assume some conditions on the aggregation: the functions for aggregation have to be strictly monotonic, scalar-free and normalised. The main results presented in Sect. 17.3, 17.4, 17.5 and 17.6, are applied in Sect. 17.7 to obtain equilibrium analysis results for network models of multilevel organisational learning processes. Finally, Sect. 17.8 is a discussion.

17.2 Modeling and Analysis of Dynamics and Adaptation for Networks In this section, the underlying network-oriented modeling approach used is briefly discussed and in relation to this the basic concepts used for equilibrium analysis.

17.2.1 Modeling by Dynamic and Adaptive Networks Following (Treur, 2020b), a temporal-causal network model is specified by the following types of network characteristics (here X and Y denote nodes of the network, also called states, which have state values X(t) and Y(t) over time t): • Connectivity characteristics. Connections from a state X to a state Y and weights ωX,Y • Aggregation characteristics. For any state Y, some combination function cY (V 1 , . . . , Vk ) defines the aggregation that is applied to the single impacts Vi = ω X i ,Y X i (t)) on Y from its incoming connections from states X 1 , …, X k . • Timing characteristics. Each state Y has a speed factor ηY defining how fast it changes. The following canonical difference equation used for simulation and analysis purposes incorporates these network characteristics ωX,Y , cY , ηY in a numerical format: Y (t + ∆t) = Y (t) + ηY [aggimpact Y (t) − Y (t)]∆t

(17.1)

where aggimpact Y (t) = cY (ω X 1 ,Y X 1 (t), . . . , ω X k ,Y X k (t)) for any state Y and X 1 to X k are the states from which Y gets its incoming connections. This expresses the general principle that network dynamics is implied (or entailed) by the network’s structure characteristics. A combination function is called normalised in a network model if the aggregated impact is 1 if all state values in it are 1, i.e., if. cY (ω X 1 ,Y , . . . , ω X k ,Y ) = 1 for all Y

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The timing characteristics specified by speed factors ηY enable to model more realistic processes for which not all states change in a synchronous manner. Network models that do not possess this option are less flexible as they silently impose synchronous processing as an artefact. The aggregation characteristics specified by the choice of combination functions cY and their parameters provide another form of flexibility to fit better to specific realistic applications. Also in this case, network models that do not possess such an option are less flexible and may silently impose artefacts that may make them fit less to specific applications. For example, for aggregation in social networks often only linear functions are used for aggregation. The above concepts enable to design network models and their dynamics in a declarative manner, based on mathematically defined functions and relations. Realistic network models are usually adaptive: often some of their network characteristics change over time. By using self-modeling networks (or network reification), a similar network-oriented conceptualisation can also be applied to adaptive networks to obtain a declarative description using mathematically defined functions and relations for them as well; see (Treur 2020b). This works through the addition of new states to the network (called self-model states or reification states) which represent network characteristics by network states. If such self-model states are dynamic, they describe adaptive network characteristics. In a graphical 3D-format (e.g., see Sect. 17.7), such self-model states are depicted at a next level (self-model level or reification level), where the original network is at a base level. As an example, the weight ωX,Y of a connection from state X to state Y can be represented (at a next reification level) by a self-model state named WX,Y . During processing based on the canonical difference Eq. (17.1), the value of this state WX,Y is used as the connection weight ωX ,Y it represents. Similarly, all other network characteristics from ωX,Y , cY (..), ηY can be made adaptive by including self-model states for them. As a selfmodeling network model is also a temporal-causal network model itself, as has been shown in (Treur, 2020b), Chap. 10, this self-modeling construction can easily be applied iteratively to obtain multiple self-model levels. This self-modeling network construction can provide higher-order adaptive network models, and has turned out quite useful to model, for example, plasticity and metaplasticity in the form of a second-order adaptive mental network with three levels, one base level and a first-order self-model level for adaptation of connections and a second-order self-model level for control over such adaptation; e.g., (Abraham and Bear 1996) and (Treur, 2020b), Ch 4. Recently, a three-level selfmodeling network architecture has also been adopted to successfully model adaptation of internal mental models and its control (Van Ments and Treur 2021; Treur and Van Ments, 2022) and to model organisational learning and its control (Canbalo˘glu et al. 2022, 2023a, d; Canbalo˘glu et al. 2023b). In (Hendrikse et al. 2023) it has been proven that every smooth adaptive dynamical system has a self-modeling network representation, which shows that this format is very general.

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17.2.2 Basic Concepts for Equilibrium Analysis of Dynamic and Adaptive Networks The following types of properties are often considered for equilibrium analysis of dynamical systems in general. Definition (stationary point, increasing, decreasing, equilibrium) Let Y be a network state • • • •

Y has a stationary point at t if dYdt(t) = 0 Y is increasing at t if dYdt(t) > 0 Y is decreasing at t if dYdt(t) < 0 The network model is in equilibrium at t if every state Y of the model has a stationary point at t.

For network models, the following criteria in terms of the network characteristics ωX,Y , cY , ηY can be derived from the generic difference Eq. (17.1); see also (Treur, 2016, 2018): Criteria for network model dynamics Let Y be a state and X 1 , …, X k the states connected toward Y. For nonzero speed factors ηY the following criteria in terms of network characteristics for connectivity and aggregation apply; here aggimpact Y (t) = cY (ω X 1 ,Y X 1 (t), . . . , ω X k ,Y X k (t)): Y has a stationary point at t Y is increasing at t Y is decreasing at t The network model is in equilibrium a t

The above criteria for a network being in an equilibrium (assuming nonzero speed factors) depend both on the connections weights ωX,Y used for connectivity and on the combination function cY used for aggregation. Note that in a self-modeling network, these criteria can be applied not only to base states but also to self-model states. In the latter case they can be used for equilibrium analysis of learning processes, as will be illustrated for organisational learning in Sect. 17.7. In subsequent sections the equilibrium analysis is addressed not at the level of specific network structures and implied dynamics but at a more abstract level of properties of network structures and properties of dynamics implied by them. More specifically, in the remainder of this chapter, it will be analysed how the criteria relate certain properties of the connectivity characteristics and aggregation characteristics: • For connectivity characteristics: how the criteria relate to properties of paths based on connections, such as – whether the network is acyclic or cyclic

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– for cyclic networks, the way in which the network is composed of its strongly connected components (the condensation graph of the network) • For aggregation characteristics: how the criteria relate to properties of the combination functions defining the network’s aggregation, such as – monotonicity – being scalar-free – comparison relations between combination functions These properties will not only apply to linear functions but also to a wider class of functions extending the class of linear functions beyond the border with the class of nonlinear functions. Exploring nonlinear functions in this class and how some of them still may relate to linear functions is one of the main aims of the current chapter.

17.3 Equilibrium Analysis under Connectivity Conditions: Acyclic Networks In the current section a relatively simple case will be addressed where a condition on the connectivity in the network (but no conditions on aggregation in the network) is considered: the case of acyclic networks.

17.3.1 Stratification for Acyclic Graphs or Networks A relatively simple but still very useful structure that can be added to any acyclic graph or network is the following form of stratification. Definition (stratification for an acyclic graph or network) For an acyclic graph or network, stratification levels 0, 1, … are (inductively) assigned to the nodes such that the following hold: • For a node Y without incoming connections from other nodes: level(Y ) = 0 • For a node Y with incoming connections from nodes X 1 , …, X k : • level(Y ) = 1 + maxi (level(X i )) A simple example of an acyclic network with 7 states is shown in Fig. 17.1. Based on their connectivity, the four indicated stratification levels are obtained. Note that for each state Y, the longest path from any level 0 state to Y determines its stratification level. For example, in Fig. 1 state X6 has level 2 since its longest path from any level 0 state is from X2 via X5 , and X7 has level 3 since its longest path from a level 0 state is from X2 via X5 and X6 .

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X1 X5 X2

X3 X6

X7

X4

Level 0

Level 1

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Fig. 17.1 Example acyclic network with connectivity that induces the indicated stratification levels

17.3.2 Using Stratification for Equilibrium Analysis of Acyclic Networks Stratification is a useful instrument to analyse equilibria of acyclic networks; the following theorem can easily be obtained. It shows how for acyclic networks equilibrium values of states (with nonzero speed factor) for all levels i > 0 depend on equilibrium values of states at a lower level < i. This dependency across levels can directly be expressed by a mathematical function expression using the network characteristics for connectivity (the connection weights ωX ,Y ) and aggregation (the combination functions cY (…)); see (Treur 2020a) and (Canbalo˘glu and Treur 2022) for further details and for proofs. Theorem 17.1 (relating equilibrium values for an acyclic network from different stratification levels) Suppose a network is acyclic and all states with incoming connections from other states have nonzero speed factors. Then the following hold. (a) In any equilibrium for each state Y of any stratification level i > 0, the equilibrium value Y depends by some mathematical function on the equilibrium values X of states X of level < i. (b) More specifically, in any equilibrium for any state Y of stratification level i > 0, its equilibrium value Y can be determined from equilibrium values Xj of states X j at lower levels < i by: Y = cY (ω X 1 ,Y X1 , . . . , ω X k ,Y Xk ) ∎

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By iterating the dependency relations across stratification levels described in Theorem 17.1, the equilibrium values of all states from all levels can be related to equilibrium values of states at level 0. This dependency can be described again by a mathematical function expression using the network characteristics for connectivity (the connection weights ωX ,Y ) and aggregation (the combination functions cY (…)). This is expressed in Corollary 17.1. Corollary 17.1 (relating all equilibrium values for an acyclic network to those of the level 0 states) Suppose a network is acyclic and all states with incoming connections from other states have nonzero speed factors. Then the following hold. (a) By applying Theorem (1b) iteratively according to the stratification levels, in a straightforward manner for each state Y of the network, a mathematical expression can be obtained showing how its equilibrium value depends on the equilibrium values of states of level 0. (b) The mathematical expression in (a) defines a mathematical function for Y in terms of the equilibrium values X of some states X of level 0 with as parameters connectivity and aggregation characteristics ωZ1,Z2 and cZ (..) of the network relating to states Z, Z 1 , Z 2 on the paths from the involved level 0 states X to state Y. This mathematical function essentially is based on an iterated composition of combination functions of the states on the paths to Y in the network, nested according to the (inverse) branching structure of these paths to Y. ∎ Note that although the mathematical functions to describe the dependencies for equilibrium values still can be expressed directly based on the connectivity and aggregation characteristics ωX,Y and cY (…) of the network, in Corollary 17.1 they get a more complex, nested structure. First, for the example acyclic network of Fig. 17.1 (assuming the combination function alogistic; for a definition of this function, see Sect. 17.4.2), by Theorem 17.1 the following relations between the equilibrium values of states at stratification levels 0 to 4 are obtained (here the Xi are the equilibrium values of states Xi ): Level 3 equilibrium value X7 : dependence on Level 1 and 2 equilibrium values X5 and X6 X7 = alogisticσ,τ (X5 , X6 ) Level 2 equilibrium value X6 : dependence on Level 0 and Level 1 equilibrium values X3 , X4 , and X5 X6 = alogisticσ,τ (X3 , X4 , X5 ) Level 1 equilibrium value X5 : dependence on Level 0 equilibrium values X5 = alogisticσ,τ (X1 , X2 )

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Next, applying the iteration indicated in Corollary 17.1, this leads to the following functions for how the equilibrium values for the level 2 and 3 states X6 and X7 depend on the ones of the level 0 states: X6 = alogisticσ,τ (X3 , X4 , X5 )   = alogisticσ,τ X3 , X4 , alogisticσ,τ (X1 , X2 ) X7 = alogisticσ,τ (X5 , X6 )   = alogisticσ,τ alogisticσ,τ (X1 , X2 ), alogisticσ,τ (X3 , X4 , X5 )    = alogisticσ,τ alogisticσ,τ (X1 , X2 ), alogisticσ,τ X3 , X4 , alogisticσ,τ (X1 , X2 )

Note that these are indeed nested combination functions according to the paths in the network to X6 and X7 . This illustrates how in an acyclic network, the equilibrium values of all states of the entire network are determined by the equilibrium values of the level 0 states. In Sect. 17.7, other examples of expressions of nested combination functions as indicated in Corollary 17.1 will be shown for the application to a network model for organisational learning. Note also that for realistic domains, networks are often not acyclic: usually they include at least some cycles or even many of them. Then the above Theorem 17.1 and Corollary 17.1 are not applicable to the network as a whole. However, even for such cyclic networks, sometimes it can be useful to consider subnetworks that still are acyclic and apply the above Theorem 17.1 and Corollary 17.1 to them. As an example, this will be illustrated for the application to organisational learning addressed in Sect. 17.7. Moreover, following (Treur 2020a) in Sect. 17.6 it will be shown how the approach based on stratification applied for Theorem 17.1 and Corollary 17.1 to the nodes of the (acyclic) network can also be applied not to the nodes but to (the condensation graph of) the strongly connected components of any network. In that section, some further results are obtained for networks with any type of (possibly cyclic) connectivity. The results there also show relations between equilibrium values of states from different stratification levels (and with the states at level 0) and in that sense are to a certain extent similar to those of Theorem 17.1 and Corollary 17.1 but much more general.

17.4 Equilibrium Analysis under Aggregation Conditions: Monotonicity and Comparison for Combination Functions In this section, some conditions on the aggregation in the network (but no conditions on the connectivity in the network) are considered. More specifically, it is explored how specific properties of the type of aggregation used in a network model enable to derive some further results for equilibrium analysis. As aggregation characteristics

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of a network model are defined by combination functions, this means that certain properties of these functions are considered here. In particular, it is discussed how monotonicity of combination functions and comparison (order) relations between them can be used to obtain specific (comparative) equilibrium analysis results. As the obtained results do not assume any conditions on the connectivity of the network, they apply both to acyclic and cyclic networks.

17.4.1 Equilibrium Analysis Using Monotonicity and Comparison Relations for Aggregation The following monotonicity and comparison relations for the functions used for aggregation are considered. Definition (monotonicity and comparison of functions) Let a subset R ⊆ R be given. (a) A function f : R k → R is called (monotonically) increasing if for all U 1 , …, U k ,V 1 , …, V k ∈ R such that U i ≤ V i for all i it holds f (U1 , . . . , Uk ) ≤ f (V1 , . . . , Vk ) (b) A function f : R k → R is called strictly (monotonically) increasing if for all U 1 , …, U k ,V 1 , …, V k ∈ R such that U i ≤ V i for all i and U j < V j for at least one j it holds f (U1 , . . . , Uk ) < f (V1 , . . . , Vk ) (c) For two functions f, g : R k → R, by f ≤ g the function comparison relation is denoted that for all V 1 , …, V k ∈ R it holds f (V1 , . . . , Vk ) ≤ g(V1 , . . . , Vk ) When these general properties of mathematical functions are applied in particular to the combination functions defining the aggregation characteristics of a network model, for any network model with any type of connectivity characteristics, the following theorem on equilibria can be derived. Theorem 17.2 (preservation of comparison relations over time and for equilibria) Suppose X i are the states of a network model (with only positive connection weights and at least some nonzero speed factors) and all are using monotonically increasing combination functions ci . Assume 0 < ∆t ≤ 1/maxY (ηY ); e.g., assume ηY ≤ 1 for all Y and 0 < ∆t ≤ 1. Then the following hold.

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(a) Suppose two simulation traces X i (t) and X’i (t) are given with initial values X i (0) ≤ X’i (0). Then it holds X i (t) ≤ X’i (t) for all t and i and for any achieved equilibrium, for the equilibrium values Xi and X’i of X i and X’i it holds Xi ≤ X’i for all i. (b) Moreover, suppose X’i are again the states of the same network model but this time using monotonically increasing combination functions c’i . Then the following hold: (c) If ci ≤ c’i for all i and for the initial values it holds X i (0) ≤ X’i (0) for all i, then it holds X i (t) ≤ X’i (t) for all t and i. (d) If ci ≤ c’i for all i and for the initial values it holds X i (0) ≤ X’i (0) for all i, then for any achieved equilibrium for all i for the equilibrium values Xi and X’i of ∎ X i and X’i it holds Xi ≤ X’i .

17.4.2 Equilibrium Analysis Based on Monotonicity and Comparison for Specific Functions Next, for a number of often used types of combination functions, which all are monotonically increasing, their comparison (order) relations are identified, so that it becomes clear how Theorem 2 can be applied to them for equilibrium analysis. Definition (weighted Euclidean functions, weighted geometric functions, logistic functions, and min and max functions) (a) A function g is a weighted euclidean function of order n if g(V1 , . . . , Vk ) =

√ n w1 V1 n + ... + wk Vk n

for some weights w1 ,.., wk . If the sum of its weights is 1, it is called a weighted euclidean average function. A weighted euclidean function of order n = 1 is called a linear function. (b) A function g is a weighted geometric function if g(V1 , . . . , Vk ) = V1 w1 . . . Vk wk for some weights w1 , .., wk . If the sum of its weights is 1, it is called a weighted geometric mean function. (c) The scaled euclidean function eucln,λ of order n is defined by / eucln,λ (V1 , . . . , Vk ) =

n

V1 n + · · · + Vk n λ

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and the scaled geometric mean function sgeomeanλ is defined by / sgeomeanλ (V1 , . . . , Vk ) =

k

V1 ∗ · · · ∗ Vk λ

Moreover, the scaled sum function is defined as ssumλ (V1 , . . . , Vk )= eucl1,λ (V1 , . . . , Vk ) When λ = 1, the latter two are also denoted by geomean and sum. (d) The simple and advanced logistic functions slogisticσ,τ and alogisticσ,τ are defined by slogisticσ,τ (V1 , . . . , Vk ) =

1 1 + e−σ(V1 +···+Vk −τ)

 1 (1 + e−στ ) − alogisticσ,τ (V1 , . . . , Vk ) = 1 + eστ 1 + e−σ(V1 +···+Vk −τ) 

1

(e) The scaled minimum and maximum functions smin and smax are defined by sminλ (V1 , . . . , Vk ) = min(V1 , . . . , Vk )/λ smaxλ (V1 , . . . , Vk ) = max(V1 , . . . , Vk )/λ When λ = 1, they are also denoted by min and max. All above-defined functions are monotonically increasing in V 1 , …, V k , as they are built in a suitable way as compositions of basic monotonic functions such as sum, product and division functions, power functions and exponential functions. Note that as alogisticσ,τ (0, . . . , 0) = 0, from this it follows in particular that alogisticσ,τ (V1 , . . . , Vk ) ≥ 0 for all V1 , . . . , Vk ≥ 0. Next, in subsequent propositions some comparison relations between these functions are identified, first for the logistic functions. Proposition 17.1 (comparison for logistic functions) (a) Suppose τ’ < τ and σ > 0. Then for any V1 , . . . , Vk ≥ 0 it holds 0 ≤ alogisticσ,τ (V1 , . . . , Vk ) < slogisticσ,τ (V1 , . . . , Vk ) < slogisticσ,τ' (V1 , . . . , Vk ) < 1

(b) Moreover, for any σ > 0, and V1 , . . . , Vk ≥ 0 it holds lim alogisticσ,τ (V1 , . . . , Vk ) = lim slogisticσ,τ (V1 , . . . , Vk ) = 0

τ→∞

τ→∞

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lim slogisticσ,τ (V1 , . . . , Vk ) = 1

τ→−∞

∎ Next comparison relations between Euclidean functions and minimum and maximum functions are identified. Proposition 17.2 (comparison between Euclidean and min and max functions) (a) Suppose the scaling factor is set at λ = k, then for any V1 , . . . , Vk ≥ 0 it holds min(V 1 , . . . , Vk ) ≤ eucln,k (V1 , . . . , Vk ) ≤ max(V 1 , . . . , Vk ) and lim eucln,k (V1 , . . . , Vk ) = max(V1 , . . . , Vk )

n→∞

(b) More in general, for any λ > 0 it holds /

/ k n k ≤ eucln,λ (V1 , . . . , Vk ) ≤ max(V 1 , . . . , Vk ) min(V 1 , . . . , Vk ) λ λ n

and lim eucln,λ (V1 , . . . , Vk ) = max(V1 , . . . , Vk )

n→∞

∎ Similarly, comparison relations between geometric functions and minimum and maximum functions are identified. Proposition 17.3 (comparison between geometric mean and min and max functions) (a) Suppose the scaling factor is set at λ = 1, then for any V1 , . . . , Vk ≥ 0 it holds min(V1 , . . . , Vk ) ≤ sgeomean1 (V1 , . . . , Vk ) ≤ max(V 1 , . . . , Vk ) (b) More in general, for any λ > 0 and any V1 , . . . , Vk ≥ 0 it holds / / n 1 n 1 ≤ sgeomeanλ (V1 , . . . , Vk ) ≤ max(V 1 , . . . , Vk ) min(V 1 , . . . , Vk ) λ λ

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Based on the comparison relations for combination functions identified in the three above propositions, Theorem 17.2 can be applied. As an example, in this way the following two corollaries of Theorem 17.2 are obtained on comparative equilibrium analysis: they compare equilibrium values obtained for various types of functions. Corollary 17.2 (comparison relations for equilibrium values: logistic and sum functions) Assume only positive connection weights and at least some nonzero speed factors and ∆t ≤ 1/maxY (ηY ) (e.g., assume ηY ≤ 1 for all Y and ∆t ≤ 1). (a) Suppose X i are the states for a network model using advanced logistic combination functions ci = alogistic and X’i for the same network model using simple logistic combination functions c’i = slogistic with the same parameters σi and τi for each state X i . Moreover, suppose two simulation traces X i (t) and X’i (t) are given with initial values X i (0) ≤ X’i (0) for all i, then for any achieved equilibrium with equilibrium values Xi and X’i it holds Xi ≤ X’i for all i. (b) Suppose X i are the states for a network model using simple logistic combination functions ci = slogistic with parameters σi and τi and X’i for the same network model using simple logistic combination functions c’i = slogistic with the parameters σi and τ’i for each state X i such that τ’i ≤ τi . Moreover, suppose two simulation traces X i (t) and X’i (t) are given with initial values X’i (0) ≤ X i (0) for all i, then for any achieved equilibrium with equilibrium values Xi and X’i it holds Xi ≤ X’i for all i. (c) Suppose X i are the states for a network model using advanced logistic combination functions ci = alogistic with parameters σi and τi and X’i for the same network model using scaled sum combination functions c’i = ssum with the parameters λ’i for each state X i . Moreover, suppose two simulation traces X i (t) and X’i (t) are given with initial values X’i (0) ≤ X i (0) for all i. If 0 ≤ λ’i ≤ τi or λ’i ≤ 2 min(σi , τi ), and an equilibrium is achieved with equilibrium values Xi and X’i then it holds Xi ≤ X’i for all i. Corollary 17.3 (comparison relations for equilibrium values: Euclidean, geometric, minimum and maximum functions) Assume only positive connection weights and at least some nonzero speed factors and ∆t ≤ 1/maxY (ηY ) (e.g., assume ηY ≤ 1 for all Y and ∆t ≤ 1). (a) Suppose X i are the states for a network model using as combination functions ci Euclidean combination functions eucln,k (V1 , . . . , Vk ) with scaling factor λ = k or geometric mean combination functions sgeomean1 (V1 , . . . , Vk ) with scaling factor λ = 1 and X’i for the same model using maximum combination functions c’i . If for the initial values it holds X i (0) ≤ X’i (0) for all i, then for any achieved equilibrium with equilibrium values Xi and X’i it holds Xi ≤ X’i for all i. (b) Suppose X i are the states for a network model using as combination functions ci Euclidean combination functions eucln,k (V1 , . . . , Vk ) with scaling factor λ = k or geometric mean combination functions sgeomean1 (V1 , . . . , Vk ) with scaling factor λ = 1 and X’i for the same model using combination functions minimum

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functions c’i . Moreover, suppose two simulation traces X i (t) and X’i (t) are given with initial values X’i (0) ≤ X i (0) for all i. If an equilibrium is achieved with ∎ equilibrium values Xi and X’i , then it holds X’i ≤ Xi for all i.

17.5 Equilibrium Analysis Under Aggregation Conditions: Scalar-Freeness In this section, equilibrium analysis is addressed for networks satisfying another aggregation condition: the combination functions are assumed scalar-free.

17.5.1 Functions for Aggregation that Are Scalar-Free It is sometimes believed that for dynamical models the borderline between linear and nonlinear functions is also the borderline between well-analyzable behavior and less well-analyzable behavior. In contrast to this, it has been found that this borderline between well-analyzable behavior and less well-analyzable behavior lies somewhere within the domain of nonlinear functions: between one class (called monotonic scalar-free functions) covering both linear and nonlinear functions and another subclass of the class of nonlinear functions not satisfying these. More specifically, whether or not combination functions are scalar-free is an important factor determining whether or not by social contagion all members of a well-connected social network converge to the same level of emotion, opinion, information, belief, intention, or any other mental or physical state; e.g., (Treur 2020a) and (Treur, 2020b), Chaps. 11 and 12. The class of scalar-free functions includes all linear functions but also includes a number of types of nonlinear functions, such as the weighted euclidean functions and weighted geometric functions (as will be defined below). In this section some further analysis is made of scalar-free functions, thereby also using a weakened variant of them called weakly scalar-free functions. The definitions are as follows. Definition (weakly scalar-free and scalar-free functions) Consider functions f : R k → R and θ : R → R for some subset R ⊆ R which is R or R>0 . (a) A function f : R k → R is called weakly scalar-free for function θ if for all V 1 , …, V k ∈ R and all α ∈ R it holds f (αV 1 , . . . , αV k ) = θ (α) f (V1 , . . . , Vk ) (b) A function f : R k → R is called scalar-free if for all V1 , . . . , Vk ∈ R and all α ∈ R it holds f (αV 1 , . . . , αV k ) = α f (V1 , . . . , Vk ) Examples (weakly scalar-free functions) There are many examples of weakly scalar-free functions. For example, the functions f (V ) = V k and f (V1 , . . . , Vk ) = V1 ∗ · · · ∗ Vk on proper domains are weakly scalar-free with function θ (α) = α k . The

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example f (V1 , V2 , V3 ) = w1 V1 V2 + w2 V2 V3 + w3 V3 V1 is weakly scalar-free with function θ (α) = α 2 .

17.5.2 Properties and Comparative Equilibrium Analysis for Scalar-Free Functions The following basic properties can easily be verified, see Canbalo˘glu and Treur (2022) for proofs. Proposition 17.4 (scalar-free and increasing functions) (a) Suppose f is increasing and weakly scalar-free for function θ. Then for all V 1 , …, V k ∈ R it holds f (1, . . . , 1)θ (min(V1 , . . . , Vk )) ≤ f (V1 , . . . , Vk ) ≤ f (1, . . . , 1)θ (max(V1 , . . . , Vk ))

When moreover f is scalar-free, then f (1, . . . , 1)min(V1 , . . . , Vk ) ≤ f (V1 , . . . , Vk ) ≤ f (1, . . . , 1)max(V1 , . . . , Vk ) (b) Any weighted Euclidean or geometric function with positive weights wi is monotonically increasing and scalar-free. (c) If g(V1 , . . . , Vk ) =

√ n w1 V1 n + ... + wk Vk n

is a weighted Euclidean function with positive weights wi , then g is scalar-free and increasing; moreover, it holds √ √ n w1 + ... + wk min(V1 , . . . , Vk ) ≤ g(V1 , . . . , Vk ) ≤ n w1 + ... + wk max(V1 , . . . , Vk )

If g is a weighted Euclidean average function (i.e., the sum of the weights wi is 1), then min(V1 , . . . , Vk ) ≤ g(V1 , . . . , Vk ) ≤ max(V1 , . . . , Vk ) (d) If g(V1 , . . . , Vk ) = V1w1 . . . Vkwk

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is a weighted geometric function with positive weights wi , then g is scalar-free and increasing; moreover, it holds min(V1 , . . . , Vk ) ≤ g(V1 , . . . , Vk ) ≤ max(V1 , . . . , Vk )

∎

Note that Proposition 17.4 places some of the specific types of functions considered in Sect. 17.4 (weighted Euclidean and weighted geometric functions) in the wider perspective of scalar-free functions. Proposition 17.5 (scalar-free and strictly increasing functions) (a) Any function composition of scalar-free functions is scalar-free (b) Any function composition of strictly increasing functions is strictly increasing (c) All linear functions with positive coefficients are scalar-free and strictly increasing (d) Any scalar-free function f is weakly scalar-free for θ = id, the identity function. Theorem 17.3 (comparison for any scalar-free function to min and max) Suppose X i are the states for a network model (with only positive connection weights and at least some nonzero speed factors) using monotonically increasing combination functions ci and X’i for the same model using monotonically increasing combination functions c’i . Assume 0 < ∆t ≤ 1/maxY (ηY ); e.g., assume ηY ≤ 1 for all Y and 0 < ∆t ≤ 1. (a) If for the initial values it holds X i (0) ≤ X’i (0), the ci are monotonically increasing and scalar-free with ci (1, …, 1) = 1, and c’i is the maximum function c’i = max then for any achieved equilibrium with equilibrium values Xi and X’i it holds Xi ≤ X’i for all i. (b) If for the initial values it holds X’i (0) ≤ X i (0), the ci are monotonically increasing and scalar-free with ci (1, …, 1) = 1, and each c’i is the minimum function c’i = min then for any achieved equilibrium with equilibrium values Xi and X’i it ∎ holds X’i ≤ Xi for all i. Note that Theorem 17.3 generalizes to the class of scalar-free functions, the comparative equilibrium analysis that was found in Sect. 17.4 for specific examples of scalar-free functions: weighted Euclidean and weighted geometric functions.

17.6 Equilibrium Analysis under Aggregation Conditions: Using the Strongly Connected Components In this section an equilibrium analysis approach is discussed that takes into account how the network is composed of its strongly connected components.

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17.6.1 Introducing Stratification for the Strongly Connected Components of a Network As an illustration, consider the example of a mental network model with connectivity depicted in Fig. 17.2. This is a mental network model for how a person is sensing (sensor state sss ) a stimulus s in the world (word state wss ), represents this (representation state srss ), and is triggered to prepare (preparation state psa ) and perform (execution state esa ) action a, after evaluation of the predicted (predicted effect representation state srse ) effect e of this action. In simulations it can be seen that because of a constant value a of stimulus wss all state values are increasing until they reach an equilibrium value a as well. The question then is whether these observations based on one or more simulation experiments are in agreement with a mathematical equilibrium analysis. This will be addressed in two ways. In the current section a general perspective is followed, and theorems are discussed that have been found based on the network’s strongly connected components described in (Treur 2020a). The perspective is based on the notion of (strongly connected) component of a network; this is a maximal subnetwork C such that every node within C can be reached from every other node via a path following the direction of the connections; e.g., (Bloem et al. 2006; Fleischer et al. 2000; Harary et al. 1965; Łacki, 2013; Wijs et al. 2016). From this literature, it is known that these components partition the set of nodes in disjoint subsets and the connections between them induce a socalled condensation graph with the components as nodes which is always acyclic. In Fig. 17.3 these components are shown for the example network: C1 to C5 . In Treur (2020a) the notion of stratification was introduced for the condensation graph based on this a partition of a network so that each component gets a level (or stratum) assigned; see Sect. 17.3 for a more precise definition of this notion of stratification of an acyclic network or graph in general. In this case the levels are 0 to 4 as indicated in Fig. 17.3.

Fig. 17.2 Connectivity of the example network model

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Fig. 17.3 Stratified strongly connected components for the example network model

17.6.2 Using the Stratification to Relate Equilibrium Values for Different Components Based on the levels defined by this notion of stratification, a few general theorems and corollaria have been found and proven and presented in Treur (2020a); see also (Treur, 2020b), Ch 12 and 15. For aggregation these are not limited to linear functions and for connectivity no condition at all is demanded; some of these results are the following. Theorem 17.4 (relating equilibrium values of states in components at different levels) If the following aggregation conditions are fulfilled • The combination functions are normalised, scalar-free and strictly increasing then in an achieved equilibrium the following hold: (a) In any level 0 component C • All states in C have the same equilibrium value V • This V is between the highest and lowest initial value of the states within C. (b) If for any level i > 0 component C the components C 1 , .., C k are the strongly connected components from which C gets an incoming connection, then • The equilibrium values of the states in C are between the highest and lowest equilibrium values of the states in C 1 , .., C k • If all states in C 1 , …, C k have the same equilibrium value V, then also all states in C have this same equilibrium value V. ∎ Corollary 17.4 (dependence of all equilibrium values on the values in level 0 components) If the following aggregation conditions are fulfilled. • The combination functions are normalised, scalar-free and strictly increasing then in an achieved equilibrium:

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(a) The equilibrium values of all states in the network • are between the highest and lowest equilibrium values of the states in the level 0 components • are between the highest and lowest initial values of the states in the level 0 components (b) If all states in all level 0 components C have the same equilibrium value V, then all states of the whole network have that same equilibrium value V ∎ For the special case of a strongly connected network (consisting of one component), this implies: Corollary 17.5 (strongly connected networks) If the following connectivity and aggregation conditions are fulfilled. • The network is strongly connected • The combination functions are normalised, scalar-free and strictly increasing then in an achieved equilibrium: • All states have the same equilibrium value V • This equilibrium value V is between the highest and lowest initial values of the states ∎ Given that in the example network model there is only one level 0 component with constant value a, by Theorem 17.4 or Corollary 17.4 above it can be concluded that all states will have equilibrium value a, as long as the aggregation conditions are fulfilled. Note that in an acyclic network, each state forms a (singleton) strongly connected component. Applying Theorem 17.4 and its corollaries to this special case will again provide Theorem 17.1 and Corollary 17.1 from Sect. 17.3. That shows that the above results generalise the results from Sect. 17.3.

17.7 Application for Equilibrium Analysis of Multilevel Organisational Learning In this section, results from the previous sections will be applied to equilibrium analysis for the domain of multilevel organisational learning (Crossan et al. 1999; Kim, 1993; Wiewiora et al. 2020, 2019). In particular, this will be addressed for the type of adaptive computational network models for multilevel organisational learning based on self-modeling networks (Treur 2020b) as addressed in (Canbalo˘glu et al. 2022, 2023a, d); see also (Canbalo˘glu et al. 2023b), Chaps. 5, 6 and 7 (this volume). The relations for equilibrium values found are confirmed by the simulations that were performed.

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17.7.1 Computational Modeling of Multilevel Organisational Learning In recent work (Canbalo˘glu et al. 2022, 2023a, d), it has been found out how multilevel organisational learning processes can be modeled in a systematic and conceptually transparent manner by self-modeling networks. To illustrate how the equilibrium analysis methods from the previous sections can be applied, the model described in Canbalo˘glu et al. (2023d) is considered in particular; see also Canbalo˘glu et al. (2023c), Chap. 7 (this volume). A picture of the overall connectivity of this secondorder adaptive network model is shown in Fig. 4. Here, mental models (Craik, 1943; Treur and Van Ments, 2022) are used to represent what is learnt. They are relational structures describing (by nodes and connections) blueprints of processes in the world that may occur or that are suggested to be followed in certain circumstances; for example, they can be used to specify medical protocols or workflow. Within an overall model for mental or social processes, mental models are modeled according to different levels, in relation to what is done with them: • at the base level, the use of mental models by internal simulation • at the first-order self-model level, the learning or adaptation (e.g., revision or forgetting) of them • at the second-order self-model level, the control of the adaptation. The focus is here on the learning by the first-order self-model level in the middle plane. This level includes 21 W-states representing the connection weights for seven mental models (each with three connections: a → b, b → c, c → d). From these seven mental models, four are from individuals A, B, C, D (left-hand side), two of them are shared mental models from teams T1 and T2 (middle), and one is the shared mental model from the organisation O (right-hand side). In the literature on multilevel organisational learning such as (Crossan et al. 1999; Kim, 1993; Wiewiora et al. 2020, 2019), feed forward learning indicates how shared team mental models can be learned from individual mental models and how shared mental models of the organisation can learned from shared team mental models (or in some cases also directly from individual mental models, in particular when there are no teams). This is modeled by the connections from left to right in the middle plane in Fig. 4. In addition, in such literature, feedback learning indicates how teams can learn their mental models from a shared organisation mental model and how individuals can learn their mental models from shared team mental models (or in some cases also directly from a shared organisation mental model, in particular when there are no teams). This is modeled by the connections from right to left in the middle plane in Fig. 17.4. Such learning processes depend on some forms of control, for example, involving (among others) managers to initiate or approve certain steps or proposed steps, e.g., (Canbalo˘glu et al. 2023b). For the equilibrium analysis addressed here, for the sake of presentation it is assumed that all required control actions are positive: they indicate green lights for all considered learning processes. Next, in subsequent sections it is

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Fig. 17.4 Example of an adaptive network model for multilevel organisational learning

shown how the equilibrium analysis results presented in the previous Sects. 17.3, 17.4, 17.5 and 17.6 can be illustrated for this type of organisational learning model.

17.7.2 Applying Equilibrium Analysis Under Connectivity Conditions to a Network Model for Multilevel Organisational Learning In this section, the equilibrium analysis approach discussed in Sect. 17.3 is applied to the example network model for multilevel organisational learning with connectivity depicted in Fig. 17.4. In particular, this means application of Theorem 17.1 and Corollary 17.1. However, a similar analysis can also be obtained by applying Theorem 17.4 and Corollary 17.4 from Sect. 6 as they generalise Theorem 17.1 and Corollary 17.1 as noted at the end of Sect. 17.6. Subsequently, feed forward learning, feedback learning, and a sequential combination of them are addressed. Feed forward learning For equilibrium analysis of feed forward learning, the subnetwork depicted in Fig. 17.5 is considered. Here it is assumed that due to the control that is applied the backward connections (from right to left) have weights 0. As this provides an acyclic network, Theorem 17.1 and Corollary 17.1 apply. Therefore, the following can be concluded for an equilibrium:

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Fig. 17.5 Only feed forward learning. The W-states of the four persons A to D form stratification level 0, the W-states of the two teams T1 and T2 form level 1, and the W-states of O form level 2

• Expressing equilibrium values of shared team mental models in terms of those of individual mental models – The equilibrium value of state Wa_T1,b_T1 for team T1’s shared team mental model is a function (the combination function of Wa_T1,b_T1 ) of the equilibrium values of states Wa_A,b_A and Wa_B,b_B for the individual mental models of A and B; for the case of connection weights 1 this is (here for any W-state, the underlined W indicates the equilibrium value of the W-state):   Wa_T1,b_T1 = cWa_T1,b_T1 Wa_A,b_A , Wa_B,b_B Here, cWa_T1,b_T1 (..) is the combination function used for aggregation for state Wa_T1,b_T1 . Similarly, this can be done for Wb_T1,c_T1 and Wc_T1,d_T1 , and for T2 instead of T1. • Expressing equilibrium values of a shared organisation mental model in terms of those of shared team mental models – The equilibrium value of state Wa_O,b_O for the organisation O’s shared mental model is a function (the combination function of Wa_O,b_O ) of the equilibrium values of states Wa_T1,b_T1 and Wa_T2,b_T2 for the team mental models for T1 and T2; for the case of connection weights 1 this is:   Wa_O,b_O = cWa_O,b_O Wa_T1,b_T1 , Wa_T2,b_T2 Here, cWa_O,b_O (..) is the combination function used for aggregation for state Wa_O,b_O . Similarly, this can be done for Wb_O,c_O and Wc_O,d_O . • Expressing equilibrium values of a shared organisation mental model in terms of those of individual mental models – The equilibrium value of state Wa_O,b_O for the organisation O’s shared mental model is a function (the combination function of Wa_O,b_O composed with those of Wa_T1,b_T1 and Wa_T2,b_T2 ) of the equilibrium values of states Wa_A,b_A , Wa_B,b_B Wa_C,b_C , and Wa_D,b_D for the individual mental models of A, B, C, and D; for the case of connection weights 1 this is:

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  Wa_O,b_O = cWa_O,b_O Wa_T1,b_T1 , Wa_T2,b_T2    cWa_T1,b_T1 Wa_A,b_A , Wa_B,b_B   = cWa_O,b_O , cWa_T2,b_T2 Wa_C,b_D , Wa_C,b_D Here, cWa_O,b_O (..) is the combination function used for aggregation for state Wa_O,b_O and cWa_T1,b_T1 (..) and cWa_T2,b_T2 (..) are those for Wa_T1,b_T1 and Wa_T2,b_T2 . Similarly, this can be done for Wb_O,c_O and Wc_O,d_O . For example, if the max function is used as combination function for all states and the connections in Fig. 17.5 all have weight 1, then following the network connectivity the equilibrium value Wa_O,b_O for state Wa_O,b_O can be expressed in terms of the equilibrium values Wa_T1,b_T1 , Wa_T2,b_T2 , Wa_A,b_A , Wa_B,b_B , … for the teams and individuals as follows:   Wa_O,b_O = max Wa_T1,b_T1 , Wa_T2,b_T2      = max max Wa_A,b_A , Wa_B,b_B , max Wa_C,b_D , Wa_C,b_D   = max Wa_A,b_A , Wa_B,b_B , Wa_C,b_D , Wa_C,b_D In this way, it is predicted that the model will form a shared organisation mental model by maximally incorporating the knowledge of each of the individuals. Feedback Learning For equilibrium analysis of feedback learning, the subnetwork depicted in Fig. 17.6 can be considered. Here it is assumed that due to the control that is applied the forward connections (from left to right) have weights 0. Again, as this provides an acyclic network, Theorem 17.1 and Corollary 17.1 apply. Therefore, the following can be concluded for any equilibrium: • Expressing equilibrium values of shared team mental models in terms of those of a shared organisation mental model

Fig. 17.6 Only feedback learning. Each W-state is by itself a strongly connected component as singleton. The W-states of O form stratification level 0, the W-states of the two teams T1 and T2 form level 1, and the W-states of the four persons A to D form level 2

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– The equilibrium value of state Wa_T1,b_T1 for team T1’s shared team mental model is a function (the combination function of Wa_T1,b_T1 ) of the equilibrium value of state Wa_O,b_O for the organisation O’s shared mental model; for the case of connection weights 1 this is:   Wa_T1,b_T1 = cWa_T1,b_T1 Wa_O,b_O Here, cWa_T1,b_T1 (..) is the combination function used for aggregation for state Wa_T1,b_T1 . Similarly, this can be done for Wb_T1,c_T1 and Wc_T1,d_T1 , and for T2. • Expressing equilibrium values of individual mental models in terms of those of shared team mental models – The equilibrium value of state Wa_A,b_A for the individual mental model of A is a function (the combination function of Wa_A,b_A ) of the equilibrium value of state Wa_T1,b_T1 for team T1’s shared team mental model; for the case of connection weights 1 this is: Wa_A,b_A = cWa_A,b_A (Wa_T1,b_T1 ) Here, cWa_A,b_A (..) is the combination function used for aggregation for state Wa_A,b_A . Similarly, this can be done for Wb_A,c_A and Wc_A,c_A , and for persons B, C, and D instead of A. • Expressing equilibrium values of individual mental models in terms of those of a shared organisation mental model – The equilibrium value of state Wa_A,b_A for the individual mental model of A is a function (the combination function of Wa_A,b_A composed with the one of Wa_T1,b_T1 ) of the equilibrium value of state Wa_O,b_O for the organisation O’s shared mental model; for the case of connection weights 1 this is:   Wa_A,b_A = cWa_A,b_A Wa_T1,b_T1    = cWa_A,b_A cWa_T1,b_T1 Wa_O,b_O Here, cWa_A,b_A (..) is the combination function used for aggregation for state Wa_A,b_A and cWa_T1,b_T1 (..) is the combination function used for aggregation for state Wa_T1,b_T1 . Similarly, this can be done for for Wb_A,c_A and Wc_A,c_A , and for persons B, C, and D instead of A. As a more specific example, if the max function is used as combination function for all states as was done in Canbalo˘glu et al. (2023d) and the connections in Fig. 6 all have weight 1, then the equilibrium value Wa_A,b_A for state Wa_A,b_A can be expressed in terms of the equilibrium values Wa_T1,b_T1 and Wa_O,b_O for the teams and individuals as follows:

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  Wa_A,b_A = max Wa_T1,b_T1    = max max Wa_O,b_O = Wa_O,b_O This shows how each person gets a perfect individual mental model based on perfect knowledge transfer from the shared mental model of the organisation. This perfection depends on the connection weights 1. If (some of) these connection weights are < 1, less perfect learning can be modeled. Feedforward learning until equilibrium followed by feedback learning until equilibrium: Next a scenario is considered whereby applying control in a first phase feed forward learning takes place (forward connections weight 1, backward connections weight 0) until an equilibrium is reached and subsequently in a second phase feedback learning (forward connections weight 0, backward connections weight 1) until again an equilibrium is reached. In this case, we can combine the two equilibrium analyses above in a sequential manner. Then nesting of combination functions of 4 levels deep takes place as follows.   Wa_A,b_A = cWa_A,b_A Wa_T1,b_T1    = cWa_A,b_A cWa_T1,b_T1 Wa_O,b_O     = cWa_A,b_A cWa_T1,b_T1 cWa_O,b_O Wa_T1,b_T1 , Wa_T2,b_T2      = cWa_A,b_A (cWa_T1,b_T1 (cWa_O,b_O cWa_T1,b_T1 Wa_A,b_A , Wa_B,b_B , cWa_T2,b_T2 Wa_C,b_D , Wa_C,b_D

For example, specifically assuming the max function for all combination functions:   Wa_A,b_A = max Wa_T1,b_T1    = max max Wa_O,b_O     = max max max Wa_T1,b_T1 , Wa_T2,b_T2      = max(max(max max Wa_A,b_A , Wa_B,b_B , max Wa_C,b_D , Wa_C,b_D   = max Wa_A,b_A , Wa_B,b_B , Wa_C,b_D , Wa_C,b_D This predicts that using this type of aggregation, every individual gets a mental model representing equal knowledge, based on the maximal knowledge available among individuals A, B, C, and D.

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17.7.3 Application of Equilibrium Analysis for Comparison Relations Next, it is illustrated how equilibrium analysis based on comparison relations as presented in Sects. 17.4 and 17.5 can be applied to the considered network model for multilevel organisational learning. In particular, this involves application of Theorems 17.2 and 17.3 and Corollaries 17.2 and 17.3. For example: • Theorem (17.2a) indicates that higher initial values will lead to higher equilibrium values. For example, applied to feed forward learning as considered in Sect. 7.2, this makes that for monotonically increasing combination functions used for aggregation, higher initial values for all W-states will lead to higher equilibrium values for all W-states. • As another example, Corollary (17.2a) expresses that when slogistic is used, then a higher threshold value will lead to lower equilibrium values. Applied to feed forward learning as considered in Sect. 7.2, this provides the following: Wa_O,b_O ≤ W'a_O,b_O when W'a_O,b_O is achieved using a lower threshold value • Theorem 17.3 expresses, for example, that all normalised monotonically increasing scalar-free functions lead to equilibrium values Wa_O,b_O between the equilibrium values W''a_O,b_O and W'a_O,b_O obtained when min or max functions are used:

W''a_O,b_O ≤ Wa_O,b_O ≤ W'a_O,b_O

17.7.4 Application of Equilibrium Analysis Based on Strongly Connected Components Finally, it is discussed how Theorem 17.4 and Corollary 17.4 from Sect. 17.6 can be applied. As these can be considered generalisations of the results for acyclic networks in Sect. 17.3, they can also be used to obtain what is discussed in Sect. 17.2 (noticing that in these cases each state of the network forms a strongly connected component). However, here they are applied to the case that feed forward and feedback learning take place in a fully integrated manner. Then the picture with both left-to-right and right-to-left arrows shown in Fig. 17.7 applies. Now not each state forms a strongly connected component but there are onle three larger strongly connected components (each consisting of 7 W-states), indicated in Fig. 17.7 by different colours:

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Fig. 17.7 Full integration of feed forward learning and feedback learning. Three strongly connected components C1 for all connections a → b (purple highlighted), C2 for all connections b → c (green highlighted), C3 for all connections c → d (yellow highlighted). These three components have no mutual connections and therefore have mutually independent but internally common equilibrium values C1 = {Wa_Z ,b_Z |Z ∈ {A, B, C, D, T1, T2, O}}

(highlighted purple in Fig. 17.7)

C2 = {Wb_Z ,c_Z |Z ∈ {A, B, C, D, T1, T2, O}}

(highlighted green in Fig. 17.7)

C3 = {Wc_Z ,d_Z |Z ∈ {A, B, C, D, T1, T2, O}}

(highlighted yellow in Fig. 17.7)

It can be noted that there are no mutual connections between these three components; therefore all three have stratification level 0. By Theorem 17.4a) it follows that in an equilibrium, for each of the three components Ci all states in it will have the same equilibrium value: C1 : Wa_Z ,b_Z = Wa_Z ' ,b_Z ' for all Z , Z ' ∈ {A, B, C, D, T1, T2, O} C2 : Wb_Z ,c_Z = Wb_Z ' ,c_Z ' for all Z , Z ' ∈ {A, B, C, D, T1, T2, O} C3 : Wc_Z ,d_Z = Wc_Z ' ,d_Z ' for all Z , Z ' ∈ {A, B, C, D, T1, T2, O} But note that these common equilibrium values within each of the three components may differ for different components due to the lack of mutual connections between the components.

17.8 Discussion In this chapter, equilibrium analysis was addressed for network models. A main application focus was on organisational learning (Crossan et al. 1999; Kim, 1993; Wiewiora et al. 2020, 2019) and computational network models for it (Canbalo˘glu et al. 2021, 2023, 2022a, 2023a). This chapter covers material of Canbalo˘glu and Treur (2022). Note that the focus of this chapter was on behaviour of adaptive network models where equilibria do occur. This is applicable, for example, in situations where some forms of organisation or structuring take place such as in well-organised organisational learning. Of course, also other situations exist where, for example, influential

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context factors change all the time, and their influences are not well-organised. This may lead to types of behaviour where equilibria do not occur.

References Abraham, W.C., Bear, M.F.: Metaplasticity: the plasticity of synaptic plasticity. Trends Neurosci. 19(4), 126–130 (1996) Anton, H.: Elementary Linear Algebra, 5th edn. Wiley, New York (1987) Bloem, R., Gabow, H.N., Somenzi, F.: An algorithm for strongly connected component analysis in n log n symbolic steps. Form. Meth. Syst. Des. 28, 37–56 (2006) Canbalo˘glu, G., Treur, J.: Context-sensitive mental model aggregation in a second-order adaptive network model for organisational learning. In: Proceedings of the 10th International Conference on Complex Networks and their Applications. Studies in Computational Intelligence, vol. 1015, pp 411–423. Springer Nature (2021a) Canbalo˘glu, G., Treur, J.: Using Boolean functions of context factors for adaptive mental model aggregation in organisational learning. In: Proceedings of the 12th international conference on brain-inspired cognitive architectures, BICA’21. Studies in Computational Intelligence, vol. 1032, pp 54–68. Springer Nature (2021b) Canbalo˘glu, G., Treur, J.: Equilibrium analysis for linear and non-linear aggregation in network models: applied to mental model aggregation in multilevel organisational learning. J. Inf. Telecommun. 6(3), 289–340 (2022) Canbalo˘glu, G., Treur, J., Roelofsma, P.H.M.P.: Computational modeling of organisational learning by self-modeling networks. Cogn. Syst. Res. 73, 51–64 (2022) Canbalo˘glu, G., Treur, J., Wiewiora, A.: Computational modeling of multilevel organisational learning: from conceptual to computational mechanisms. In: Computational Intelligence, Proceedings of InCITe’22. Lecture Notes in Electrical Engineering, vol. 968, pp. 1–17. Springer Nature (2023a) Canbalo˘glu, G., Treur, J., Wiewiora, A.: Computational modeling of the role of leadership style for its context-sensitive control over multilevel organizational learning. In: Yang, XS., Sherratt, S., Dey, N., Joshi, A. (eds), Proceedings of the 7th International Congress on Information and Communication Technology, ICICT’22. Lecture Notes in Networks and Systems, vol. 447, pp. 223–239. Springer Nature (2023b) Canbalo˘glu, G., Treur, J., Wiewiora, A. (eds.). Computational Modeling of Multilevel Organisational Learning and its Control Using Self-Modeling Network Models (this volume). Springer Nature (2023c) Canbalo˘glu, G., Treur, J., Roelofsma, P.H.M.P.: An adaptive self-modeling network model for multilevel organizational learning. In: Proceedings of the 7th International Congress on Information and Communication Technology, ICICT’22, vol. 2. Lecture Notes in Networks and Systems, vol. 448, pp. 179–191. Springer Nature (2023d) Crossan, M.M., Lane, H.W., White, R.E.: An organizational learning framework: from intuition to institution. Acad. Manag. Rev. 24, 522–537 (1999) Dummit, D.S., Foote, R.M.: Abstract Algebra, 3rd edn. Wiley, Hoboken, NJ (2004) Fleischer, L.K., Hendrickson, B., Pınar, A.: On identifying strongly connected components in parallel. In: Rolim, J. (ed.) Parallel and Distributed Processing. IPDPS 2000. Lecture Notes in Computer Science, vol. 1800, pp. 505–511. Springer (2000) Harary, F., Norman, R.Z., Cartwright, D.: Structural Models: An Introduction to the Theory of Directed Graphs. Wiley, New York (1965) Hendrikse, S.C.F., Treur, J., Koole, S.L.: Modeling emerging interpersonal synchrony and its related adaptive short-term affiliation and long-term bonding: a second-order multi-adaptive neural agent model. Int. J. Neural Syst. (2023). https://doi.org/10.1142/S0129065723500387

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Kim, D.H.: The link between individual and organizational learning. Sloan Manag. Rev., Fall, 37–50. Reprinted in: Klein, D.A. (ed.) The Strategic Management of Intellectual Capital. RoutledgeButterworth-Heinemann, Oxford (1993) Łacki, J.: Improved deterministic algorithms for decremental reachability and strongly connected components. ACM Trans. Algorithms 9(3), Article 27 (2013) Nering, E.D.: Linear Algebra and Matrix Theory, 2nd edn. Wiley, New York (1970) Treur, J.: Verification of temporal-causal network models by mathematical analysis. Vietnam. J. Comput. Sci. 3, 207–221 (2016) Treur, J.: Relating emerging network behaviour to network structure. In: Proceedings of the 7th International Conference on Complex Networks and their Applications, ComplexNetworks’18, vol. 1. Studies in Computational Intelligence, vol. 812, pp. 619–634. Springer Publishers (2018) Treur, J.: Analysis of a network’s asymptotic behaviour via its structure involving its strongly connected components. Netw. Sci. 8(S1), S82–S109 (2020a) Treur, J.: Network-oriented modeling for adaptive networks: designing higher-order adaptive biological, mental and social network models. Springer Nature Publishers (2020b) Treur, J., Van Ments, L. (eds.): Mental Models and their Dynamics, Adaptation, and Control: a Self-Modeling Network Modeling Approach. Springer Nature (2022) Van Ments, L., Treur, J.: Reflections on dynamics, adaptation and control: a cognitive architecture for mental models. Cogn. Syst. Res. 70, 1–9 (2021) Wiewiora, A., Chang, A., Smidt, M.: Individual, project and organisational learning flows within a global project-based organisation: exploring what, how and who. Int. J. Project Manage. 38, 201–214 (2020) Wiewiora, A., Smidt, M., Chang, A.: The ‘How’ of multilevel learning dynamics: a systematic literature review exploring how mechanisms bridge learning between individuals, teams/projects and the organisation. Eur. Manag. Rev. 16, 93–115 (2019) Wijs, A., Katoen, J.P., Bošnacki, D.: Efficient GPU algorithms for parallel decomposition of graphs into strongly connected and maximal end components. Formal Methods Syst. Des. 48, 274–300 (2016)

Part VIII

Finalising

This part discusses further perspectives on organisational learning and its dynamics, adaptation and control and the way to model these processes by self-modeling network models. It describes further prospects and research directions.

Chapter 18

Discussion: Perspectives on Computational Modeling of Multilevel Organisational Learning Gülay Canbalo˘glu, Jan Treur, and Anna Wiewiora

Abstract In this chapter, key findings presented in this volume are summarised and evaluated to demonstrate the usefulness and great potential of the adaptive dynamical system approach based on self-modeling networks in providing a useful structure to formalise, analyse and simulate multilevel organisational learning processes. Moreover, future perspectives are discussed for further development and application based on what already has been achieved. Keywords Multilevel organisational learning · Computational modeling · Adaptive dynamical systems · Self-modeling networks

18.1 Introduction The literature on multilevel organisational learning is either conceptual or uses qualitative approaches (case studies or interviews) to explore learning processes and learning mechanisms, e.g., (Kim 1993; Crossan et al. 1999; Wiewiora et al. 2019, 2020). Although this literature has clarified the learning landscape, mathematical or computational formalisation of learning processes were missing. One of the challenges in examining organisational learning is its dynamic and context-sensitive nature. In addition, a range of factors influencing learning flows makes the process of learning complex, but at the same time rich and interesting to evaluate. G. Canbalo˘glu · J. Treur (B) Social AI Group, Department of Computer Science, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands e-mail: [email protected] G. Canbalo˘glu e-mail: [email protected] A. Wiewiora School of Management, QUT Business School, Queensland University of Technology, Brisbane, Australia e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 G. Canbalo˘glu et al. (eds.), Computational Modeling of Multilevel Organisational Learning and Its Control Using Self-modeling Network Models, Studies in Systems, Decision and Control 468, https://doi.org/10.1007/978-3-031-28735-0_18

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Mathematical and computational modeling approaches provide a promising avenue for investigating learning processes in a more systematic manner. In this volume (Canbalo˘glu et al. 2023), the self-modeling network modeling approach described in (Treur 2020a, b) was used as a vehicle. This approach is particularly useful as it allows to capture the interplay between different levels, adaptation mechanisms and control mechanisms involved, thereby addressing the high extent of context-sensitivity. The self-modeling network modeling enables us to address the effects of large numbers of contextual factors and has proven successful in modeling the three-level cognitive architecture for use, adaptation, and control of adaptation for mental models, see (Treur and Van Ments 2022). This modeling approach enabled to design and conduct simulation experiments and perform mathematical equilibrium analysis for different cases of multilevel organisational learning processes. In this chapter, we consolidate the key findings and simulations presented in this book to demonstrate the usefulness and great potential of the self-modeling networks approach in providing a useful structure to formalise, analyse and simulate multilevel organisational learning processes as complex adaptive dynamical systems.

18.2 Self-Modeling Network Models Following (Treur 2020a, b), a temporal-causal network model is characterised by (here X and Y denote nodes of the network, also called states): ● Connectivity characteristics Connections from a state X to a state Y and their weights ωX,Y ● Aggregation characteristics For any state Y, some combination function cY (..) defines the aggregation that is applied to the impacts ωX,Y X(t) on Y from its incoming connections from states X ● Timing characteristics Each state Y has a speed factor ηY defining how fast it changes for given causal impact. The above concepts enable us to design network models and their dynamics in a declarative manner, based on mathematically defined functions and relations. By using a self-modeling network (also called a reified network), a network-oriented conceptualisation can also obtain a declarative description of adaptive networks using mathematically defined functions and relations, for more details, see (Treur 2020a, b), see also Chap. 3 of this volume (Canbalo˘glu et al. 2023). In this case new states called self-model states are added to the network which represent adaptive network characteristics. In a graphical 3D-format such additional states are depicted at a next level (called self-model level or reification level), where the original network is at the base level. As an example, the weight ωX,Y of a connection from state X to state Y is represented at a next level by a self-model state named WX,Y . Similarly, an adaptive speed factor ηY can be represented by a self-model state named HY and an

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adaptive excitability threshold parameter τY can be represented by a self-model state named TY . Moreover, a persistence factor μ of a state Y of used for adaptation can be represented by a self-model state MY . This self-modeling network construction can easily be applied iteratively to obtain multiple orders of self-models at multiple (firstorder, second-order, …) self-model levels. In this way an adaptive learning speed for state WX,Y can be modeled by introducing a second-order self-model state HZ where Z = WX,Y also simply denoted by HW X,Y . Similarly, second-order self-model states MW X,Y can be used to model adaptive persistency of the learning. It has been proven in (Hendrikse et al. 2023) that any smooth adaptive dynamical system has a canonical self-modeling network representation, which shows that this format is very general; see also Chap. 16 of this volume (Canbalo˘glu et al. 2023).

18.3 Computational Architecture for Use, Adaptation, and Control of Adaptation To model learning processes within an organisation in a transparent manner, it is important to distinguish the different levels use, adaptation, control of adaptation of the processes: see Fig. 18.1, left-hand side for a conceptual cognitive architecture based on these levels. Following Kim (1993), in the first place learning can be conceptualised as adaptation of mental models. Secondly, although some examples of learning within an organisation may take place without exerting explicit control over it, many forms of learning require some explicit context-sensitive decisions to let them happen, for example, by a higher manager who has responsibility for the quality and learning of some group of members of the organisation. Therefore, not only ‘adaptation’ but also ‘control of adaptation’ from the abovementioned triple is crucial to obtain realistic context-sensitive computational models of learning within an organisation and multilevel organisational learning.

Control of adaptation

Adaptation

Use

Three-level conceptual architecture

Second-order self-model WWW, CW, MW, TW, HW states

First-order self-model W states

Base network

Self-modeling network architecture

Fig. 18.1 Formalising the three-level conceptual architecture by a self-modeling network architecture

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Self-modeling networks can easily be used to model each of these three levels and their interactions, as has been shown for different cases in different chapters in this volume (Canbalo˘glu et al. 2023). In practically all chapters of this volume, for the level of adaptation, first-order self-model W-states W X i ,Y have been used that represent weights of connections from mental model states X i to a mental model state Y within individual or shared mental models that play a role within the organisation and its learning. This enables to differentiate the impacts from different mental model states X i on a given mental model state Y. Alternative choices might have been possible as well, such as T-states TY for excitability thresholds for mental model states Y. However, then the impacts from different mental model states X i on the given state Y cannot be differentiated, which is undesirable. Moreover, this would also have imposed limitations on the combination functions used for aggregation for the W-states, as they would need to include such a threshold parameter, while, for example, averaging functions usually do not have this.

18.4 What Has Been Addressed In a self-modeling network format, control of any type of adaptation of network characteristics (modeled by first-order self-model states) can be modeled by secondorder self-model states. In this volume (Canbalo˘glu et al. 2023) for the control of adaptation, multiple second-order self-model states have been used for different types of control: ● WWW -states for adaptive connectivity between the W-states ● CW -states representing adaptive combination function weights for different types of adaptive aggregation of W-states ● MW -states representing adaptive persistency of the learning for W-states ● TW -states representing adaptive excitability thresholds for W-states ● HW -states for adaptive learning speed for W-states Table 18.1 provides a brief global overview of these self-model states with references to different chapters of this volume (Canbalo˘glu et al. 2023) where they are used and for what purpose. In Table 18.2, a more detailed overview is shown of different types of contextsensitive control for different types of learning. It can be seen here that HW -states for adaptive adaptation speed of W-states have been used throughout for all types of learning to activate or accelerate the learning or stop it in a context-sensitive manner. Furthermore, WWW -states for adaptive connection weights between Wstates have been used for all types of learning to model context-sensitive effects, except individual learning. Moreover, CW -states for adaptive aggregation for Wstates have been used for context-sensitive shared mental model formation for feed forward learning.

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Table 18.1 Overview of different types of control over the various adaptation processes for organisational learning addressed in this volume (Canbalo˘glu et al. 2023); the indicated chapters refer to this volume Control of adaptation via adaptive connectivity

Control of adaptation via adaptive aggregation

Control of adaptation via adaptive timing

Controlled adaptation of mental model W-states via WWW -states for adaptive connections between W-states: • between individual mental models in dyads, teams, or organisation: Ch 12–13 • between individual, team, and organisation mental models in feed forward and feedback learning: Ch 6–15

Controlled adaptation of Controlled adaptation of mental model W-states via: mental model W-states via • CW -states for adaptive • HW -states for adaptive weights of the combination adaptation speed of functions used by W-states W-states: Ch 6–12, 14–15 for aggregation: Ch 9–10 • MW -states for adaptive persistence of the learnt effects of W-states: Ch 6–10 • TW -states for adaptive excitability thresholds of W-states: Ch 15

18.5 Further Work Being Addressed In further work it is being addressed how a virtual AI Coach can support safety in hospitals, in particular of medical teamwork. For an overview of this project, see (Canbalo˘glu et al. 2022). This AI Coach has knowledge about the shared mental model that is used by a team and then can: ● Monitor in how far the shared mental model is followed ● Detect omissions or deviant actions ● Support the team to get back on track to the shared mental model In addition, this AI Coach can play a central role in multilevel organisational learning by: ● ● ● ●

Representing and maintaining shared mental models Supporting team members in learning or memorising a shared mental model Speaking up about errors Reporting errors to management

In the meantime, this has been explored computationally for some case studies concerning shared mental models in the neonatal domain: ● To support the breathing of the baby (Xu et al. 2023) ● To avoid postpartum depression (Weigl et al. 2023) ● To support speaking up behaviour (Doornkamp et al. 2023) Another topic that needs further work concerns individual differences, for example, highly knowledgeable experts with deviant but good mental models. Also, the roles of leadership and organisational culture can be addressed further, for example, the effect of leadership on organisational learning, leadership change,

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Table 18.2 More detailed overview of computational mechanisms for organisational learning and control explored in this volume (Canbalo˘glu et al. 2023); the chapters indicated in the right-hand column refer to this volume Types of learning addressed

Adaptation modeled by Control of adaptation first-order self-model modeled by second-order states self-model states

Individual learning

Learning from internal simulation Observational learning by self-observation

Self-model W-states for Hebbian learning with upward and downward links to mental model base states Observation links or pathways from world states of self to mental model states; self-model W-states to control observation

Self-model HW -states to control learning rate: Ch 6–10, 14–15. Self-model MW -states to control persistence of learning of W-states: Ch 6–10, 14. Self-model TW -states to control excitability thresholds of W-states: Ch 15

Dyad learning

Observational learning based on observation of others Instructional learning by communication

Self-model W-states for observation links from world states of others to mental model base states to control observation. Self-model W-states for Hebbian learning with upward and downward links to mental model states

Self-model HW -states to control learning rate: Ch 12. Self-model WWW -states for control of observation of other individuals: Ch 15. Self-model WWW -states to control communication via self-model W-states for different individuals: Ch 12–13

Aggregation of different individual W-states to form team and/or organization W-states. Using proper combination functions and proper parameters of them

Self-model HW -states to control learning rate: Ch 6–12. Self-model WWW -states to control feed forward learning: Ch 8, 11–15. Self-model CW -states to control feed forward aggregation: Ch 9–10

Aggregation of individual W-states and team and/or organization W-states to update the individual W-states. Using proper combination functions and proper parameters of them

Self-model HW -states to control learning rate: Ch 6–10. Self-model WWW -states to control feedback communication: Ch 6–10, 13–15

Multilevel organizational Feed forward learning learning

Feedback learning

18 Discussion: Perspectives on Computational Modeling of Multilevel …

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the effect of culture on organisational learning, culture change, and organisational learning of culture.

References Canbalo˘glu, G., Treur, J., Wiewiora, A.: Computational Modeling of Multilevel Organisational Learning and its Control Using Self-Modeling Network Models. Springer Nature (this volume) (2023) Canbalo˘glu, G., Van Ments, L., Treur, J., Klein, J., Roelofsma, P.H.M.P.: Adaptive shared mental models for medical teams. In: Arezes, P., Garcia, A. (eds) Safety Management and Human Factors, Proceedings of the 13th International Conference on Applied Human Factors and Ergonomics, AHFE’22. AHFE Open Access, vol. 64. AHFE International, USA (2022). https:// doi.org/10.54941/ahfe1002634 Crossan, M.M., Lane, H.W., White, R.E.: An organizational learning framework: from intuition to institution. Acad. Manag. Rev. 24, 522–537 (1999) Doornkamp, S., Jabeen, F., Treur, J., Taal, H.R., Roelofsma, P.H.M.P.: A controlled adaptive network model of a virtual coach supporting speaking up by healthcare professionals to optimise patient safety. Cogn. Sys. Rest. 81(1): 37–49 (2023). https://doi.org/10.1016/j.cogsys.2023.02.002 Hendrikse, S.C.F., Treur, J., Koole, S.L.: Modeling emerging interpersonal synchrony and its related adaptive short-term affiliation and long-term bonding: a second-order multi-adaptive neural agent model. Int. J. Neural Syst. (2023). https://doi.org/10.1142/S0129065723500387 Kim, D.H.: The link between individual and organisational learning. Sloan Management Review, Fall 1993, pp. 37–50. Also in: Klein, D.A. (ed.) The Strategic Management of Intellectual Capital. Routledge-Butterworth-Heinemann, Oxford (1993) Treur, J.: Modeling higher-order adaptivity of a network by multilevel network reification. Network Science 8, S110–S144 (2020a) Treur, J.: Network-oriented modeling for adaptive networks: designing higher-order adaptive biological, mental and social network models. Springer Nature, Cham (2020b) Treur, J., Van Ments, L. (eds.): Mental Models and Their Dynamics, Adaptation, and Control: A Self-Modeling Network Modeling Approach. Springer Nature (2022) Weigl, L.M., Jabeen, F., Treur, J., Taal, H.R., Roelofsma, P.H.M.P.: Modeling learning for a better safety culture within an organisation using a virtual AI coach: reducing the risk of postpartum depression by more communication with parents. Cogn. Syst. Res. 80, 1–36 (2023) Wiewiora, A., Smidt, M., Chang, A.: The ‘How’ of multilevel learning dynamics: a systematic literature review exploring how mechanisms bridge learning between individuals, teams/projects and the organization. Eur. Manag. Rev. 16, 93–115 (2019) Wiewiora, A., Chang, A., Smidt, M.: Individual, project and organizational learning flows within a global project-based organization: exploring what, how and who. Int. J. Project Manage. 38, 201–214 (2020) Xu, Y., Jabeen, F., Treur, J., Taal, H.R., Roelofsma, P.H.M.P.: Adaptive agent network models with internal mental models supporting patient safety. In: Proceedings of the 15th International Conference on Social Computing and Networking, SocialCom’22. IEEE Computer Society Press (2023)

Index

A Adaptive computational network model, 261 Adaptive dynamical system, 11, 48, 159, 290, 385, 387, 389, 415, 441, 455–457, 461–463, 471, 474 Adaptive network models, 9, 11, 39, 44, 51, 52, 55, 57–59, 64, 95, 101, 103–106, 113, 123, 129–136, 141, 153, 155, 160, 172, 185, 186, 195, 197–202, 208, 223, 229–234, 241, 273, 289, 297, 298, 300, 302, 303, 310, 333, 336, 348, 368, 372, 374, 375, 394, 409, 414, 415, 422, 424–427, 459, 476, 493, 494, 500 Adaptive self-modeling network model, 10, 57, 94, 124, 207, 217, 237, 253, 310, 374, 457, 474 Aggregation process, 9, 185–187, 192, 194, 196, 207, 217, 218, 223–225, 235, 237

B Boolean functions, 9, 217, 218, 225, 226, 229–231, 237

C Communication, 10, 21, 22, 46, 47, 57, 61–64, 77, 78, 81, 82, 85–87, 166, 168, 256, 259, 261, 264, 266, 271, 299, 301, 306, 327–329, 333–337, 340–348, 410, 418, 510

Computational analysis, 8, 10, 172, 173, 290, 310 Computational modeling, 8, 10, 73, 74, 83, 89, 94, 124, 185, 217, 253, 254, 272, 273, 309, 310, 409, 493 Context-sensitive control, 8–10, 39, 40, 46, 48, 64, 88, 185–187, 189, 194–198, 201, 205–207, 211, 217, 225, 226, 243, 253, 267–269, 298, 426, 508 Controlled adaptation, 509

E Equilibrium analysis, 11, 385, 389, 390, 455–457, 463–465, 468, 469, 471, 473–475, 477–479, 481–483, 486–490, 492–494, 496, 498–500, 506

L Leader qualities, 371, 372, 377, 379 Leadership, 4, 7, 8, 10, 29, 76, 254, 273, 327–331, 333, 335, 344, 346, 365, 367, 371, 373, 380, 391–393, 416–419, 422, 441, 509 Leadership style, 7, 10, 253, 254, 256, 258, 259, 261, 269, 272, 273, 301, 310, 328–331, 334, 335, 348, 367, 373 Learning mechanisms, 7, 8, 18, 20, 25, 27–30, 75, 76, 196, 229, 263, 419, 426, 505 Learning scenarios, 17, 20, 24, 26, 28, 30, 254, 256, 261, 273, 290, 309, 310

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 G. Canbalo˘glu et al. (eds.), Computational Modeling of Multilevel Organisational Learning and Its Control Using Self-modeling Network Models, Studies in Systems, Decision and Control 468, https://doi.org/10.1007/978-3-031-28735-0

513

514 M Match officials, 9, 153, 155, 160, 163, 164, 166, 168 Mechanisms, 4, 8, 9, 11, 17, 18, 20–22, 25, 29, 74–76, 83, 85, 87, 90, 93, 97, 112, 123, 130, 140, 154, 188, 219, 256, 262, 264, 269, 273, 409–413, 416, 419–426, 428, 429, 432, 433, 437–442, 506 Mental model, 4–6, 8, 9, 11, 18, 51–53, 55–58, 60–65, 74, 76–82, 85, 87–90, 93–98, 100–104, 107, 109, 112, 113, 124, 125, 127–130, 132–134, 137, 138, 140, 141, 154, 155, 157, 159–162, 164–166, 172, 173, 185–188, 191–196, 198, 199, 201, 203, 204, 206, 207, 217–220, 223–225, 228, 229, 232, 235, 255, 258, 261–264, 268, 269, 271–273, 289–292, 294, 297–302, 304–310, 328, 329, 335–337, 368, 374, 375, 377, 378, 420, 422–426, 428–430, 432, 433, 436, 438, 440, 441, 457, 459, 474, 476, 493, 495–497, 506–510 Mistake handling, 7, 375, 441 Multilevel learning, 8, 17–22, 24–30, 76, 256, 290, 292, 309, 310, 365, 366 Multilevel organisational learning, 17, 19, 27, 29, 47, 73, 89, 90, 123–128, 134, 140, 253–256, 272, 289–291, 293, 297, 298, 309, 327, 328, 330, 346, 419, 420, 457, 473–475, 492–494, 499, 505–507, 509 N Network model, 7–11, 27, 33, 35–40, 44, 47, 48, 52–55, 57–61, 64, 65, 83, 93–95, 98–106, 110, 112, 113, 123, 124, 126–134, 136, 140, 141, 153, 155, 157, 160, 161, 171, 172, 185, 187, 189–191, 194–202, 207, 217–223, 225, 228–234, 237, 241, 257, 259–262, 264, 273, 289, 291, 295, 297–303, 310, 332, 333, 335–337, 348, 368–372, 374, 375, 388–390, 394, 409, 410, 413–415, 422, 424–427, 440, 455–461, 463, 464, 467, 469–477, 481–483, 486, 489–492, 494, 499, 500, 506 Network-oriented modeling, 34, 48, 52, 54, 83, 98, 155, 157, 189, 221, 257, 295, 332, 368

Index Network reification, 34, 38, 55, 99, 191, 223, 260, 297, 368, 458, 476

O Organisational culture, 20, 21, 23, 27, 30, 75, 254, 310, 363–365, 367, 369, 374, 375, 377, 392, 393, 409–411, 416–418, 420, 421, 423, 428, 509 Organisational learning, 17–20, 24, 26, 45, 73–76, 87, 89, 90, 93–95, 97, 98, 100, 101, 104, 107, 109, 112, 123, 127, 137, 140, 153–157, 161, 164–166, 169, 172, 185–189, 192–194, 196–198, 200, 201, 203, 207, 217–220, 223, 224, 228, 230, 231, 233, 234, 237, 253–256, 258, 273, 290, 291, 293, 297, 298, 300, 303, 304, 309, 327–329, 331, 340, 341, 363, 364, 366–369, 380, 381, 391–394, 409, 411, 412, 420–422, 428, 433, 436, 437, 440–442, 459, 464, 467, 468, 472, 473, 476, 477, 481, 494, 500, 505, 509–511 Organisational learning mechanisms, 74, 76, 421, 422, 440

P Project-based organisation, 24, 256, 289–292, 298, 309 Project learning, 76

S Safety culture, 11, 409, 411, 428 Self-model, 390 Self-modeling network, 6–8, 10, 11, 33, 34, 36, 38–42, 47, 48, 52, 54–57, 61, 64, 73, 74, 83–85, 87, 90, 94, 96, 98–101, 110, 112, 124, 126–128, 140, 185–187, 189–192, 194, 196, 207, 217–219, 221–223, 227, 228, 237, 254, 257, 260, 289–291, 295, 297, 310, 328, 332, 333, 368–371, 385, 387, 389, 390, 393, 455–459, 461–464, 471, 476, 477, 492, 493, 506–508 Self-modeling network model, 389 Shared mental model, 4, 6, 8–10, 27, 75, 77, 79, 80, 82, 87–90, 93, 95–99, 101, 102, 104, 107, 109, 110, 112, 124, 125, 127–129, 134, 137, 140, 153–157, 160, 161, 163–166, 172,

Index 173, 185–189, 192–194, 196–198, 201, 203–207, 211, 217–220, 223–225, 228–230, 233–235, 237, 243, 253, 264–266, 268, 269, 271, 272, 291, 294, 298, 299, 328, 329, 334, 367, 374, 375, 420, 424, 426, 428, 433, 435, 493, 495, 497, 498, 508, 509 Simulation, 3, 8–11, 27–30, 35, 37, 46, 52–58, 61–64, 68, 73, 77, 83, 85, 86, 90, 94–96, 98–104, 107, 108, 110, 112, 124–129, 134, 136, 138, 139, 153–156, 158–160, 163, 164, 167–170, 172, 186, 187, 189, 190, 192–194, 198, 201, 203–205, 218–221, 223, 224, 230, 235, 236,

515 238–240, 253, 254, 257, 264, 267, 269–271, 273, 291, 292, 295, 299, 300, 302, 305–309, 328, 332, 334, 335, 340–346, 369, 370, 379, 381, 385, 390, 392, 411–413, 415, 428–440, 458, 469, 475, 483, 486, 487, 490, 492, 493, 506, 510

T Teamwork, 9, 96, 153, 154, 187, 219, 335, 373, 509 Third-order adaptive computational network model, 291 Transformational change, 11, 409–411, 413, 419, 440