Ontology Makes Sense : Essays in Honor of Nicola Guarino [1 ed.] 9781614999553, 9781614999546

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Copyright © 2019. IOS Press, Incorporated. All rights reserved. Ontology Makes Sense : Essays in Honor of Nicola Guarino, IOS Press, Incorporated, 2019. ProQuest Ebook Central,

Copyright © 2019. IOS Press, Incorporated. All rights reserved. Ontology Makes Sense : Essays in Honor of Nicola Guarino, IOS Press, Incorporated, 2019. ProQuest Ebook Central,

Copyright © 2019. IOS Press, Incorporated. All rights reserved.

ONTOLOGY MAKES SENSE

Ontology Makes Sense : Essays in Honor of Nicola Guarino, IOS Press, Incorporated, 2019. ProQuest Ebook Central,

Frontiers in Artificial Intelligence and Applications The book series Frontiers in Artificial Intelligence and Applications (FAIA) covers all aspects of theoretical and applied Artificial Intelligence research in the form of monographs, selected doctoral dissertations, handbooks and proceedings volumes. The FAIA series contains several sub-series, including ‘Information Modelling and Knowledge Bases’ and ‘Knowledge-Based Intelligent Engineering Systems’. It also includes the biennial European Conference on Artificial Intelligence (ECAI) proceedings volumes, and other EurAI (European Association for Artificial Intelligence, formerly ECCAI) sponsored publications. The series has become a highly visible platform for the publication and dissemination of original research in this field. Volumes are selected for inclusion by an international editorial board of well-known scholars in the field of AI. All contributions to the volumes in the series have been peer reviewed. The FAIA series is indexed in ACM Digital Library; DBLP; EI Compendex; Google Scholar; Scopus; Web of Science: Conference Proceedings Citation Index – Science (CPCI-S) and Book Citation Index – Science (BKCI-S); Zentralblatt MATH. Series Editors: J. Breuker, N. Guarino, J.N. Kok, J. Liu, R. López de Mántaras, R. Mizoguchi, M. Musen, S.K. Pal and N. Zhong

Volume 316

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Recently published in this series Vol. 315. A. Lupeikiene, O. Vasilecas and G. Dzemyda (Eds.), Databases and Information Systems X – Selected Papers from the Thirteenth International Baltic Conference, DB&IS 2018 Vol. 314. L.C. Jain, X. Zhao, V.E. Balas and F. Shi (Eds.), Information Technology and Intelligent Transportation Systems – Proceedings of the 3rd International Conference on Information Technology and Intelligent Transportation Systems (ITITS 2018) – Xi’an, China, September 15–16, 2018 Vol. 313. M. Palmirani (Ed.), Legal Knowledge and Information Systems – JURIX 2018: The Thirty-first Annual Conference Vol. 312. T. Endrjukaite, A. Dudko, H. Jaakkola, B. Thalheim, Y. Kiyoki and N. Yoshida (Eds.), Information Modelling and Knowledge Bases XXX Vol. 311. M. Coeckelbergh, J. Loh, M. Funk, J. Seibt and M. Nørskov (Eds.), Envisioning Robots in Society – Power, Politics, and Public Space – Proceedings of Robophilosophy 2018 / TRANSOR 2018 Vol. 310. N. Petkov, N. Strisciuglio and C. Travieso-González (Eds.), Applications of Intelligent Systems – Proceedings of the 1st International APPIS Conference 2018 Vol. 309. A.J. Tallón-Ballesteros and K. Li (Eds.), Fuzzy Systems and Data Mining IV – Proceedings of FSDM 2018 ISSN 0922-6389 (print) ISSN 1879-8314 (online)

Ontology Makes Sense : Essays in Honor of Nicola Guarino, IOS Press, Incorporated, 2019. ProQuest Ebook Central,

Ontology Makes Sense Essays in honor of Nicola Guarino

Edited by

Stefano Borgo Laboratory for Applied Ontology, ISTC-CNR, Trento

Roberta Ferrario Laboratory for Applied Ontology, ISTC-CNR, Trento

Claudio Masolo Laboratory for Applied Ontology, ISTC-CNR, Trento

and

Laure Vieu

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Institut de Recherche en Informatique de Toulouse, CNRS, Toulouse and Laboratory for Applied Ontology, ISTC-CNR, Trento

Amsterdam • Berlin • Washington, DC

Ontology Makes Sense : Essays in Honor of Nicola Guarino, IOS Press, Incorporated, 2019. ProQuest Ebook Central,

© 2019 The authors and IOS Press. All rights reserved. No part of this book may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without prior written permission from the publisher. ISBN 978-1-61499-954-6 (print) ISBN 978-1-61499-955-3 (online) Library of Congress Control Number: 2019934699 Publisher IOS Press BV Nieuwe Hemweg 6B 1013 BG Amsterdam Netherlands fax: +31 20 687 0019 e-mail: [email protected]

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Preface

This book is written in homage to Nicola Guarino. It is a tribute to his many scientific contributions to the new discipline, applied ontology, he struggled to establish. Nicola Guarino is widely recognized as one of the pioneers in formal and applied ontology. Renowned – and sometimes even criticized – for his deep interest for the subtlest details of theoretical analysis, all throughout his career he has held the conviction that all science has to be for the benefit of society at large, hence his motto that ontologies are not just for making information systems interoperable, but also – and more importantly – for making people (users of the systems) understand each other. He was among the first to realize that, to capture the intended meaning of the terms used by an information system, applied ontology has necessarily to be an interdisciplinary enterprise. Nicola’s early career developed in the areas of data systems and expert systems in physics and biomedical engineering. The lack of methodologies in expert systems led him to turn to philosophical logic as a source of inspiration, prompting him to attend the meetings of the analytic philosophy group at the University of Padua, and to discover a whole new world. It was the end of the 1980s and in that period the term ‘ontology’ started to be used to indicate a shared vocabulary across a community. Recognizing the potentials of this idea, Nicola began studying philosophical work. Knowing that language remains one of the pivotal elements in knowledge acquisition and representation, he paired it with the study of linguistic analysis. The combination of the two fields proved to be fundamental to shape his research vision, which could be summarized as: ontological analysis is hard, yet unavoidable to address the pervasive need for explicit, meaningful and transparent information systems. In other words, ontology makes sense. This book is also a praise to Nicola’s continuous efforts to build a community around the new discipline. Thanks to these efforts, we have nowadays an international association, a dedicated journal and a flagship conference, which have become a reference to all members of the community. In 1998 Nicola inaugurated the conference series ‘Formal Ontology in Information Systems’ (FOIS), which marked the beginning of the new research area; twenty years later, FOIS is still the preferred venue for people to meet, and to present and discuss applied ontology issues. Soon he realized that the discipline was mature enough to have dedicated laboratories so, together with his collaborators in Padua, he joined the Institute of Cognitive Sciences and Technologies (ISTC CNR) and founded the Laboratory for Applied Ontology (LOA)1 with a 1 www.loa.istc.cnr.it

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unit in Trento, which will be his home for the rest of his research activity, and one in Rome. Throughout the years, the LOA has always been composed of researchers with very different backgrounds, like computer scientists, engineers, philosophers, mathematicians, linguists, social and cognitive scientists and so on, in line with Nicola’s idea that interdisciplinarity is at the core of the applied ontology vision. After some years, he considered the need of establishing a journal specifically dedicated to ontological content, marking the distinction of foundational ontology, an approach based on deep and rigorous ontological analysis, from the approaches focused on syntactical and logical concerns, the so-called lightweight ontologies used in the Semantic Web. To this end, in 2005 he and Mark Musen founded the Applied Ontology journal.2 What was still needed was a place open to the community for discussion and coordination of activities in applied ontology. This came in 2009, when the International Association for Ontology and its Applications (IAOA)3 was founded. The IAOA association helped to move beyond previously established national associations and to organize an international applied ontology community. Nicola served as IAOA President for four years (2009-2013) and has been in the Advisory Board since then. Nicola has always believed in the importance of having a research network spread at an international level, with nodes exchanging ideas, information and experience on scientific views and applications of ontology. One example is the International Laboratory on Interacting Knowledge Systems (ILIKS), a European joint virtual laboratory connecting the LOA, the IRIT in Toulouse and the University of Trento, that he established in collaboration with Laure Vieu (IRIT CNRS), and that collected research groups with expertise in computer science, engineering, cognitive science, education and economics. Finally, this book is the result of the enthusiastic answers we, the editors, had from researchers around the world who belong to this community, who have been influenced by and, in turn, influenced the work of Nicola. Many others unfortunately could not comply with the strict schedule set for this book but made themselves available in other ways, e.g. to review the material and to participate in the public event organized for the presentation of the book. Contributed papers reflect the large variety of research topics that marked Nicola’s impact on the applied ontology community. We clustered them according to five general areas addressed by Nicola in his career and that are briefly described below. For each area we provide a few main references and invite the readers to explore the complete bibliography of Nicola’s work to fully appreciate his views and interests. I - What Is an Ontology? In the nineties, Nicola published a series of papers devoted to develop an accurate analysis of some crucial notions that the community of knowledge engineering, at that time, was starting to refer to. In particular, he reacted to Gruber’s definition 2 www.iospress.nl/journal/applied-ontology 3 iaoa.org

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of ontology – an ontology is “an explicit specification of a conceptualization” – by proposing his own analysis of what an ontology is, grounded on the formal characterization of the notions of conceptualization and ontological commitment, and on the careful distinction between ‘Ontology’ – the philosophical discipline – and ‘ontologies’ – the engineering artifacts. In his view, the term conceptualization has a semantic connotation, denoting an intensional relational structure (given in terms of possible worlds) that reflects a particular conceptual system. ‘Ontologies’ are instead logical theories devoted to capture given conceptualizations (their ontological commitments), i.e., theories whose intended models are intensional relational structures. At the same time, he started to stress the necessity, in the fields of knowledge representation and conceptual modeling, to introduce an ontological level to make explicit the meaning of the assumed primitives and to distinguish different kinds of ontologies according to their level of generality. In particular, he argued for the fundamental role of top-level ontologies – i.e., ontologies that describe very general notions (e.g. identity, parthood, dependence, or causation) or kinds of entities that are involved in the representation of most application domains (e.g., space, time, matter, object, or event) – in both the systematic development of ontologies and the improvement of interoperability and integration of information systems.

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Main references – N. Guarino. The ontological level. In R. Casati, B. Smith and G. White, editors, Philosophy and the cognitive sciences, pages 443–456. Hoelder-PichlerTempsky, 1994. – N. Guarino, M. Carrara, and P. Giaretta. Formalizing Ontological Commitment. In Proceedings of the National Conference on Artificial Intelligence (AAAI-94), pages 560–567. Morgan Kaufmann, 1994. – N. Guarino and P. Giaretta, Ontologies and knowledge bases: towards a terminological clarification. In N. Mars, editor, Towards Very Large Knowledge Bases, pages 25–32. IOS Press, 1995. – N. Guarino. Formal Ontology, Conceptual Analysis and Knowledge Representation. International Journal of Human and Computer Studies, 43(5– 6):625–640, 1995. – N. Guarino. Formal Ontology in Information Systems. In N. Guarino, editor, Proceedings of the First International Conference on Formal Ontology in Information Systems (FOIS’98), pages 3–15. IOS Press, 1998. – N. Guarino, D. Oberle, and S. Staab. What Is an ontology?. In S. Staab and R. Studer, editors, Handbook on ontologies, pages 1–17. Springer, 2009. – N. Guarino. The ontological level: Revisiting 30 years of knowledge representation. In A. T. Borgida, V. Chaudhri, P. Giorgini, and E. Yu, editors, Conceptual modeling: Foundations and applications: Essays in honor of John Mylopoulos, pages 52–67. Springer, 2009. II - Knowledge Engineering Beside clarifying the central notions of ontology and conceptualization, Nicola realized the complexity of, and the huge effort required for, the development of well-founded ontological resources. He then started to work on methodologies Ontology Makes Sense : Essays in Honor of Nicola Guarino, IOS Press, Incorporated, 2019. ProQuest Ebook Central,

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and tools able to manage the lifecycle of ontologies and to facilitate their use in information systems. OntoClean was the first analytical methodology to evaluate and validate the ontological adequacy of taxonomies: by characterizing the classes in the taxonomy by means of philosophical notions (like essence, identity, rigidity and unity), it allows to impose some formal constraints on the structure of such taxonomy. The IST Project WonderWeb4 was one of the first efforts to build a whole infrastructure to support the use of ontologies for large-scale applications in the Semantic Web. In addition to the ontology language OWL and a series of techniques and tools to support the integration, sharing, evolution, editing, storage, etc. of ontologies, an important outcome of this project was the Dolce ontology. Despite the reference role for foundational ontologies played by Dolce since then, it has never been conceived as a standard. Nicola and his collaborators always believed in the importance of having an integrated library of foundational ontologies, reflecting different commitments and purposes, rather than a single monolithic ontology. This is in line with the adoption of an interdisciplinary, cognitive, approach to ontology that Nicola argued for at length.

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Main references – N. Guarino and C. Welty. A formal ontology of properties. In International Conference on Knowledge Engineering and Knowledge Management, pages 97–112. Springer, 2000. – N. Guarino and C. Welty. Identity, Unity, and Individuality: Towards a formal toolkit for ontological analysis. In W. Horn, editor, Proceedings of The European Conference on Artificial Intelligence (ECAI’2000), pages 219– 223. IOS Press, 2000. – C. Welty and N. Guarino. Supporting Ontological Analysis of Taxonomic Relationships. Data and Knowledge Engineering 39(1):51–74, 2001. – A. Gangemi, N. Guarino, C. Masolo, A. Oltramari, and L. Schneider. Sweetening ontologies with DOLCE. In International Conference on Knowledge Engineering and Knowledge Management, pages 166–181. Springer, 2002. – C. Masolo, S. Borgo, A. Gangemi, N. Guarino, and A. Oltramari. The WonderWeb library of foundational ontologies and the DOLCE ontology, WonderWeb Deliverable D18 (final), 2003. – N. Guarino and C. Welty. An Overview of OntoClean. In S. Staab and R. Studer, editors, Handbook on ontologies, pages 151–171. Springer, 2009. III - Ontologies and Language Nicola’s cognitive approach to ontology led him to systematically refer to existing linguistic analyses of complex semantic phenomena. This was particularly significant for various features of Dolce. For instance, the chosen approach to qualities was influenced by linguistic questions related to B. Partee’s analysis of “the room’s temperature is ninety and rising”, and perdurant subcategories reflected famous distinctions in verb classes. So a deep relationship between ontology and 4 wonderweb.man.ac.uk

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language generally acknowledged in philosophy of language – although less so in metaphysics – is at the root of Nicola’s work. On the other hand, a significant impact of his methodological work can be found in the reorganization of linguistic resources like WordNet5 and in cultural standards like CIDOC6 . Nicola and his colleagues contributed to elucidate recurring ontological flaws in linguistic resources, and in proposing the first alignment of WordNet with Dolce’s top-level. Main references – N. Guarino. Some ontological principles for designing upper level lexical resources. In A. Rubio, N. Gallardo, R. Castro, and A. Tejada, editors, First International Conference on Language Resources and Evaluation, pages 527–534. European Language Resources Association, 1998. – N. Guarino, C. Masolo, and G. Vetere. Ontoseek: Content-based access to the web. IEEE Intelligent Systems and their Applications, 14(3):70–80, 1999. – A. Gangemi, N. Guarino, C. Masolo, and A. Oltramari. Sweetening WordNet with Dolce. AI magazine, 24(3):13–24, 2003. – A. Gangemi, N. Guarino, C. Masolo, and A. Oltramari. Interfacing WordNet with DOLCE: towards OntoWordNet. In Ontology and the Lexicon: A Natural Language Processing Perspective, pages 36–52. 2010.

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IV - Ontological Categories and Relationships Nicola introduced the ontological level as a bridge between the linguistic and cognitive levels, that he called the subjective levels, and the formal and logical ones, that motivate theories whose interpretation remains arbitrary. The ontological level helps to constrain the interpretation of the vocabulary primitives by setting postulates about the meaning of these terms. But how can the ontological level identify these meanings? To answer this question one has to delineate the boundary of the domains to be modeled, that may be at different levels of generality, ranging from top-level to application level. He thus proposed to see applied ontology as the science which “develops theories of the types of entities existing in (people’s assumptions about) given domains of reality, and of the relations between these types.”7 The Dolce ontology was developed following such a view. In Nicola’s mind, the ontologist should make available a set of distinct theories that characterize types of entities and relations according to the different ontological stand one may adopt. Among these theories, some deal with notions that – although somehow specific – are necessary to talk about things in the world like space, time, change, physical objects, parts, events. In this vein, Nicola wrote some seminal papers in the nineties to study, from the conceptual and formal viewpoint, the relations of parthood and connection (theories known as mereology and mereotopology). In particular, his research focused on the use of 5 wordnet.princeton.edu 6 cidoc-crm.org 7 From

a presentation of the Laboratory for Applied Ontology by Nicola Guarino.

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these relations in applications and in natural language, and on their capabilities to characterise space, matter and (physical) objects. Later on, he worked at the construction of a framework to characterize social reality and, in doing this, he and his colleagues proposed a theory of social roles where the ontological nature of these entities is spelled out. More recently, Nicola resumed the investigation of the notion of event and of the connection between the tensed and tenseless views, showing how these can be integrated in the same ontological framework. In the same period, he has also analyzed the interplay between events and relationships, where the latter are seen as truthmakers of relations.

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Main references – N. Guarino, Concepts, Attributes and Arbitrary Relations: Some Linguistic and Ontological Criteria for Structuring Knowledge Bases. Data and Knowledge Engineering, 8(2):249–261, 1992. – A. Artale, E. Franconi, N. Guarino, and L. Pazzi. Part-whole relations in object-centered systems: An overview. Data & Knowledge Engineering, 20(3):347–383, 1996. – S. Borgo, N. Guarino, and C. Masolo. A pointless theory of space based on strong connection and congruence. In L. Carlucci Aiello and S. Shapiro, editors, KR 96, Principles of Knowledge Representation and Reasoning, pages 220–229. Morgan Kaufmann, 1996. – C. Masolo, L. Vieu, E. Bottazzi, C. Catenacci, R. Ferrario, A. Gangemi, and N. Guarino. Social roles and their descriptions. In D. Dubois and C. Welty, editors, Proceedings of the 9th Int. Conf. on Principles of Knowledge Representation and Reasoning (KR 2004), pages 267–277. AAAI Press, 2004. – N. Guarino and G. Guizzardi. “We need to discuss the Relationship”: Revisiting Relationships as Modeling Constructs. In International Conference on Advanced Information Systems Engineering, pages 279–294. Springer, 2015. – N. Guarino and G. Guizzardi. Relationships and Events: Toward a General Theory of Reification and Truthmaking. In G. Adorni G., S. Cagnoni S., M. Gori, and M. Maratea, editors, Advances in Artificial Intelligence, pages 237–249. Springer, 2016. – N. Guarino. On the semantics of ongoing and future occurrence identifiers. In H. C. Mayr, G. Guizzardi, H. Ma, and O. Pastor, editors, Conceptual Modelling, Proceedings of the 36th International Conference, ER 2017, pages 477–490. Springer, 2017. V - Ontologies and Applications A paramount contribution of Nicola in the field of conceptual modeling and knowledge engineering consisted in providing an ontological foundation of the primitives used in their models, showing the necessity of making explicit the ontological commitments. Such analyses have prompted new perspectives on conceptual modeling languages as UML (Unified Modeling Language) and contributed to the elaboration of OntoUML.

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More recently, Nicola began to focus on notions used in social ontology, working in eGovernment applications, in particular in the emerging discipline of service science, where he brought an important conceptual clarification on the different uses of the term ‘service’ in the business and ICT domains, by relying on a foundational analysis of the notions of commitment and activity. The attention to the economic perspective led to a related study of the notions of value and risk and to the modeling of the main principles of tax legislation and the core concepts of personal income taxes. Starting from the analysis of services, Nicola soon realized that a sound representation of them could not do without an analysis and representation of the organization and social environment in which such services take place. Ontological modeling was then applied to whole socio-technical systems, and the resulting transparency of the organizational procedures and relative responsibilities became a fundamental element of resilience of the systems themselves. The application of such perspective led to a thorough analysis of business process modeling components, which allows to connect the organization and the information domains.

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Main references – N. Guarino, G. Guizzardi. In the defense of ontological foundations for conceptual modeling. Scandinavian Journal of Information Systems, 18(1): Article 1, 2006. – R. Ferrario and N. Guarino. Towards an Ontological Foundation for Services Science. In D. Fensel and P. Traverso, editors, Future Internet – FIS 2008, Lecture Notes in Computer Science 5468, pages 152–169. Springer Verlag, 2009. – N. Guarino, R. Ferrario, E. Bottazzi, and G. Sartor. Open Ontology-Driven Sociotechnical Systems: Transparency as a Key for Business Resiliency. In M. De Marco, D. Te’eni, V. Albano, and S. Za,editors, Information Systems: Cross-roads for Organization, Management, Accounting and Engineering, pages 535–542, Springer Verlag, 2012. – I. Distinto, N. Guarino, and C. Masolo. A well-founded ontological framework for modeling personal income tax. In Proceedings of the Fourteenth International Conference on Artificial Intelligence and Law (ICAIL’13), pages 33–42. ACM, 2013. – G. Guizzardi, N. Guarino, and J.P.A. Almeida. Ontological Considerations About the Representation of Events and Endurants in Business Models. In M. La Rosa, P. Loos, and O. Pastor, editors, Business Process Management. BPM 2016, Lecture Notes in Computer Science 9850, pages 20–36, Springer Verlag, 2016. – T.P. Sales, F. Bai˜ao, G. Guizzardi, J.P.A. Almeida, N. Guarino, and J. Mylopoulos. The Common Ontology of Value and Risk. In J. Trujillo et al., editors, Conceptual Modeling. ER 2018. Lecture Notes in Computer Science 11157, pages 121–135 Springer Verlag, 2018.

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As one can see from this list of topics and the contributions in this volume, Nicola’s achievements have impacted the work of many researchers around the world. Nicola’s role was even more important to some, among whom us, the editors of this book, as it significantly shaped their own careers. We are sure that in the future Nicola’s work and dedication will continue to influence this community as well as many researchers aiming to establish ontologically sound bases for their research areas. Acknowledgments ohlich, for their continuous We thank IOS Press, and in particular Maarten Fr¨ support, the contributors and the reviewers of this volume for their help in making this collection a reality.

Trento, January 2019

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Stefano Borgo Roberta Ferrario Claudio Masolo Laure Vieu

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Contents Preface Stefano Borgo, Roberta Ferrario, Claudio Masolo and Laure Vieu

v

I. What Is an Ontology? Carnapian Engineering Achille C. Varzi

3

Philosophy and the Ontologies of Knowledge Representation in AI Pierdaniele Giaretta

24

Artificial Intelligence Within the Bounds of Ontological Reason Alessandro Oltramari

37

On Ontological Categories Pawel Garbacz

49

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II. Knowledge Engineering Knowledge Engineering Riichiro Mizoguchi

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The Discipline of Ontological Engineering Michael Grüninger

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Embracing the Formal Revolution in Applied Ontology: The Impact of Nicola Guarino Leo Obrst

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III. Ontologies and Language Ontology, Language, Meaning: Semiotic Steps Beyond the Information Artifact John A. Bateman

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When WordNet Met Ontology Christiane Fellbaum and Amanda Hicks

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Formal Ontology to the Proof of Facts Guido Vetere

152

IV. Ontological Categories and Relationships Guarino’s Possibilism Antony Galton

167

Processes Endure, Whereas Events Occur Gilles Kassel

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Towards a New Foundational Ontology of Properties, Attributives and Data Heinrich Herre

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Ontological Dependence, Spatial Location, and Part Structure Friederike Moltmann

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V. Ontologies and Applications Taking It to the Next Level: Nicola Guarino, Formal Ontology and Conceptual Modeling Giancarlo Guizzardi and John Mylopoulos

223 242

Enriching Data Models with Behavioral Constraints Alessandro Artale, Diego Calvanese, Marco Montali and Wil van der Aalst

257

Value-Aware Enterprise Modelling Paul Johannesson and Birger Andersson

278

Author Index

293

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Towards a Logical Foundation of Reification in Modelling Languages Alessandro Artale and Enrico Franconi

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I. What Is an Ontology?

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Carnapian Engineering Achille C. Varzi∗ Department of Philosophy, Columbia University Abstract. Ontology has come to gain huge currency in the information sciences, with techniques, applications, and results vastly exceeding the traditional concerns of philosophy. How did that happen? Where are we heading to? I do not have the answers. But I know what it took and what is needed. It took—and we need—the skills of a good Carnapian engineer, someone capable and willing to build bridges across fields even though each side regards them as a troublesome intruder. Keywords. Ontology, formal ontology, metaphysics, information science

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1. No ontology without Ontology Ontology: the science of what is. While the word is of modern coinage,1 the field of inquiry it denotes is as old as a science can be, indeed as old as philosophy. Yet ontology is also, in many ways, a new discipline. For just as it developed over the centuries as a central chapter of theoretical metaphysics, so in recent years ontology has become a central concern in applied information science. Researchers in various fields have come to realize that a solid foundation for their projects calls for an explicit theorization of the types of entities and relations that make up their respective domains of inquiry, and as the need to integrate such projects has grown, so has the need to identify common general principles over ad hoc, case-based solutions—principles that have come to be characterized as ‘ontological’. It is difficult to locate the exact origins of this insight, but one of its earliest official expressions—and one of the earliest formulations of the corresponding agenda—may be traced back to the International Workshop on Formal Ontology in Conceptual Analysis and Knowledge Representation held in Padua, Italy, in March 1993 on the initiative of Nicola Guarino and Roberto Poli. It is worth quoting from their preface to the Proceedings volume: Problems of conceptual analysis and of the acquisition of commonsense knowledge still represent a major bottleneck in the development of information systems. In mature areas like databases as well as in more recent fields like knowledge engineering, the rigorous analysis of the domain and the choice among the available representation primitives are difficult tasks, ∗ Department of Philosophy, Columbia University, New York, NY 10027, USA; e-mail: [email protected]. 1 The

oldest extant records (in Latin and Greek, respectively) appear in two works of the early 17th century, Jacob Lorhard’s Ogdoas Scholastica (1606) and Rudolf G¨ockel’s Lexicon philosophicum (1613) (see [1] for details). The first occurrence of the term in English as recorded by the Oxford English Dictionary appears in Harvey’s Archelogia philosophica nova (1663), which defines ontology as ‘a Discourse of a Being’, followed by Bailey’s Dictionary (1721), which defines it as ‘an Account of being in the Abstract’. Ontology Makes Sense : Essays in Honor of Nicola Guarino, IOS Press, Incorporated, 2019. ProQuest Ebook Central,

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A.C. Varzi / Carnapian Engineering

appearing to rest on a mixture of introspection (as to what is intuitively right) and technical realization of the resulting theory. Existing knowledge acquisition tools tend to be oriented around applications, and therefore a new knowledge base must usually be constructed from scratch when a new problem is undertaken. Due to the high costs of this process, recent initiatives like DARPA’s Knowledge Sharing Efforts have underlined the opportunity of increasing the quality of formalized bodies of knowledge in such a way that it is possible to share and reuse at least parts of them for a variety of different purposes. The development of so-called generic ontologies plays an essential role in this connection. [2, p. i]

In fact, by the time of the Padua workshop, participants in the Knowledge Sharing initiative2 were already speaking of ‘ontologies’ in this sense: If we could develop shared sets of explicitly defined terminology, sometimes called ontologies, we could begin to remove some of the arbitrary differences at the knowledge level. Furthermore, shared ontologies could provide a basis for packaging knowledge modules— describing the contents or services that are offered and their ontological commitments in a composable, reusable form. [3, p. 38]

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However, that was about it. Equating ontologies with sets of explicitly defined terminology was of no guidance, conceptually and methodologically, as to how those sets ought to be put together; identifying the ontology of a system with ‘a vocabulary and a set of constraints on the way terms can be combined to model a domain’ (p. 40) was of no guidance as to how the relevant constraints should be determined. What emerged at the Padua Workshop was precisely the need to go beyond such a crude characterization. The development of composable, reusable ontologies cried for a methodology, a theoretical framework, an ontological science in the good old sense. It is for this reason that while the preface to the Proceedings emphasized the essential role of generic ‘ontologies’ (in the plural), the title of the Workshop featured ‘ontology’ (in the singular). Moreover, the emphasis in the title was on formal ontology, with a double reference to the meaning of the adjective made popular by such contemporary authors as Nino Cocchiarella, on the one hand, and the meaning inherited from Husserl’s classical conception, on the other. The former is nearly tantamount to ‘rigorous’: Formal ontology is the result of combining the intuitive, informal method of classical ontology with the formal, mathematical method of modern symbolic logic, and ultimately identifying them as different aspects of one and the same science. [4, p. 640].

Not much news there, particularly for applications in domains where formalization and mathematical rigor are already common practice, if not a prerequisite. The latter understanding of ‘formal’, however, is much more significant, especially when combined with ‘ontology’. According to Husserl, formal ontology is not just ontology suitably formalized; it is ontology bereft of all domain-specific considerations, the science of what is, no matter what it is, the study of the general ‘laws of being’, whose validity should possess the same sort of universality and topic-neutrality that characterize the general ‘laws of truths’ of formal logic: The systematic place for its discussion [is] in the pure (a priori) theory of objects as such, in which we deal with ideas pertinent to the category of object [. . . ] as well as the a priori truths which relate to these. [5, p. 435] 2 Sponsored by DARPA but also, among others, by the National Science Foundation (SNF) and the Corporation for National Research Initiatives (CNRI).

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Thus understood, formal ontology may not yet be enough of a ‘scientific’ framework for developing specific ontological modules—what Husserl himself would call ‘material ontologies’. One would need, in addition, a general theory of the sort of objects (entities) that may feature in each module and of how they relate to one another—an ‘upper ontology’, in modern parlance. But that is already something that we can appreciate only insofar as we engage with the picture from a broad perspective. And it was the need for such a perspective that the Padua Workshop emphasized, setting an agenda that went far beyond the scope of the Knowledge Sharing initiative and putting information scientists in actual conversation with philosophers, de facto as well as de jure. Since then, the project developed rapidly. Guarino himself played a pivotal role in establishing a major conference series to foster the conversation (FOIS – Formal Ontology in Information Systems, launched in 19983 ) along with the first research institute devoted entirely to the project (LOA – Laboratory for Applied Ontology, est. 20034 ), the first dedicated journal (Applied Ontology, est. 20055 ), and the first international consortium fully aimed at promoting interdisciplinary research and collaboration (IAOA – International Association for Ontology and its Applications, est. 20096 ). Many others have followed in these footsteps, and today we can easily find handbooks [6, 7, 8, 9], textbooks [10, 11, 12, 13], and collections [14, 15, 16, 17] providing comprehensive overviews and detailed digests of this fast-evolving field. The range of applications is enormous, spanning from conceptual modeling and knowledge representation to knowledge engineering, knowledge management, database design, object-oriented analysis, information retrieval and extraction, query processing, natural language processing, machine translation, library science, enterprise integration, cloud computing, machine learning, agentbased systems design, general and precision medicine, healthcare simulation modeling, biomedical informatics, genomic and nutritional epidemiology, chemical and pharmaceutical engineering, mechanical engineering, electronic commerce, geographic information systems, legal information systems, biological information systems, electronic government, service science, the semantic web, the internet of things, and much more. In 2012, the State of the Future report of the Millennium Project went as far as to include a new 51-page chapter (‘Future of Ontologists’) based entirely on the thought that information-science ontology may soon have ‘an impact on humanity more profound than the one caused by the Internet’ [18, p. 121] No one of course may claim or take credit for all this. But it would not be an exaggeration to say that the picture would be quite different had the magic word, ‘ontology’, been used merely as a fancy substitute for the crude notion of an ‘explicitly defined terminology’. Nor would the picture be so rich had the meaning of ‘ontology’ been limited to its plural use. At the Padua Workshop, Tom Gruber presented a paper based on his definition of an ontology as ‘an explicit specification of a conceptualization’ [19, p. 2]. The definition had just appeared in print elsewhere [20, p. 199] and would eventually gain high currency among information scientists, in this form or slightly amended (e.g. to include the requirement that the specified conceptualization be generally accepted, or ‘shared’, as urged by Willem Borst [21, p. 12]). No doubt this was a step up from the crude notion elicited by the Knowledge Sharing initiative. But, again, it left pretty much 3 Website:

iaoa.org/fois www.loa.istc.cnr.it 5 Website: www.iospress.nl/journal/applied-ontology 6 Website: iaoa.org 4 Website:

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everything up for grabs. The real boost came from the realization that the very possibility of sharing ontologies depends on developing them on the basis of shared criteria, and that these criteria, in turn, can only come from a genuine engagement with the discipline that comes with that name. In a slogan: no ontology without Ontology.

2. Welcome to the quagmire With all this, no realization occurs alone. It didn’t take long to realize, too, that the project would be everything but straightforward. In the paper Guarino wrote for the special issue of the International Journal of Human-Computer Studies following up the 1993 Workshop,7 the last section ended with an invitation to ponder a passage from Drew McDermott’s review of Lenat and Guha’s 1990 book, Building Large Knowledge-Based Systems [23]:

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Those were the good old days. l remember them well. Naive physics. Ontology for Liquids. Commonsense Summer. It was a heady time, and this book rekindles the old excitement. Wouldn’t it be neat if we could write down everything people know in a formal language? Damn it, let’s give it a shot! [. . . ] We—and Lenat and Guha—are on a slippery slope here. If we want to be able to represent anything, then we get further and further from the practicalities of frame organization, and deeper and deeper into the quagmire of logic and philosophy. [24, pp. 54, 58]

Guarino’s concluding comment was candidly forthright: ‘I believe that this quagmire is well worthwhile getting into’ [25, p. 637]. And so it has been. In the years that followed, Guarino and his collaborators did not refrain from diving (and digging) into a number of philosophical questions that the project immediately generated—questions concerning e.g. the constitution of physical objects [26], the structure of space [27], the principles governing identity, unity, and subsumption [28, 29, 30], the nature of properties [31], the ontological status of roles and social objects [32], the distinction between events and processes [33, 34], the part-whole relation [35, 36], and more. All of this while continuing to promote the need and benefits of an ontology-based information science [37, 38, 39, 40, 41] and at the same developing a detailed upper-level ontology, DOLCE [42, 43, 44], along with a rigorous methodology for analyzing and validating specific ontologies in terms of formal meta-properties, OntoClean [45, 46, 47]. But the quagmire is deep and wide. The discipline of ontology is tortuous and full of traps. Willard Quine famously emphasized one sort of trap when he focused on one aspect of ontology, the aspect concerned with the material question ‘What is there?’ [48]. In a way, the answer is obvious: ‘Everything’. At least this is the obvious answer insofar as existence is not expressed by an ordinary predicate but by the apparatus of quantification: to be is to be the value of a bound variable [49].8 There simply cannot be things that do not exist. However, to say ‘Everything’ is to say nothing. As Quine hastened to add, it is merely to say that there is what there is, an empty tautology, unless one goes on to specify the contents of the domain over which one quantifies—and here there remains plenty of room for disagreement. You may think that ‘everything’ covers particulars as 7 The special issue [22] contains 18 articles, 9 of which came from the 38 papers (including Gruber’s) comprising the Workshop proceedings. 8 Pace a certain philosophical tradition that insists on treating ‘exists’ as a predicate, inspired by Meinong’s theory of objects [50] and variously defended in contemporary literature [51].

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well as universals, I may think it only covers the former; you may think the domain of quantification includes abstract particulars along with concrete ones, I may think it only includes the latter; you may think the only concrete particulars are material bodies, I may think they include immaterial entities as well, such as holes or shadows; and so on. Guarino’s digging into the quagmire led him to figure out his position on many such matters, and everyone should do the same. But that’s hard business, and it’s bound to result in different accounts. And this is just the beginning. What exactly does it mean to disagree, ontologically speaking? Suppose you and I disagree about whether there is, or is not, orange juice in the refrigerator. Is that a case of ontological disagreement? Suppose we disagree on whether there is a hole inside a chunk of cheese, or a rabbit-shaped shadow on the wall. Ontological disagreement? Or suppose you and I agree on the existence of certain entities but disagree on their nature—say, we agree that there are people but disagree on what (as opposed to who) they are. You think people are enduring entities, things that persist across time by being fully present at each time at which they actually exist; I think people are perduring entities, which persist across time by virtue of having a distinct proper part—a temporal part—for each time at which they exist. What are we to make of our original agreement concerning people’s existence? Did we agree, ontologically speaking, or did we not? And if we say we did, how and where is the relevant disagreement going to show up in our theories, in our formalisms? Similar worries apply to other questions that define the business of ontology. For instance, we said that formal ontology—the science of what is, no matter what it is— is supposed to consist of highly general, domain-independent principles, principles that capture the fundamental ‘laws of being’. How do we figure out those laws? For Husserl, they must be discovered a priori, but what does that mean, effectively? And what sort of laws are they anyway? For Husserl, the pure theory of ‘objects as such’ must deal with ideas ‘pertinent’ to the general category of object, ideas such as ‘Whole and Part, Subject and Quality, Individual and Species, Genus and Species, Relation and Collection, Unity, Number, Series, ordinal Number, Magnitude, etc.’ [5, p. 435]. Do we agree? How are these ‘ideas’ to be selected, exactly? What exactly is it that makes them ‘formal’, as opposed to others? How can we fill in the ‘etc.’? Even before we can address any of these questions, there’s the big question of how to interpret the ‘is’ of ontology. The science of what is; but what is ‘is’ supposed to mean? Never mind looking for a substantive account of what it takes for something to be. (Does being require spatio-temporal location? Does it require having causal powers? Etc.)9 Let’s stick to Quine’s quantificational account: to be is neither more nor less than to be the value of a bound variable. Is the range of our variables meant to reflect our ontological commitments, our beliefs, our conceptualization of the world, or is it meant to reflect the content of the world itself? Is ontology about reality as we represent it, or is it about reality as it is? This sort of question, and the opposition between conceptualism and realism that it elicits, is responsible for some of the most profound and dramatic divides in the history of philosophical ontology, and there’s no way out of it. We may wish to ignore it for some purposes. But if we go for the quagmire, that is the first question that is going to hit us. 9 And never mind Heidegger: “We understand the word ‘is’ (‘being’), we know the meaning; but we are unable to say what we ‘really’ mean by it. We understand it, but we do not grasp it. We do not have a concept of ‘is’. We understand ‘is’ and ‘being’, but in a non-conceptual way.” [52, p. 149]

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None of these considerations is meant as big news. Anyone working in the field— especially anyone who attended the FOIS conferences and kept abreast of the quarterly issues of Applied Ontology—will find them familiar, perhaps even annoyingly so. Yet this is not to say we can just move on. On the contrary, after twenty-five years of tremendous growth and developments, this seems a good time to take stock and reopen the discussion, at least to remind ourselves that it was never closed. Let me offer a taste of what this would involve with reference to three aspects in which I think the questions raised above are still worthwhile and, indeed, pressing.

3. Realism vs. conceptualism Starting from the end, consider the opposition between a realist understanding of ontology and a non-realist, purely conceptualist one. We find statements of both views from the very beginning. Gruber’s original account, for example, was clearly of the latter sort. The definition recalled above continues thus: An ontology is an explicit specification of a conceptualization. The term is borrowed from philosophy, where an ontology is a systematic account of Existence. For knowledge-based systems, what ‘exists’ is precisely that which can be represented. [20, p. 199; cf. 19, p. 2]

We are told what a ‘conceptualization’ is, namely, an ‘abstract, simplified view of the world that we wish to represent for some purpose’. But there is no claim whatsoever as to how a view and the corresponding knowledge base relate to the underlying world. In particular, there is no reference to the idea that knowledge, unlike belief, should be factive, i.e., truth-entailing.10 By contrast, Guarino’s approach was driven precisely by that idea, with all the realism that comes with it:

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A knowledge base will acquire a value per se only to the extent that the knowledge it contains is in fact true, such as to correspond to the world beyond the knowledge base. Therefore, the study of ontology, intended as a branch of philosophy dealing with the a priori nature of reality, can be of benefit to the knowledge-construction process in yielding high-value knowledge bases. [25, p. 626]

Of course there is a difference in the way the word ‘ontology’ was used in the two cases. Gruber was using it as a count noun, telling us what an ontology is; Guarino was using ‘ontology’ as a proper name, the name of the philosophical discipline (elsewhere written with uppercase initial). We already emphasized that the difference is important. And it surely is in this connection. Indeed, when it comes to the countable use, Guarino himself would not refrain from defining ontologies in terms of ‘conceptualizations’ [54, 55]. Nonetheless the emphasis on the underlying reality and its a priori nature was clearly different, reflecting a different approach in the way we should go about developing reusable ontological modules. Gruber would eventually settle on purely pragmatic guidelines: One can say that ontology is a tool and product of engineering and thereby defined by its use. From this perspective, what matters is the use of ontologies to provide the representational machinery with which to instantiate domain models in knowledge bases, make queries to knowledge-based services, and represent the results of calling such services. [56, p. 1964] 10 This is—and was—in line with standard practice in the AI field of so-called knowledge representation. It’s unfortunate and by now it’s a lost battle, but ‘belief representation’ would have been a more appropriate label; see e.g. [53].

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Guarino would insist that use and reusability go hand in hand and should be driven by a systematic effort to understand every conceptualization, even when resulting ‘from our sensory system, our culture, and so on’ [30, p. 113], in terms of the general structure of the underlying reality—the thesis of ‘the independence of domain knowledge’:

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Reusability across multiple tasks or methods can and should be systematically pursued even when modeling knowledge related to a single task or method: the more this reusability is pursued, the closer we get to the intrinsic, task-independent aspects of a given piece of reality (at least, in the commonsense perception of a human agent). In this systematic quest for reusability, the potential role of a discipline like formal ontology appears evident. [38, p. 294]

The tension between these different approaches has of course different strengths and implications precisely inasmuch as we think it’s worth getting into the quagmire. For a while it was taken seriously, setting the agenda of an intense debate. Barry Smith, for one, emphatically pressed the need to get clear about the role of reality and reference thereof, fearing that the knowledge-representation and related communities, when doing ontology, might ultimately embrace ‘one or other form of idealist, skeptical, or constructionist philosophy’ [57, p. 73]. This led to a vehement exchange on the pages of Applied Ontology, with Smith and collaborator Werner Ceusters defending the realist approach [58] and Garry Merrill questioning it [59, 60]. The exchange was felt to be so climacteric that IOS Press, the journal’s publisher, decided to make the articles available online free of charge and without restrictions, issuing two press releases to invite ‘everyone who cares about principles of ontology engineering, about what constitutes a good ontology, and about the future of ontology in e-science’ to ponder this ‘much important, unsettled business’.11 A remarkable event indeed, promptly followed by hundreds of postings on many online fora. But, alas, the quagmire really is deep and wide. And after all the excitement, the topic was gently dropped and the business remains unsettled. Why is it important to settle it? Not only because of its intrinsic interest. One important reason, which no information-science ontologist can swiftly brush aside, is that the alternative between realism and conceptualism tends to translate into a parallel alternative between monism and pluralism in scientific practice, i.e., between the view that there is just one way of getting things right versus the view that many ways—even incommensurable or mutually incompatible ways—can be equally correct. No doubt we can have a plurality of ontologies, which is to say, many ways of building an ontology for specific purposes, and it is a fact that such ontologies may not agree even on matters of common concern. Otherwise the quest for sharing and reusability would be a cinch. But what about the higher-level guidelines? Should each ontology conform to the same set of general, formal principles? More concretely: should each domain ontology conform to the same upper-level ontology, providing that the latter is precisely the sort of theoretical framework that can benefit from the discipline of Ontology? The realist has a swift and straight answer: Yes. It is true that, as John Searle put it, ‘realism does not say how things are but only that there’s a way that they are’ [61, p. 155]. Yet this is enough to warrant a strong form of scientific monism, generally as well as in the present context. For all the legitimacy of the many domain ontologies that may flourish, reflecting our first-order ontological disagreements, a realist attitude towards Ontology will nonetheless aim at delivering ‘a definitive and exhaustive classification of entities in all spheres of being’ [62, p. 155]. We may disagree on what there is, or on 11 Both

press releases are still available at http://www.applied-ontology.org/ontologicalrealism.

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various other matters of contingent fact. But the laws of being are not up for grabs. They are what they are, determining a kind of ‘generalized chemistry’ [63, p. iii] to which everything must conform. By contrast, a conceptualist is hardly going to push this line. I say ‘hardly’ because strictly speaking conceptualism does not entail world pluralism. A lot depends on the details of one’s semantic theory, especially with regard to reference and truth.12 But details such as these can only be found deep down in the quagmire. As a matter of general attitude, conceptualists don’t care about the world; they care about conceptualizations. And the laws of conceptualizations are up for grabs. So why is this important? I mentioned that among the many achievements of Guarino and his research group is the development of a rich and powerful upper ontology, DOLCE. The principles of DOLCE have been developed explicitly ‘with the vision that a unique universal ontology for knowledge representation cannot exist’ [66, p. 372]. But DOLCE is not the only product of this sort. Several other upper ontologies have been developed over the years, from CYC [67] and BORO [68] to SUMO [69], BFO [70], UFO [71], GFO [72], and many others (including YAMATO [73], short for ‘Yet Another More Advanced Top-level Ontology’). Such abundance of systems is by itself indicative of how much the field has grown since the early days. But each system deviates from the others in significant ways, not only by employing different methods and techniques but also, crucially, by relying on different ontological categories and principles. And herein lies the trouble. If the main reason to embark on ontology-based information science was to overcome the ‘database Tower of Babel’ problem, as Smith called it [62, p. 158], after all this work we seem to find ourselves with a parallel problem at a higher level—what Wacław Ku´snierczyk calls the ‘ontology Tower of Babel’ problem [74, p. 41]. Quis custodiet ipsos custodes? The monist realist will insist on their bold answer: the supreme custodian is the World, like it or not. But the conceptualist? This is not just an abstract philosophical question. It is as concrete and pressing, from an information-science perspective, as the start-off question raised by Knowledge Sharing initiative.

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4. The whence and whither of disagreement The second issue concerns the very notion of ontological agreement. I mentioned the possibility that you and I agree that people exist but disagree on what they are: you think people are enduring entities, I think they are perduring entities. Obviously the case generalizes. With regard to ordinary objects, too, you and I may agree on their existence while holding dffferent views concerning their nature and identity conditions. I may think a house is merely an aggregate of walls and roof; you may think it is something else, something more. You may think a statue is constituted by its matter; I may think the statue is the matter. And what goes for people and ordinary objects goes for everything—events, properties, relations, functions, roles, groups, musical compositions, fictional characters, mathematical entities, angels, what have you. In each of these cases, it would seem that we may find ourselves agreeing on whether something is despite disagreeing on what it is. Hence the question: would these be cases where you and I can be said to share an ontology, albeit perhaps imperfectly? 12 Indeed, one could make a similar point about realism: strictly speaking it does not entail monism. For example, in the philosophy of biology there is a well-respected view (known as ‘pluralistic realism’) that tries to reconcile realism about species with taxonomic pluralism [64, 65].

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Philosophically, this is a deeply controversial question [75]. Yet, for all their differences, virtually every theory developed from an information-science perspective delivers, or tends to deliver, the same answer: No. This is certainly true of those theories that follow Gruber’s definition of ‘ontology’ (or variants thereof). If an ontology is a specification of a ‘conceptualization’, and if a conceptualization, in turn, is a ‘view of the world’, then it may seem as though we agree on what there is but, on closer look, our ontologies diverge. On closer look, we may agree that, say, the sentence ‘People exist’ is true. But if we hold a different conception of what people are, then you and I are attaching different meanings to the word ‘people’ and, therefore, to the whole sentence. You take the sentence to express the proposition that people1 (enduring-people) exist; I take it to express the proposition that people2 (perduring-people) exist. Since people1 and people2 are different sorts of things, the commitments we incur in asserting the sentence are different, and hence so are our ontologies. However, the point is not limited to Gruberian ontologies. Every ontology, insofar as it is governed by suitable upper-level principles, will yield the same verdict. The reason is that every upper-level ontology is bound to include a subsumption relation of sorts, an ‘is a’ relation, and this will suffice to associate every item in the domain with a characterization of sorts. The ‘is a’ taxonomy will classify every thing according to what it is. At least, it will do so in terms of the categories available in the language, which is precisely why an ontology informed by the philosophical discipline that goes by that name is supposed to be better, and ultimately more informative, than one informed by loose intuitions and common-sense distinctions. Upper ontologies are not just inventories of the contents of our domain of quantification; they are structured inventories. And if we disagree on the structure, we disagree on the whole. (In this sense, the relevant notion of ‘ontology’ differs from Quine’s as well as from Husserl’s, reflecting instead the conception of Roman Ingarden and his school [76].) Now, by itself there is nothing wrong with this picture. But it’s worth pondering its presumptions as well as its consequences. To begin with the former, do we really want to rule out the possibility of mere ontological disagreement? Surely, generally speaking there is nothing incoherent in the idea that two parties may have different opinions concerning one and the same entity. This is obvious in the case of ordinary opinions. For you the statue of David is splendid; for me it isn’t. It doesn’t follow that we are referring to two distinct objects—one splendid and one unimpressive. For you Cattelan is an artist; for me he is not. It doesn’t follow that we are referring to two Cattelans. The same may be said of contrasting opinions in scientific contexts. Renaissance people used to think that water was one of the simple elements of the sublunar world; with Lavoisier we came to recognize that water is instead a compound of hydrogen and oxygen. It doesn’t follow that the Renaissancers thought they were drinking something else than what we think we are drinking. Otherwise the very notion of scientific progress would become empty, if not meaningless.13 Well, then, the same might be said of contrasting opinions of the sort illustrated above—call them metaphysical opinions. You and I have different conceptions of people? It doesn’t follow that we are speaking of different things; we may sincerely disagree on what people are. And if an oracle told us that the correct metaphysic is endurantist, contrary to what I thought, I would not react by denying the existence of people. Simply, I would accept the news and revise my conception accordingly. Isn’t this 13 This is one important lesson of Hilary Putnam’s treatment of scientific terms (and theories) in ‘The Meaning of ‘Meaning” [77].

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what we all try to achieve when we argue with our colleagues? We all try to make them change their views on a certain subject, not to change the subject. All of this is ruled out from start in the way domain ontologies are typically governed by upper-level ontologies. And there is more. For not only is there no incoherence in the idea that two parties may hold different metaphysical opinions concerning the same entities; there is nothing incoherent even in the idea that we may proclaim our ontological credo without embarking at all on metaphysical speculations. Consider what happens in mathematics. Most mathematicians would avow that they are serious about numbers— that numbers are indeed among the values of their bound variables. Yet few would be willing to go further and say something committal about the nature of such values—about what numbers are. How are we going to model the beliefs of such agents? Are we going to fill in some details on their behalf, insisting e.g. on the abstract nature of numbers? Are we going to identify numbers with Fregean extensions of second-level concepts? With cumulative sets? Which ones—the Zermelo sequence, ∅, {∅}, {{∅}}, {{{∅}}}, . . . , or the von Neumann sequence, ∅, {∅}, {∅, {∅}}, {∅, {∅}, {∅, {∅}}}, . . . ? Surely we have several options, and if we look at philosophical Ontology we may find more. But it seems presumptuous, indeed ludicrous, to represent our mathematicians as holding such views. And mathematics is but one example. Many biologists, for instance, feel the same way in regard to the metaphysical disputes about species (e.g. whether species are classes or individuals). The same may apply to ordinary beliefs concerning people, houses, statues, etc. I can hear my neighbor: ‘People? Of course people exist! But don’t ask me whether they endure or perdure, I don’t even know what that means and I don’t care. I believe in people whatever they are.’ One might protest that merely asserting the existence of something without saying what it is would be empty talk. To say that people exist ‘whatever they are’ would be completely uninformative, and similarly for species, numbers, etc. However, that is not what happens in such cases. In the case of numbers, mathematicians do not leave us entirely in the dark: whatever they are, numbers must enjoy a specific range of attributes, say, those attributes that define the axiomatic corpus of Peano arithmetic. In saying that numbers exist, therefore, mathematicians are committing themselves to the existence of entities that enjoy those attributes; their commitment is perfectly clear.14 Likewise, in the case of entities such as people, houses, or statues. There is a whole range of attributes that such things are supposed to have in virtue of the application conditions, or ‘meaning postulates’, that come with the correct use of the relevant words—attributes such as being featherless, biped, and somewhat rational (people), having a certain structure and serving the purpose of providing shelter (house), being the product of sculpturing, modeling, or casting (statue), and so on. Such postulates reflect a cluster of common-sense truths and do not, therefore, constitute a rigorous axiomatic theory comparable to Peano arithmetic (though early AI projects in naive physics [79] and the commonsense world [80]—the ‘good old days’ evoked by McDermott—had precisely that ambition). Still, such postulates are constitutive of our linguistic competence and suffice to fix the extensions of our predicates. And it is precisely because my neighbor is linguistically competent that we understand her when she says ‘People exist’. So much for the presumption worry: our upper-level ontologies appear to build too much metaphysics into our domain ontologies. Indeed, here the project of a philosophy14 That is, clear ‘up to isomorphism’, as some like to say. I take this to be the main lesson of Paul Benacerraf’s ‘What Numbers Could not Be’ [78].

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inspired approach risks backfiring. The more they are inspired by the philosophical discipline of Ontology, rather than by ordinary dictionaries, the higher the risk of going overboard. But there is something to be said also about the practical consequences of this state of affairs. Specifically, it’s clear that ruling out from the start the possibility of mere ontological disagreement multiplies the challenges of integration and interoperability, resulting in greater chaos in the ontology Tower of Babel. So this is our second example of a philosophical issue worth pondering. One suggestion would be to rethink the way we tend to structure our top-level distinctions. We have seen that there are two criteria for taxonomizing things (or specifying concepts): according to what they are (or mean) insofar as this is required for reference fixing, and according to some deeper, full-bodied metaphysical categories. In both cases, the relevant structural relation is a form of subsumption. But it need not be the same. We could split the ‘is a’ relation into two, one governed by meaning postulates, the other governed by metaphysical axioms. The former would constitute the lexical, or terminological, module of the theory; the latter its metaphysical module. And we can try to work out effective ways of maximizing sharing on the basis of the corresponding forms of agreement that may apply across ontologies: mere ontological agreement and full-bodied agreement, respectively. But it’s easier said than done. And, of course, drawing a clear line between the two sorts of subsumption relations would not be easy—possibly a source of yet another Babel Tower.

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5. The formal sphere The third and final point concerns the idea that in building an ontology we can benefit especially from the discipline of formal ontology. As noted, this idea has been the hallmark of Guarino’s project from the beginning, to the point of using the adjective, ‘formal’, both in the title of the 1993 Workshop (Formal Ontology in Conceptual Analysis and Knowledge Representation) and in the official denomination of the regular conference series established five years later (Formal Ontology in Information Systems). And while the sense of ‘formal’ that is synonymous with ‘rigorous’ is obviously important, it is especially in the sense inherited from Husserl that the idea proved powerful in relation to the quest for information sharing and reusability. As a science of what is, no matter what it is, Husserlian ontology provides us with tools that should be applicable across the board, no matter the specific motivations and tasks of each particular knowledge base. Regardless of whether the domain includes objects along with events, concrete entities along with abstract ones, and so on, it must exhibit some general features and obey some general laws,. And ontology—understood formally—is the science of such features and laws, a sort of ‘logic of being’. Indeed, the use of ‘logic’ here is more than metaphorical. For Husserl, formal ontology deals with the ‘interconnections of things’ exactly as formal logic deals with the ‘interconnections of truths’ [5, p. 225]. Just as formal logic deals with laws that are formal in the sense that they apply to any proposition, no matter what it says, so the laws of formal ontology are formal in the sense that they apply to any entity, no matter what it is. Just as, for instance, the transitivity of entailment (if p entails q and q entails r, then p entails r) does not depend on what propositions are assigned to the variables ‘p’, ‘q’, and ‘r’, so the transitivity of, say, identity (if x is identical to y and y is identical to z,

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then x is identical to z) does not depend on what entities are assigned to the variables ‘x’, ‘y’, and ‘z’. Both laws exhibit the same sort of generality and topic-neutrality. Both are meant to hold as a matter of necessity and should be discovered, in some sense, a priori. One can see why Guarino was invigorated by the project. And one can see why the first edition of FOIS opened with a plenary talk by Barry Smith devoted precisely to clarifying the formal logic-ontology parallel [81]. In the field of Knowledge Representation, formal logic was the tool (so much so that the full denomination of the field is actually ‘Knowledge Representation and Reasoning’). Adding formal ontology as a second tool would require some homework, but it could literally double the potential. The point I want to stress, with reference to the brief remarks made earlier, is that despite the elegance of Husserl’s parallel, the exact scope of what counts as formal ontology remains to be determined. So it’s not just a matter of doing the homework; one needs to do serious work, work that even philosophers have come to recognize only recently.15 The issue is really two-sided. One side concerns the bounds of the theory, the other its contents. With regard to the first side, earlier I quoted Husserl’s list of formalontological relations, which includes Whole and Part, i.,e., dependence and parthood, and I have just mentioned identity as another obvious example. But of course one need be more precise. Are these truly formal in the intended sense, i.e., do they all apply to anything that might conceivably exist, no matter what it is? And are they the only relations of this kind? The formal character of the identity relation can hardly be questioned. As Quine famously put it, no entity without identity [83, p. 20]. In fact, it is precisely because it is absolutely general and domain-independent that identity is often treated as a formal logical relation. Quine himself was firm about this, emphasizing that identity ‘knows no preference’; it ‘treats of all objects impartially’ [84, p. 62]. Nevertheless, precisely because it is an objectual relation rather than a sentential operator—because it relates things in the world rather than truths about the world—it is best to treat identity as pertaining to formal ontology, not logic. The formal character of dependence is perhaps equally unquestionable. Generally speaking, the idea is that x depends on y if, and only if, x could not exist without y.16 There may be worries concerning the exact meaning of the modal locution ‘could not exist’. However, because existence is not a predicate, there is no restriction on the possible values of x and y, which range over the entire domain of quantification. So, again, it would appear that the relation of dependence enjoys the right sort of generality. But what about parthood? This is perhaps the most common relation, along with subsumption, to feature in the upper-level ontologies that took Guarino’s advice seriously, including Guarino’s own DOLCE, and indeed most philosophers would agree that this relation applies not only to material objects, or to entities located in space and time, but to all entities whatever—that it is topic-neutral and thus applies across all ontological categories. Others, however, disagree. For example, the thought that there are mereologically structured universals is sometimes found to be problematic. In David Lewis’s example [86, p. 34], each methane molecule consists of one carbon atom and four hydrogen atoms. Are the universals carbon and hydrogen part of the universal methane? If they aren’t, does that mean that the three universals (as opposed to their instances) have nothing in common? If they are, does it follow that hydrogen is part of methane four times 15 The 16 This

remarks that follow draw on the second part of [82]. is actually a simplification and is open to counterexamples [85], but we can skip the details.

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over? What could that possibly mean? How could one thing be part of another more than once? Of course, if we agree that parthood includes identity as a limit case (so-called ‘improper parthood’), we may always treat all problematic cases as mereological atoms, things that have no further parts except for themselves. That would be enough to warrant the claim that parthood knows no restriction. But it’s a slippery move. By the same pattern, one might extend any relation R to R-plus-identity and treat all R-problematic cases as atomic in the relevant sense. That would hardly be a reason to treat the extended reflexive relation as a piece of formal ontology in addition to identity. Similar remarks apply to the other relations included by Husserl’s list, though this example should suffice to highlight the difficulty of the task. On the other hand, surely there may be other, non-artificial relations that do fit the bill. To fix the scope of formal ontology we must rule out the bad candidates but we must also make sure to rule in all the good candidates. Popular examples would include membership, inherence, and connectedness, all of which have been studied extensively. I do not intend to settle the question here. Just as logicians have been having a hard time figuring out a good way of demarcating the bounds of logic, demarcating the bounds of ontology, in the formal sense of the term, is no straightforward business. What I want to stress, rather, is that here the difficulty may depend at least in part on our ontological beliefs, now in the Quinean, material sense of ‘ontological’. We are looking for relations that are topicneutral and take absolutely all possible entities as arguments, and that requires unlimited open-mindedness. Who’s got the gift? Surely there may be more things in heaven and earth than are dreamt of in our philosophies.17 If nobody had ever dreamt of such things as universals, let alone recognized their ontological dignity, the above worry concerning the formal character of parthood would not have arisen. If all we had dreamt of were material substances, a cornucopia of spatiotemporal relations would have qualified as formal in the relevant sense. And so on. There is, in fact, a hidden quantifier in the characterization of what counts as formal, a quantifier ranging over all possible (i.e., conceivable) entities. And it is by no means clear that we can grasp its range without engaging in material-ontological considerations. This, then, is one side of the issue: what are the exact bounds of formal ontology? The other side concerns the contents of the theory. Regardless of how far it extends, the truths of formal ontology are supposed to possess the same sort of generality and topic-neutrality that characterizes the truths of formal logic. Yet, as soon as we start digging, we realize that this characterization is very hard to pin down without begging the question. Consider identity. Surely not every identity-theoretic principle qualifies as formalontological in the intended sense. We must draw a line somewhere. For instance, few are willing to endorse the principle known as identity of indiscernibles: it fails in some possible worlds (e.g. a perfectly symmetric world [88]), if not in this world of ours (as quantum mechanics would seem to suggest [89]). The converse principle, the indiscernibility of identicals, is more robust and certainly less controversial, but even that has been found problematic in some contexts, e.g., vis-`a-vis the phenomenon of qualitative change. Drawing a line is always difficult. And in this case it seems clear that the difficulty depends once again on a careful consideration of what there is, here or in some other possible world. Perhaps we should just stick to the very basics: identity is reflexive, 17 As there are philosophies that have dreamt of things that are neither on earth nor in heaven. This is a separate issue, but not entirely off-topic [87].

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transitive, and symmetric—an equivalence relation. Yet these properties have been questioned, too. For instance, you don’t have to be a hard-core dialetheist to think that there are or might be non-self-identical objects; it might suffice to consider again the elusive citizens of the quantum world, as Schr¨odinger famously argued [90]. We may find that utterly absurd. But it is hard to give expression to our feelings while claiming full and unbiased neutrality. Or consider parthood. Few would be willing to buy into the whole body of classical extensional mereology [91]. Some of its basic principles, such as extensionality and unrestricted composition, are highly controversial, and treating them as expressing formalontological truths would be missing the point. Such principles are best construed as expressing specific views on how things are, even on what things there are. Nelson Goodman [92], for instance, took mereological extensionality to be the hallmark of a nominalist stance—hence of a very precise material-ontological view. Likewise, to accept unrestricted composition is to countenance the existence of a fusion for any non-empty collection of things—something that has all those things as parts and has no part that is disjoint from each of them. Perhaps the fusion is nothing over and above the things that compose it, as David Lewis emphatically argued [93]. But to the extent that it qualifies as something else than those things, it is clear that our attitude towards this principle is bound to reflect our domain ontology. So what mereological principles do we have in mind, insofar as parthood is supposed to be a formal-ontological relation? A standard candidate is the principle known as weak supplementation, to the effect that no entity can be comprised of a single proper part. Peter Simons [94] regards this as a bare minimum that we can require of a relation, along with reflexivity, antisymmetry, and transitivity, if it is to count as parthood at all.18 Yet even here there is room for disagreement. Possible counterexamples include, for instance, recent theories of material constitution, which hold that a material object (a statue) and the matter that constitutes it (a lump of clay) are proper parts of each other although neither has parts disjoint from the other [95]. One may be inclined to dismiss such counterexamples as unintelligible precisely because they violate weak supplementation, but one might as well go the other way around and regard the independent plausibility of those theories as evidence against the principle. How can we settle the issue without begging the question, if not by resorting to material-ontological considerations of some sort? Even the partial-ordering axioms have sometimes been disputed. The antisymmetry of parthood, for instance, is immediately challenged by the constitution theories just mentioned (the statue and the clay are part of each other but non-identical). But it could be argued that the axiom is too strong regardless: in view of certain developments in non-well-founded set theory (i.e., set theory tolerating cases of self-membership and, more generally, of membership circularities [96]), one might for instance suggest building mereology on the basis of an equally less restrictive notion of parthood that allows for closed loops [97]. Such a suggestion could hardly be dismissed if we are insisting on the formal status of parthood: if sets have to have a mereological structure, it is natural to identify the parts of a set with its subsets. So, either we refuse to countenance nonwell-founded sets—and that is a straightforward claim about what there is—or we must concede that such sets violate antisymmetry. 18 At least insofar as parthood is construed broadly to include identity as a limit case; proper parthood would be transitive but irreflexive and asymmetric.

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These are just examples. Nonetheless, for parthood as well as for identity (and the case for dependence is not different), they ought to be indicative of how difficult it is to come up with good, neutral criteria for drawing a line between purely formal principles and substantive theses. Of course we have a similar problem in logic. Sometimes a logical principle is challenged on the grounds of a disagreement concerning the meaning of certain logical operators. This is the case, for instance, with the principle of double negation in intuitionistic logic, or disjunctive syllogism in some relevant logics. In such cases, perhaps Quine’s attitude says it all: change of logic, change of subject [84, p. 80]. In other cases, however, the disagreement has nothing to do with matters of meaning; it concerns precisely the material-ontological neutrality of the principles in question [98]. Think of the controversies on the existential presuppositions of subalternation in Aristotle’s syllogistic, or of universal instantiation in contemporary predicate logic. Think of the failure of distributivity in quantum logic. Think of the problematic status of the Barcan formulas in modal predicate logic. Even the most fundamental principles of classical logic, such as the law of non-contradiction or the law of excluded middle, have sometimes been questioned on such grounds: that there are no inconsistent facts, or that every fact is fully determinate, appear to be claims that reflect explicit material-ontological commitments. It should not be surprising, therefore, that the same sort of worry arises when we shift our attention from the general theory of truths as such to the general theory of objects as such, which is to say from formal logic to formal ontology. But that is no excuse. If we want to use formal ontology, we need to figure out what it is.

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6. The Carnapian engineer All of this is meant to illustrate the need (and practical importance) to continue pondering the deep challenges that come with the project of developing good, well-founded ontology-based information systems. It’s not just that it is worth getting into the quagmire, as Guarino nicely put it in the passage quoted earlier; it is necessary that we do so, or else we might as well learn to live in the database Tower of Babel, with its own morass of idiosyncrasies and ad hoc solutions. Precisely because my goal is illustrative, I have no conclusions to offer. But I’d like to add one final comment, concerning the spirit rather than the letter of these challenges. And it is entirely ad personam. In October 2014, Nicola Guarino delivered a lecture at Carnegie Mellon University entitled ‘Twenty Years of Applied Ontology’. As the title suggests, the lecture was intended as a state-of-the-art overview of applied ontology, taking the Padua Workshop as the official birth date of the discipline. The abstract, still available online,19 is worth quoting in its entirety. More than 20 years have passed since the first international workshop on formal ontology and information systems held in Padova, Italy, in March 1993. What is now called Applied Ontology is an established interdisciplinary area of research which builds on philosophy, cognitive science, linguistics and logic with the purpose of understanding, clarifying, making explicit and communicating people’s assumptions about the nature and structure of the world. This orientation towards helping people understanding each other distinguishes applied ontology from philosophical ontology, and motivates its unavoidable interdisciplinary nature. In this talk I will review—under a personal perspective—the main achievements of Applied 19 At

www.cs.cmu.edu/calendar/fri-2014-10-31-1000/cmu-ontology-studies-and-engineering-seminar-cose.

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Ontology in the last 20 years and the open challenges we are facing today, focusing in particular on the methodology of ontological analysis and on its applications in the context of information systems design.

This is short and swift, and it is exactly what you would expect from the abstract of such a lecture. But there is also a hint to a ‘personal perspective’, suggesting the lecture might contain more than ordinary business. I was not present, so I cannot say. However I found the slides of the talk on the internet.20 I looked for the personal perspective, and at first sight it seemed as though it was left entirely to the verbal part of the lecture; the slides are full of diagrams and data. But then I looked again, and I noticed that somewhere towards the middle (slide 43), there is a quotation from Carnap’s ‘Intellectual Autobiography’. That, too, is worth quoting in full: If one is interested in the relations between fields which, according to customary academic divisions, belong to different departments, then he will not be welcomed as a builder of bridges, as he might have expected, but will rather be regarded by both sides as an outsider and troublesome intruder. [99, p. 11]

This may well be the most elegant way I have ever seen to add a personal touch to a professional lecture without sounding too personal or upfront. And it says it all. It says the passion, the difficulties, the real challenges that come with this sort of work. If there are any Carnapian engineers out there, and if they ever decide to form a society, Nicola will, I hope, receive the honorific he deserves.21

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References [1] M. Devaux and M. Lamanna, ‘The Rise and Early History of the Term Ontology (1606-1730)’, Quaestio, 9 (2009), 173–208. [2] N. Guarino and R. Poli (eds.), International Workshop on Formal Ontology in Conceptual Analysis and Knowledge Representation, Padua, Ladseb-CNR, 1993. [3] R. Neches, R. R. Fikes, T. Finin, T. R. Gruber, T. Senator, and W. R. Swartout, ‘Enabling Technology for Knowledge Sharing’, AI Magazine 12/3 (1991): 36–56. [4] N. B. Cocchiarella, 1991, ‘Ontology II: Formal Ontology’, in H. Burkhardt and B. Smith (eds.), Handbook of Metaphysics and Ontology, Munich, Philosophia, 1991, pp. 640–647. [5] E. Husserl, Logische Untersuchungen, Niemeyer, Halle, 1900–1901; 2nd edition, 1913 (vol. 1 and vol. 2.i) and 1921 (vol. 2.ii); Eng. trans. by J. N. Findlay, Logical Investigations, London, Routledge and Kegan Paul, 1970. [6] C. Calero, F. Ruiz, and M. Piattini (eds.), Ontologies for Software Engineering and Software Technology, Berlin, Springer, 2006. [7] K. Munn and B. Smith (eds.), Applied Ontology: An Introduction, Frankfurt, Ontos, 2008. [8] R. Sharman, R. Kishore, and R. Ramesh (eds.), Ontologies. A Handbook of Principles, Concepts and Applications in Information Systems, Berlin, Springer, 2007. 20 Also available online, www.slideshare.net/NicolaGuarino1/21-years-of-applied-ontology, though here the title says—more accurately—‘Twentyone years’. 21 Many thanks to the referees for their helpful comments on an earlier draft of this paper.

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[9] S. Staab and R. Studer (eds.), Handbook on Ontologies, Berlin, Springer, 2004; second edition: 2009. [10] D. Fensel, Ontologies. A Silver Bullet for Knowledge Management and Electronic Commerce, Berlin, Springer, 2001. [11] A. G´omez-P´erez, M. Fern´andez-L´opez, and O. Corcho, Ontological Engineering, with Examples from the Areas of Knowledge Management, e-Commerce and the Semantic Web, London, Springer, 2004. [12] G. Jakus, V. Milutinovic, S. Omerovi´c, and S. Tomaˇziˇc, Concepts, Ontologies, and Knowledge Representation, New York, Springer, 2013 [13] E. H. Y. Lim, J. N. K. Liu, and R. S. T. Lee, Knowledge Seeker: Ontology Modelling for Information Search and Management. A Compendium, Berlin, Springer, 2011. [14] J. Davies, R. Studer, and P. Warren (eds.), Semantic Web Technologies: Trends and Research in Ontology-based Systems, Chichester, Wiley, 2006. [15] Y. Kompatsiaris and P. Hobson (eds.), Semantic Multimedia and Ontologies. Theory and Applications, London, Springer, 2008. [16] R. Poli, M. Healy, and A. Kameas (eds.), Theory and Applications of Ontology: Computer Applications, Berlin, Springer, 2010. [17] M. C. Su´arez-Figueroa, A. G´omez-P´erez, E. Motta, and A. Gangemi (eds.), Ontology Engineering in a Networked World, Berlin, Springer, 2012. [18] J. C. Glenn, T. J. Gordon, and E. Florescu, 2012 State of the Future. Executive Edition, Washington (DC), The Millennium Project, 2012. [19] T. R. Gruber, ‘Toward Principles for the Design of Ontologies Used for Knowledge Sharing’, in [2], pp. 1–17; revised version in [22], pp. 907–928. [20] T. R. Gruber, ‘A Translation Approach to Portable Ontologies’, Knowledge Acquisition, 5 (1993), 199–220. [21] W. N. Borst, Construction of Engineering Ontologies for Knowledge Sharing and Reuse (Ph.D. dissertation), Enschede, University of Twente, 1997. [22] N. Guarino and R. Poli (eds.), The Role of Formal Ontology in the Information Technology, special issue of International Journal of Human-Computer Studies, 43 (1995), 623–965. [23] D. B. Lenat and R. V. Guha, Building Large Knowledge-Based Systems: Representation and Inference in the Cyc Project, Reading (MA), Addison-Wesley, 1990. [24] D. McDermott, review of [23], Artificial Intelligence, 61 (1993), 53–63. [25] N. Guarino, ‘Formal Ontology, Conceptual Analysis and Knowledge Representation’, in [22], pp. 625–640. [26] S. Borgo, N. Guarino, and C. Masolo, ‘An Ontological Theory of Physical Objects’, in L. Ironi (ed.), Qualitative Reasoning. Proceedings of the 11th International Workshop, Pavia, IAN-CNR, 1997, pp. 223–231. [27] S. Borgo, N. Guarino, and C. Masolo, ‘A Pointless Theory of Space based on Strong Connection and Congruence’, in L. Carlucci Aiello, J. Doyle, and S. C. Shapiro (eds.), Principles of Knowledge Representation and Reasoning. Proceedings of the 5th International Conference (KR’96), Boston (MA), Morgan Kaufmann, 1996, pp. 220–229. [28] N. Guarino, ‘The Role of Identity Conditions in Ontology Design’, in C. Freksa and D. M. Mark (eds.), Spatial Information Theory. Cognitive and Computational Foundations of Geographic Information Science (COSIT’99), Berlin, Springer, 1999, pp. 221–234.

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[29] N. Guarino and C. Welty, ‘Identity, Unity, and Individuality: Towards a Formal Toolkit for Ontological Analysis’, in W. Horn (ed.), Proceedings of the 14th European Conference on Artificial Intelligence (ECAI-2000), Amsterdam, IOS Press, 2000, pp. 219–223. [30] N. Guarino and C. Welty, ‘Identity and Subsumption’, in R. Green, C. A. Bean, and S. H. Myaeng (eds.), The Semantics of Relationships: An Interdisciplinary Perspective, Dordrecht, Kluwer, 2002, pp. 111–126. [31] N. Guarino and C. Welty, ‘A Formal Ontology of Properties’, in R. Dieng and O. Corby (eds.), Knowledge Engineering and Knowledge Management: Methods, Models, and Tools. Proceedings of the 12th International Conference (EKAW 2000), Berlin, Springer, 2000, pp. 97–112. [32] C. Masolo, L. Vieu, E. Bottazzi, C. Catenacci, R. Ferrario, A. Gangemi, and N. Guarino, ‘Social Roles and their Descriptions’, in D. Dubois, C. Welty, and M.-A. Williams (eds.), Principles of Knowledge Representation and Reasoning. Proceedings of the 9th International Conference (KR2004), Menlo Park (CA), AAAI Press, 2004, pp. 267–277. [33] N. Guarino, ‘On the Semantics of Ongoing and Future Occurrence Identifiers’, in H. C. Mayr, G. Guizzardi, and O. Pastor (eds.), Conceptual Modeling. Proceedings of the 36th International Conference (ER 2017), Cham, Springer, 2017, pp. 477–490. [34] G. Guizzardi, N. Guarino, and J. P. A. Almeida, ‘Ontological Considerations about the Representation of Events and Endurants in Business Models’, in M. La Rosa, P. Loos, and O. Pastor (eds.), Business Process Management. Proceedings of the 14th International Conference (BPM 2016), Cham, Springer, 2016, pp. 20–36. [35] A. Artale, E. Franconi, N. Guarino, and L. Pazzi, ‘Part-Whole Relations in ObjectCentered Systems: An Overview’, Data & Knowledge Engineering, 20 (1996), 347–383. [36] A. Artale, N. Guarino, and M. C. Keet, ‘Formalising Temporal Constraints on Part-Whole Relations’, in G. Brewka and J. Lang (eds.), Principles of Knowledge Representation and Reasoning. Proceedings of the 11th International Conference (KR’08), Menlo Park (CA), AAAI Press, 2008, pp. 673–683. [37] N. Guarino, ‘The Ontological Level’, in R. Casati, B. Smith, and G. White (eds.), Philosophy and the Cognitive Sciences. Proceedings of the 16th International Wittgenstein Symposium, Vienna, H¨older-Pichler-Tempsky, 1994, pp. 443–456. [38] N. Guarino, ‘Understanding, Building, and Using Ontologies’, International Journal of Human-Computer Studies, 46 (1997), 293–310. [39] N. Guarino, ‘Formal Ontology in Information Systems’, in N. Guarino (ed.), Formal Ontology in Information Systems. Proceedings of the 1st International Conference (FOIS’98), Amsterdam, IOS Press, 1998, pp. 3–15. [40] N. Guarino, ‘The Ontological Level: Revisiting 30 Years of Knowledge Representation’, in A. T. Borgida, V. Chaudhri, P. Giorgini, and E. Yu (eds.), Conceptual Modeling: Foundations and Applications. Essays in Honor of John Mylopoulos, Berlin: Springer, 2009, pp. 52–67. [41] N. Guarino and G. Guizzardi, ‘In the Defense of Ontological Foundations for Conceptual Modeling’, Scandinavian Journal of Information Systems, 18 (2006), 115– 126.

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[42] A. Gangemi, N. Guarino, C. Masolo, A. Oltramari, and L. Schneider, ‘Sweetening Ontologies with DOLCE’, in A. G´omez-P´erez and V. R. Benjamins (eds.), Knowledge Engineering and Knowledge Management. Proceedings of the 13th International Conference (EKAW 2002), Berlin: Springer, 2002, pp. 166–181. [43] A. Gangemi, N. Guarino, C. Masolo, and A. Oltramari, ‘Sweetening WordNet with DOLCE’, AI Magazine, 24/3 (2003), 13–24. [44] C. Masolo, S. Borgo, A. Gangemi, N. Guarino, and A. Oltramari, Wonderweb deliverable D18 (Technical Report), Trento, Laboratory for Applied Ontology ISTCCNR, 2003. [45] N. Guarino and C. Welty, ‘Evaluating Ontological Decisions with OntoClean’, Communications of the ACM, 45/2 (2002), 61–65. [46] N. Guarino and C. Welty, ‘An Overview of OntoClean’, in [9], pp. 151–172. [47] C. Welty and N. Guarino, ‘Supporting Ontological Analysis of Taxonomic Relationships’, Data & Knowledge Engineering, 39 (2001), 51–74. [48] W. V. O. Quine, ‘On What There Is’, Review of Metaphysics, 2 (1948), 21–38. [49] W. V. O. Quine, ‘Designation and Existence’, Journal of Philosophy, 36 (1939), 701–709. ¨ [50] A. Meinong, ‘Uber Gegenstandstheorie’, in A. Meinong, R. Ameseder, and E. Mally (eds.), Untersuchungen zur Gegenstandstheorie und Psychologie, Leipzig, Barth, 1904, pp. 1–50; Eng. trans. by I. Levi, D. B. Terrell, and R. M. Chisholm, ‘On the Theory of Objects’, in R. M. Chisholm (ed.), Realism and the Background of Phenomenology, Glencoe (IL), Free Press, 1960, pp. 76–117. [51] F. Berto, Existence as a Real Property. The Ontology of Meinongianism, Dordrecht, Springer, 2013. [52] M. Heidegger, Vom Wesen der Wahrheit. Zu Platons H¨ohlengleichnis und The¨atet, Wintersemester 1931/32 (ed. H. M¨orchen), Frankfurt, Klostermann, 1988; Eng. trans. by T. Sadler, The Essence of Truth: On Plato’s Cave Allegory and Theaetetus, London, Continuum, 2002. [53] W. Rapaport, ‘Logical Foundations for Belief Representation’, Cognitive Science, 10 (1986), 371–422. [54] N. Guarino and P. Giaretta, ‘Ontologies and Knowledge Bases: Towards a Terminological Clarification’, in N. J. I. Mars (ed.) Towards Very Large Knowledge Bases: Knowledge Building and Knowledge Sharing, Amsterdam, IOS Press, 1995, pp. 25–32. [55] N. Guarino, D. Oberle, and S. Staab, ‘What Is an Ontology’, in the second edition of [9], pp. 1–17. ¨ [56] T. R. Gruber, ‘Ontology’, in L. Liu and M. T. Ozsu (eds.) Encyclopedia of Database Systems, Berlin, Springer, 2009, pp. 1963–1965. [57] B. Smith, ‘Beyond Concepts: Ontology as Reality Representation’, in A. C. Varzi and L. Vieu (eds.), Formal Ontology in Information Systems. Proceedings of the 3rd International Conference (FOIS-2004), Amsterdam, IOS Press, 2004, pp. 73–84. [58] B. Smith and W. Ceusters, ‘Ontological Realism: A Methodology for Coordinated Evolution of Scientific Ontologies’, Applied Ontology, 5 (2010), 139–188. [59] G. H. Merrill, ‘Ontological Realism: Methodology or Misdirection?’, Applied Ontology, 5 (2010), 79–108.

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[60] G. H. Merrill, ‘Realism and Reference Ontologies: Considerations, Reflections, and Problems’, Applied Ontology, 5 (2010), 189–221. [61] J. R. Searle, The Construction of Social Reality, New York, Free Press, 1995. [62] B. Smith, ‘Ontology’, in L. Floridi (ed.), The Blackwell Guide to the Philosophy of Computing and Information, Oxford, Blackwell, 2003, pp. 155–166. [63] B. Smith and C. Welty, ‘Ontology: Towards a New Synthesis’, in C. Welty and B. Smith (eds.), Formal Ontology in Information Systems. Proceedings of the 2nd International Conference (FOIS’01), New York, ACM Press, 2001, pp. iii–ix. [64] J. Dupr´e, ‘Natural Kinds and Biological Taxa’, Philosophical Review, 90 (1981), 66–90. [65] P. S. Kitcher, ‘Species’, Philosophy of Science, 51 (1984), 308–333. [66] S. Borgo and C. Masolo, ‘Foundational Choices in DOLCE’, in the second edition of [9], pp. 361–381. [67] D. B. Lenat, ‘Cyc: A Large-Scale Investment in Knowledge Infrastructure’, Communications of the ACM, 38/11 (1995), 33–38. [68] C. Partridge, Business Objects: Re-Engineering for Re-Use, Oxford, ButterworthHeinemann, 1996. [69] I. Niles and A. Pease, ‘Towards a Standard Upper Ontology,’ in C. Welty and B. Smith (eds.), Formal Ontology in Information Systems. Proceedings of the 2nd International Conference (FOIS’01), New York, ACM Press, 2001, pp. 2–9. [70] R. Arp, B. Smith, and A. D. Spear, Building Ontologies with Basic Formal Ontology, Cambridge (MA), MIT Press, 2015. [71] G. Guizzardi and G. Wagner, ‘A Unified Foundational Ontology and some Applications of it in Business Modeling’, in J. Grundspenkis and M. Kirikova (eds.), 16th Conference on Advanced Information Systems Engineering (CAiSE’04). Workshops Proceedings, Riga, Riga Technical University, 2004, vol. 3, pp. 129–143. [72] H. Herre, B. Heller, P. Burek, R. Hoehndorf, F. Loebe, and H. Michalek, ‘General Formal Ontology (GFO). A Foundational Ontology Integrating Objects and Processes’, Technical Report, University of Leipzig, Research Group Ontologies in Medicine (Onto-Med). [73] R. Mizoguchi,‘YAMATO: Yet Another More Advanced Top-level Ontology’, in K. Taylor, T. Meyer, and M. Orgun (eds.), Advances in Ontologies. Proceedings of the 6th Australasian Ontology Workshop, Sydney, ACS, 2010, pp. 1–16. [74] W. Ku´snierczyk, ‘Nontological Engineering’, in B. Bennett and C. Fellbaum (eds), Formal Ontology in Information Systems. Proceedings of the 4th International Conference (FOIS-2006) Amsterdam, IOS Press, 2006, pp. 39–50. [75] A. C. Varzi, ‘On Doing Ontology without Metaphysics’, Philosophical Perspectives, 25 (2011), 407–423. [76] R. Ingarden, Der Streit um die Existenz der Welt, T¨ubingen, Niemeyer, 1964; partial Eng. trans. by H. R. Michejda, Time and Modes of Being, Springfield (IL), Thomas, 1964. [77] H. Putnam, ‘The Meaning of ‘Meaning”, Minnesota Studies in Philosophy of Science, 7 (1975), 131–193. [78] P. Benacerraf, ‘What Numbers Could not Be’, Philosophical Review, 74 (1965), 47–73.

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[79] P. Hayes, ‘The Naive Physics Manifesto’, in D. Michie (ed.), Expert Systems in the Micro-electronic Age, Edinburgh, Edinburgh University Press, 1979, pp. 242–270. [80] J. R. Hobbs and R. C. Moore (eds.), Formal Theories of the Commonsense World, Norwood (NJ), Ablex, 1985. [81] B. Smith, ‘Basic Concepts of Formal Ontology’, in N. Guarino (ed.), Formal Ontology in Information Systems. Proceedings of the 1st International Conference (FOIS’98), Amsterdam, IOS Press, 1998, pp. 19–28. [82] A. C. Varzi, ‘On the Boundary between Material and Formal Ontology’, in B. Smith, R. Mizoguchi, and S. Nakagawa (eds.), Interdisciplinary Ontology, Vol. 3: Proceedings of the Third Interdisciplinary Ontology Meeting, Tokyo, Keio University Press, 2010, pp. 3–8. [83] W. V. O. Quine, ‘Speaking of Objects’, Proceedings and Addresses of the American Philosophical Association, 31 (1958), 5–22. [84] W. V. O. Quine, Philosophy of Logic, Englewood Cliffs (NJ), Prentice-Hall, 1970. [85] K. Fine, ‘Ontological Dependence’, Proceedings of the Aristotelian Society, 95 (1995), 269–290. [86] D. K. Lewis, ‘Against Structural Universals’, Australasian Journal of Philosophy, 64 (1986), 25–46. [87] A. C. Varzi, ‘From Language to Ontology: Beware of the Traps’, in M. Aurnague, M. Hickmann, and L. Vieu (eds.), The Categorization of Spatial Entities in Language and Cognition, Amsterdam, Benjamins, 2007, pp. 269–284. [88] M. Black, ‘The Identity of Indiscernibles’, Mind, 61 (1952), 152–164. [89] S. French, ‘Why the Principle of the Identity of Indiscernibles is not Contingently True Either’, Synthese, 78 (1989), 141–166. [90] E. Schr¨odinger, Science and Humanism. Physics in Our Time, Cambridge, Cambridge University Press, 1952. [91] A. J. Cotnoir and A. C. Varzi, Mereology, Oxford, Oxford University Press, forthcoming. [92] N. Goodman, ‘A World of Individuals’, In J. M. Bochenski, A. Church, and N. Goodman, The Problem of Universals: A Symposium, Notre Dame (IN), University of Notre Dame Press, 1956, pp. 13–31. [93] D. K. Lewis, Parts of Classes, Oxford, Blackwell, 1991. [94] P. M. Simons, Parts. A Study In Ontology, Oxford, Clarendon Press, 1987. [95] J. J. Thomson, ‘The Statue and the Clay’, Noˆus, 32 (1998), 149–173. [96] P. Aczel, Non-Well-Founded Sets, Stanford (CA), CSLI Publications, 1988. [97] A. J. Cotnoir and A. Bacon, ‘Non-Wellfounded Mereology’, Review of Symbolic Logic, 5 (2012), 187–204. [98] A. C. Varzi, ‘Logic, Ontological Neutrality, and the Law of Non-Contradiction’, in E. Ficara (ed.), Contradictions. Logic, History, Actuality, Berlin, De Gruyter, 2014, pp. 53–80. [99] R. Carnap, ‘Intellectual Autobiography’, in P. A. Schilpp (ed.), The Philosophy of Rudolf Carnap, La Salle (IL), Open Court, 1963, pp. 1–84.

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Ontology Makes Sense S. Borgo et al. (Eds.) IOS Press, 2019 © 2019 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-61499-955-3-24

Philosophy and the Ontologies of Knowledge Representation in AI Pierdaniele GIARETTA Department of Philosophy, Sociology, Education and Applied Psychology, University of Padua

Abstract: Firstly, philosophy and science are compared by taking into account five aspects: critical attitude towards the assumptions, definitions and terminological rigor, formulation of a theory and its inferential development, control and external support, presence of a holistic approach. Secondly, for each aspect, some reasons that make the ontologies of Knowledge Representation closer to philosophy or closer to science are pointed out. Conclusions are different and not clear-cut. In the discussion of the fifth aspect Nicola Guarino’s approach is emphasized and presented in the light of Carnap’s notion of explication. Keywords: philosophy, science, ontology, theory, explication.

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1. Introduction An ontology of knowledge representation in AI is not part of the philosophical discipline of Ontology. The latter, with the capitalized “O”, can be identified with the “science” so introduced by Aristotle: “There is a science which investigates being as being and the attributes which belong to this in virtue of its own nature” ([1], IV, 1, 1003a21-22) 1. Despite some philosophers’ opinions, Ontology is not a well-established discipline. Thus, given the lack of a stable and clear status, contrasting the ontologies of knowledge representation with Ontology contributes little to characterizing the first. A positive characterization expounding their specific features is surely more useful and, in fact, much more stressed and developed in the literature. Even if the philosophical vagueness is not fully avoided in the AI ontologies, in many papers a strong effort has been made to reduce it. This contribution does not further develop a positive characterization of ontologies in AI, but focuses on the reasons for their contrast with Ontology by addressing a more general question: how much philosophy is there in the ontologies? 2 This contribution starts by comparing philosophy, to which Ontology belongs, and science, to which ontologies aim to belong even if they exploit, develop, and apply notions and tools worked out in philosophy. The comparison is made by taking into account five relevant aspects or dimensions: critical attitude towards the assumptions, definitions and terminological rigor, formulation of a theory and its inferential development, control and external support, presence of a holistic approach. Then, for



         

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each aspect, some reasons that make ontologies closer to philosophy or closer to science are pointed out. The extensive discussion of the holistic aspect takes Nicola Guarino’s approach as the main point of reference.

2. Philosophy and science The purpose of this section is to compare philosophy and science without relying on preliminary answers to the questions of “what is philosophy?” and “what is science?” 3. Both philosophy and science are assumed to be manifestations of our search for knowledge, including knowledge concerning knowledge itself. The ways in which this research is carried out are different in philosophy and science, but some differences are only matter of degree and concern ways in which the sciences themselves differ. Perhaps it is better to start from differences of this kind, which do not strictly imply an opposition between philosophy and the sciences but instead speak in general of how a theory – philosophical or scientific – can be built by means of a discourse that, besides expounding a theory, also concerns the motivations of the theory and the way to propose it. A certain difference will emerge between philosophical discourse and scientific discourse, but all but one of the aspects that will be identified are also aspects under which discourses introducing and supporting scientific theories can be differentiated. Of course, the five aspects considered are not intended to be all the aspects that could be considered.

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2.1. The critical attitude towards the assumptions It is inevitable to seek knowledge by adopting concepts, assuming principles, and stating rules to be followed. In [3] Thomas Kuhn greatly emphasizes the linguistic-taxonomic conditioning4 that he presents as if it were a cage (my term), from which one can only leave to enter another cage. Despite Kuhn's view, one can leave a linguistic-taxonomic cage not only to enter another cage, but also to see how the cage from which one came is made and possibly to compare it with other cages in which one has already entered or could enter. Out of metaphor, the suggestion is that the exercise of a critical attitude is always possible, even if it is limited. It can concern any aspect, not only the linguistic-taxonomic aspect, and therefore can also address the assumptions behind its very exercise, but we should not delude ourselves and believe we are able to elude any presuppositions. Generalizing what Karl Popper said in [6] about the role of the data with respect to science, one could argue that in general there is no fixed and unassailable point on which one can rely. One can only agree to take certain points of support firmly without being able to state incontrovertible reasons for justifying the decision to rely on them. It is generally accepted that the most radical exercise of criticism belongs to philosophy and that it is the task of philosophy to question the presuppositions, whatever



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they may be. What about the sciences? Even for sciences, exercising criticism is essential. Popper, among others, strongly supported this thesis. Indeed, it is obvious that the decision to accept or reject a theory or hypothesis within a given theoretical context requires the exercise of a critical attitude. However, the exercise of a critical attitude also manifests itself, in a more elementary way, when trying to answer questions that naturally emerge from one's field of inquiry. Sometimes the answer is found in a neighboring field, as it happened to biology when questions regarding the structure and replication of genes found a molecular response, contributing to the birth of molecular biology. It is integral to science to raise problems that can be tackled by overcoming rigid and artificial disciplinary boundaries through the construction of interfield theories. 5 In general, a critical attitude can have many different manifestations in scientific research. Some manifestations have a philosophical character. See, for example, [7], where Ernst Mach denies the existence of atoms. Even Einstein’s way of rethinking the notion of time has something philosophical. In the sciences, it is more standard that curiosity leads to raised questions in one field while answers are sought in a neighboring field. The exercise of a critical attitude is not excluded, but only subjected to various conditioning in Kuhn’s view of the scientific development. Research in normal scientific activity is limited and guided by conceptions, assumptions, constraints, prescriptions, and exemplars that make up the so-called paradigm. Eventually a paradigm is going to face difficulties, and detecting these difficulties requires the exercise of a critical attitude, even if the change of a paradigm has no rational or purely rational motivations.

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2.2 Definitions and terminological rigor                

                                                                                                                                               

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Some significant and informative references are [10], [11], [12].

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($     '         9' .>F- PET > CAT, where a role (pet) subsumes a type (cat), without risking unsound inheritance [3,4]. WordNet’s hypernym/hyponym relation encodes the intuitions of natural language speakers, so “pet > cat” means that English language speakers would readily agree that the sentence “Cats are pets.” is true. Ontological subsumption, however, uses modal set theoretic semantics, so that “pet > cat” in an ontology would mean “necessarily every cat is a pet” which is false. Imagine a particular cat, Fluffy. If a hierarchy encodes the ontological subsumption relation (rather than the hypernym-hyponym relation), then if Fluffy ceases to be a pet, it follows that Fluffy also ceases to be a cat. However, this is not correct since Fluffy could become a stray cat and thereby cease to be a pet but still be a cat.

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The fact that roles should not subsume types in conjunction with the assumption that nouns usually represent sortals leads to the conclusion that non-rigid nouns should not subsume rigid nouns.7 And indeed this is what the OntoClean methodology teaches. This general conclusion made it possible to begin evaluating synsets in WordNet for rigidity and to clean the hierarchy for sound inference. 9.5. Representing roles in KYOTO

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The KYOTO project [20] focused on the domains of biodiversity and ecology. To illustrate how roles were modelled, consider the example of how the role migration corridor should be represented in the KYOTO ontology. Figure 1 shows that migration corridor is a role and as such inherits all of the properties of the concept role. Geographic place is a subclass of endurant (an entity that can be perceived as a complete concept) and inherits all of the properties of that concept. The Path of the Pronghorn is a specific migration corridor in Wyoming, USA (and thus an individual). This is represented in the diagram where Path of the Pronghorn inherits the properties of endurant and Geographic place.

Figure 1 Example of modeling role vs. instance relations in the KYOTO ontology. Ellipses represent concepts, rectangles represent individuals, and arrows represent relations. Unlabeled arrows represent inheritance relations, i.e. those relations amongst which formally specified properties are transitively inherited.

Colloquially we can say that the Path of the Pronghorn is a migration corridor, and indeed this piece of land may only be of interest to ecologists because of this role. However, the fact that it could cease to be a migration corridor and become, for example, a housing development indicates, first, that migration corridor is a role rather than a type, and, second, that the relation between the Path of the Pronghorn and 7

The phrase "rigid noun" should be read as an ellipsis for "noun representing a rigid concept" and mutatis mutandis for "non-rigid noun."

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migration corridor should not be modelled using the instance relation but rather the has role relation. In short, the Path of the Pronghorn is an instance of a geographic place that has a role as a migration corridor.

10. Future Work WordNet's great popularity for research and application come with a responsibility to create, maintain and make available a truly useful tool. Nicola and his colleagues have shown that ontological cleanliness and consistency are a sine qua non. We briefly discuss several outstanding improvements to WordNet that could significantly enhance its usefulness. Some of these are guided by the work of Nicola.

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10.1. Systematic polysemy and the type-role distinction An influential paper by Apresjan [28] explored the systematic polysemy of many nouns. For example, the words chicken, salmon and shrimp can refer to both the animal and its flesh that serves as food. Similarly, the nouns apple, pear and cherry can denote trees, the wood of the trees, and their edible fruit. In most cases, WordNet represents these sense in separate synsets, but does not indicate their semantic relatedness. Gangemi et al. [14] discuss the case of {surgical_knife}, which in an earlier version of WordNet had two hypernyms, {surgical_instrument} and {knife}. Gangemi et al. point out that this is in fact one of many cases involving a distinction between types and roles. Given a proper distinction at the superordinate levels, types and roles can be clearly separated and double inheritance can be avoided. Synsets like {chicken} could have two hypernyms, one showing that chicken is a kind of bird, and the other that it bears a role relation to food. Pustejovsky's Generative Lexicon [29] similarly has single entries for concepts like CHICKEN, whose qualia structure includes both a "formal" aspect (corresponding to the type relation) and a "telic role" (corresponding to Gangemi et al.’s role relation). Currently, WordNet includes two separate synsets for such cases, each with its own hypernym. For example, the immediate hypernym of one sense of {shrimp} is {seafood}, whereas the other sense of {shrimp} is separated by four technical levels from {animal}; in descending order, these are {decapod}, {crustacean}, {arthropod}, {invertebrate}. This is an example where the role-type distinction noted by Gangemi et al. [14] could more accurately represent the two distinct yet related meanings of shrimp. Gangemi et al. [14] show that the type-role distinction can be used to detect cases of systematic polysemy among homomorphic hyponyms and lead to the inclusion of new synsets in cases where only the type or only the role is represented. Examples are {reindeer} and {whale}, which are represented in WordNet as animals (types), but not in their role as foods in Scandinavia and Japan. 10.2. The type-role distinction and culture-relative conceptualization In the early 1990s, the WordNet team tried to manually encode systematic polysemy of the animal-food kind. However, this effort was halted (and existing encodings were removed) when we realized that many animals, fruits, nuts, plants (types) were also foods or medicine (roles) in some cultures but not others (e.g., dogs are eaten in some Asian countries but usually not in the US or Europe). While the type-role distinction

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would make for an ontologically cleaner WordNet, it is unclear how to treat culturally dependent categorizations. 10.3. Purpose verbs Lexical-conceptual analyses of verbs [30,31] distinguish manner verbs like whisper from result verbs like break. Both kinds of verbs are currently encoded as troponyms, generic, underspecified "manner" specifications, of superordinate verbs like speak and change_integrity, respectively [7]. But just as a type-role distinction is needed in WordNet, verbs should be more finely distinguished. Fellbaum [32] proposes a further sub-class, which she calls "purpose verbs." Verbs like exercise, control, help and treat express concepts that encode telicity, a goal or purpose of an event, without referring to the manner or result of the event. Fellbaum suggests that such verbs bear a conceptual similarity to role nouns and provides diagnostics for distinguishing them from previously recognized classes that exploit lexical semantic patterns [32]. However, purpose verbs have not been distinguished in WordNet at the time of writing this paper.

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10.4. Distinguishing folk and scientific taxonomies WordNet's hierarchies are of uneven depths. In particular, hierarchies including natural kinds (esp. plants and animals) tend to be very deep, since they include synsets with both folk names and scientific terms. The latter are unfamiliar to ordinary speakers, and the seven intervening levels between {horse} and {animal}, including {oddtoed_ungulate} and {placental_mammal}, do not seem to capture speakers' intuitive classification of horses as animals; similarly, to non-botanist speakers, the two levels with synonyms containing technical terms ({pteridophyte} and {vascular_plant}) that separate the better-known terms {fern} and {plant} are likely unfamiliar. One could imagine two separate kinds of hyponymy relation, one that includes and one that "skips" the technical terms in favor of hiearchies that are more in line with ordinary speakers' intuitions. However, this solution would not be easy to implement as there is no sharp distinction between folk and scientific taxonomies. For example, MAMMAL is a reasonably familiar concept (likely more so than PLACENTAL MAMMAL), but everyday speakers' mental representation of HORSE is more likely "a kind of an animal" rather than "a kind of a mammal." 10.5. Making WordNet's levels more evenly spaced Intuitively, the distance among concepts on one level and those on the immediate super- or subordinate level varies greatly in many cases. For example, the animal sense of {white_elephant} is separated from its inherited hypernym {elephant} by one intervening node, {Indian_elephant, Elephas_maximus}. The other sense of {white_elephant} has as its immediate hypernym {possession}, a rather abstract concept. The small distance between {white_elephant} and {possession} somewhat misleadingly suggests a close semantic distance, similar to that between {white_elephant} and {elephant}.8 We do not presently have a solution for correcting the disparate semantic distances among such synsets. 8

We owe this example to Philip Resnik.

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11. Conclusion Despite the many shortcomings both in its coverage and ontological cleanliness, WordNet continues to be a popular tool for word sense disambiguation in Natural Language Processing applications that require broad lexical coverage. Moreover, WordNet plays an important role in the field of Knowledge Engineering, which relies on clean, consistent representations and structures that enable automatic reasoning. Such applications mandate improvements to WordNet that are consistent with ontological principles. The contributions of Nicola and his colleagues, in particular the identity and individuation criteria, have led to specific enhancements, such as the distinction between kinds and individuals and also the KYOTO ontology, which combines DOLCE's upper ontology with WordNet's lexical component. Nicola's influence extends well beyond the Princeton WordNet, which has inspired similar resources for dozens of languages [12,33]. Moreover, the images in two visual databases, ImageNet [34] and ShapeNet [35], are linked to WordNet's synsets and structured accordingly. These resources are intended to enable object recognition, but, as in the case of word sense disambiguation, such an application can be supported only when the images are organized in clean hierarchies. There is a lively discussion within the community of researchers working in knowledge representation, knowledge engineering, ontology and Natural Language Processing concerning WordNet's specific shortcomings. Constructive, workable solutions are occasionally proposed [36]. It is hoped that future interaction with ontologists will continue to inform the development of WordNet, leading to a resource that will better serve a broad range of applications and that is also consistent with current theoretical work. Nicola's contributions over the past decades have amply demonstrated the many ways in which WordNet (and wordnets) can benefit from the work of ontologists, and his achievements have been hugely influential.

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References [1] N. Guarino The Ontological Level. In R. Casati, B. Smith and G. White, editors, Philosophy and the Cognitive Sciences, pages 443-456. Hölder-Pichler Tempsky, Vienna, Austria, 1994. [2] A. Oltramari, A. Gangemi, N. Guarino and C. Masolo. Restructuring WordNet's Top Level: The OntoClean Approach. Proceedings of OntoLex2, pages 17-26. LREC, Las Palmas, Spain, 2002. [3] N. Guarino and C. Welty. Evaluating Ontological Decisions with OntoClean. Communications of the ACM, 45(2):61-65, 2002. [4] N. Guarino and C. Welty. An Overview of OntoClean. In R. Studer and S. Staab, editors, Handbook of Ontologies in Information Systems, pages 151-172. Springer, Berlin, 2003. [5] C. R. Huang, N. Calzolari, A. Gangemi, A. Lenci, Oltramari and L. Prévot, editors, Ontology and the Lexicon: A Natural Language Processing Perspective. Cambridge University Press, Cambridge. 2010. [6] G. A. Miller. WordNet: a Lexical Database for English, Communications of the ACM, 38(11):39-41, 1995. [7] C. Fellbaum, editor, WordNet: An Electronic Lexical Database, MIT Press, Cambridge, MA, 1998. [8] A. M. Collins and M. R. Quillian. Retrieval Time From Semantic Memory. Journal of Verbal Learning and Verbal Behavior, 8(2):240-247, 1969. [9] E. H. Rosch, Natural Categories. Cognitive Psychology, 4(3):328-350, 1973. [10] D. A. Cruse. Lexical Semantics, Cambridge University Press, Cambridge,1986. [11] G. K. Zipf, The Meaning-Frequency Relationship of Words. Journal of General Psychology, (33):251256, 1945. [12] F. Bond and R. Foster. Linking and Extending an Open Multilingual Wordnet. In Proceedings of the 51st Annual Meeting of the Association for Computational Linguistics, (1):1352-1362. Stroudsburg, PA, 2013.

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[13] T. Pedersen, S. Patwardhan and J. Michelizzi. Wordnet: Similarity: Measuring The Relatedness Of Concepts. In Demonstration Papers at HLT-NAACL 2004, pages 38-41. Association for Computational Linguistics, Stroudsburg, PA, 2004. [14] A. Gangemi, N. Guarino, C. Masolo, A. Oltramari and L. Schneider. Sweetening Ontologies with DOLCE. In A. Gomez Perez and V. R. Benjamins, editors, Knowledge Engineering and Knowledge Management. Ontologies and the Semantic Web. Proceedings of 13th International Conference, (EKAW 2002), pages 166-181. Springer, Berlin, 2002. [15] A. Gangemi, N. Guarino, C. Masolo and A. Oltramari. Sweetening WordNet with DOLCE. AI Magazine, 24(3):13, 2003. [16] C. Masolo, S. Borgo, A. Gangemi, N. Guarino and A. Oltramari. WonderWeb Deliverable D18. The WonderWeb library of foundational Ontologies and the DOLCE Ontology. ISTC-CNR, Trento, Italy, 2003. [17] G. A. Miller. Nouns in WordNet. In C. Fellbaum editor, WordNet: An Electronic Lexical Database, pages 24-45. MIT Press, Cambridge, MA, 1998. [18] K. J. Miller. Modifiers in WordNet. In C. Fellbaum editor, WordNet: An Electronic Lexical Database, pages 47-67. MIT Press, Cambridge, MA, 1998. [19] N. Guarino, Formal Ontology, Conceptual Analysis and Knowledge Representation. International Journal of Human-Computer Studies, (43):625-640, 1995. [20] P. Vossen, E. Agirre, F. Bond, W. Bosma, A. Herold, A. Hicks, S. K. Hsieh, H. Isahara, C. R. Huang, K. Kanzaki and A. Marchetti. KYOTO: A Knowledge-Rich Approach to the Interoperable Mining of Events from Text. New Trends of Research in Ontologies and Lexical Resources. Springer, Berlin, 6590, 2011. [21] G. A. Miller and F. Hristea. WordNet Nouns: Classes and Instances. Computational Linguistics, 32(1):1-3, 2006. [22] R. Brachmann. On the Epistemological Status of Semantic Networks. In N. Finder editor, Associative Networks, pages 3-50. Academic Press, New York, NY 1979. [23] B. Smith and W. Ceusters, Ontological Realism: A Methodology for Coordinated Evolution of Scientific Ontologies. Applied Ontology, 5(3-4), 139-188, 2010. [24] N. Guarino. Some Ontological Principles for Designing Upper Level Lexical Resources. In A. Rubio, N. Gallardo, R. Castro and A. Tejada, editors, Proceedings of First International Conference on Language Resources and Evaluation, pages 527-534. ELRA, Granada, Spain, 1998. [25] N. Guarino. Concepts, Attributes and Arbitrary Relations: Some Linguistic and Ontological Criteria for Structuring Knowledge Bases. Data and Knowledge Engineering, (8):249-261, 1992. [26] A. Gangemi, N. Guarino and A. Oltramari. Conceptual Analysis of Lexical Taxonomies: The Case of WordNet's Top-Level. In Proceedings of the International Conference on Formal Ontology in Information Systems, pages 285-296. ACM, New York, NY, 2001. [27] A. Hicks and A. Herold. Cross-lingual Evaluation of Ontologies with RUDIFY. International Joint Conference on Knowledge Discovery, Knowledge Engineering, and Knowledge Management, pages 512. Springer. Berlin, 2009. [28] J. Apresjan. Regular Polysemy. Linguistics, 12(142):5–32, 1974. [29] J. Pustejovsky. The Generative Lexicon. MIT Press, Cambridge, 1991. [30] B. Levin and M. R. Hovav. Lexicalized Meaning And Manner/Result Complementarity. In B. Arsenijević, B. Gehrke and R. Marín, editors, Subatomic Semantics of Event Predicates, pages 49-70. Springer, Dordrecht, Netherlands, 2013. [31] M. Rappaport Hovav and B. Levin. Building Verb Meanings. In M. Butt and W. Geuder, editors, The Projection Of Arguments: Lexical And Compositional Factors. pages 97-134. 1998. [32] C. Fellbaum. Purpose Verbs. In J. Pustejovsky, P. Bouillon, H. Isahara, K. Kanzaki and C. Lee, editors, Advances in Generative Lexicon Theory. pages 371-384. Springer Dordrecht, Netherlands, 2013. [33] P. Vossen, editor, EuroWordNet: A Multilingual Database With Lexical Semantic Networks. Kluwer Academic Publishers, Dordrecht, Netherlands, 1995. . [34] J. Deng, W. Dong, R. Socher, L. Li, K. Li and L. Fei-Fei. Imagenet: A Large-Scale Hierarchical Image Database. Computer Vision and Pattern Recognition, pages 248-255. IEEE, Ottawa, CA, 2009. [35] A. X. Chang, T. Funkhouser, G. Leonidas, Q. Hanrahan, Z. Huang and S. Savarese. Shapenet: An Information-Rich 3d Model Repository. arXiv preprint arXiv:1512.03012, 2015. [36] N. Verdezoto and L. Vieu. Towards Semi-Automatic Methods For Improving Wordnet. In Proceedings of the Ninth International Conference on Computational Semantics, pages 275-284. Association for Computational Linguistics, Stroudsburg, PA, 2011.

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Formal Ontology to the Proof of Facts Guido Vetere Universit`a Guglielmo Marconi, Italy Abstract. After the work of Nicola Guarino, formal ontology is available today as a powerful conceptual tool for information systems modelling. In particular, for shared conceptual models, the ontological characterization of predicative symbols may help clarifying their intended semantics. Yet, about twenty five years after Guarino’s seminal paper, the penetration of formal ontological tools in modelling languages, as well as the spread of highly formalized conceptual models in business information systems, is still relatively low. This paper aims at elaborating some hypotheses about this fact. Concrete conditions for stipulating semantic agreements, depending on socio-technical architectures, are compared with assumptions of descriptive metaphysics as implemented in today’s ontology engineering. As an outcome of this analysis, a clearer separation between linguistic concepts produced in human semiotic processes and metaphysic postulates emerges as a key move for overcoming difficulties and open the way to further developments. Keywords. ontological commitment, intended model, ontological level

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1. Introduction In his The Ontological Level [1], presented at the 1994 Wittgenstein Symposium in Wien, Nicola Guarino introduced the notion of ontological commitment in information systems. In Guarino’s view, an ontological commitment is a meaning stipulation which serves the purpose of reducing unintended models when interpreting concepts (logic predicates) over application domains. These stipulations, suitably formalized, should be specifically addressed in a layer called ontological level. By revising his work 15 years later [2], in spite of the rise of the Semantic Web, which, exactly in that period, brought about a multitude of shared conceptualizations called “ontologies”, Guarino had to complain about the substantial ineffectiveness of his seminal contribution. As a matter of facts, concept languages at the basis of the Semantic Web, such as RDFS and OWL, had not been instrumented with any ontological device. More in general, with Guarino’s words, a “general agreement about having ontological distinctions built in the representation language” was not in place yet. As a consequence, “assumptions concerning the basic constructs of representation languages remain[ed] implicit in the mind of the knowledge engineer, and difficult to express and to share”. General (upper-level) ontologies like DOLCE [3] were not broadly adopted in business information systems. Efforts for devising reference conceptual models were under way in many businesses, with little attention to formal aspects, however. Ten years after (that is, nowadays), the adoption of shared conceptual models has grown, but from a foundational point of view the situation has not significantly changed. The idea of providing ontology languages (basically, OWL) with specific ontological

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constructs (e.g. part, dependence) has not entered any significant development plan. OntoUML1 provides industry-level object-oriented software engineering tools with a formal ontological framework [4], but still it doesn’t enjoy the adoption it would deserve. As far as upper ontologies are concerned, no broadly adopted standards are in sight at the moment. Proposals like DOLCE, SUMO2 , UFO3 or BFO4 seem to be still confined to specialist niches. In fact, the rise of Google’s Knowledge Graph (KG), which brings a huge shared conceptualization on the Web, appears as the most relevant achievement of recent times. But the KG conceptual backbone5 is far from qualifying as a well-founded ontology. Indeed, while relevant search attributes begin to be seen as ontological features, researchers at Google seem to be scarcely interested in providing the KG with any formal ontological foundation [5]. A number of modern No-SQL databases embrace Semantic Web standards (RDF) and support ontology reasoning to some extent, however they are focused on practical schema manageability more than principled conceptual design. Ontology (as a name) has taken the meaning of global view in data integration literature and practices, but this is just a linguistic fact: as global views, ontologies are just better conceptual schemas, that is, mere logical artefacts. The Ontology-based Data Access paradigm (OBDA) [6], which is gaining popularity as a data integration conceptual framework, does not endorse ontological commitments whatsoever, at least in Guarino’s original sense. In the light of the decades-long history of the idea, one may question if specifying ontological commitments in formal terms is really valuable in information systems’ design. No doubts that sharing meaning conventions across communities and businesses is generally recognized to be of striking importance and is at the basis of long-term endeavours such as the Semantic Web. However, in terms of socio-technical feasibility, the question is whether formal ontological commitments may actually be specified in real application scenarios, and which concrete returns they can guarantee. Also, it is not clear whether formal ontology may have a role in modern Artificial Intelligence (AI), as the field is currently dominated by empirical methods which often claim to be free of postulates of any kind. This sort of “end of theory”6 , prophesied by many data scientists and deep learning enthusiasts, may have the consequence of making ontology quite useless. In sum, after more than twenty years of research, development, and debates, while any logical device whose alphabet is somehow related to common sense concepts is customarily called “ontology”, Ontology (capitalized O) is still pretty underdeveloped in the information technology industry. This contribution aims at shedding some light on the enduring lack of formal ontological foundations in conceptual languages and business conceptualizations. We will consider the notion of ontological commitment as it is known in philosophy and information technology after Guarino’s works, and will discuss various issues that may explain the lack of penetration of ontological analysis in concrete application scenarios. Finally, 1 https://ontouml.org/ 2 http://www.adampease.org/OP/ 3 https://ontology.com.br/ 4 http://basic-formal-ontology.org 5 www.schema.org 6 Wired

editorial note by Chris Anderson (May 2008), https://www.wired.com/2008/06/pb-theory/

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the paper will speculate about the role that formal ontology may play in the future of AI-based information systems.

2. Ontological commitments According to the original definition [1], given a language L on a domain D and a set of possible worlds W (interpretations of L on D), an ontological commitment is a characterization of L that should lead any agent who makes use of L on D to consistently spot unintended models, i.e. interpretations unfitted to real states of affairs. More precisely, an ontological commitment founds an equivalence relation on W called ontological compatibility, which induces a partition such that agents can single out the subset of W that fully satisfies the characterization. Having to do with possible worlds congruency, ontological characterizations are mostly concerned with the notion of rigidity, that is, truth in every possible world: ∀P.RIGID(P) → (∀x.(P(x) → P(x)))

(1)

In practice, a predicate is rigid when, if it holds for an individual, then it holds for that individual in every possible world, as in the case of human-being (vs. e.g. student). For example, if predicates in L were characterized as either sortal or non-sortal (the two categories being disjoint)7 , a set w1 ∈ 2W where some x ∈ D is interpreted as an instance of some sortal predicate p ∈ L would be ontologically incompatible with respect to a w2 ∈ 2W where x is interpreted as non-sortal. Marking predicates in L as either sortal or non-sortal would be indeed an ontological commitment, which would allow agents to agree on compatible interpretations of the language they use on the domain at hand. In Guarino’s words, for every agent

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two worlds are ontologically compatible if they describe plausible alternative states of affairs involving the same elements of the domain. Along with rigidity, formal (meta) properties such as identity, unity, and dependence form the key ingredients of the OntoClean methodology, which Guarino and Welty provided as a guideline to achieve well-founded conceptualizations [9]. Ontological commitments, however, can also ground on material bases, including the concept’s “posture” with respect to physical dimensions such as space and time. This is the case of the classical distinction of continuants (e.g. objects) and occurrents (e.g. events), which is acknowledged in most (if not all) upper ontologies. In general, an ontological commitment is a formally specified supplementation of any predicative language (conceptualization), which serves the purpose of constraining the language’s interpretation, or otherwise stimulate revisions of legacy conceptualizations: one of the advantages of the ontological level is that an unwanted formal property for a predicate may trigger a knowledge elicitation process: [...] if student sounds strange when used as a characterising [rigid] predicate, the reason may be that we have forgotten to include human-being within our axiomatisation. [1] 7 See

Peter F. Strawson [7] and David Wiggins [8].

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Agents’ meaning judgements are intensional, insofar they span over structures of possible worlds, but are ultimately grounded in extensional truth-making: two different agents [...] will share the same meaning of “cooperating” [a binary relation] if, in presence of the same world states, will pick up the same couples as instances of the cooperates-with relation. [10] In the setting outlined above, insofar as they are used to foster consistent interpretations of concepts across technical communities sharing the same business domain, ontologies should provide a sort of semantic heuristic (interpretation guideline). However, formal ontology inherits from the tradition of analytical philosophy, which is mostly concerned with meta-level investigations of natural language practices, thus qualifying as a descriptive framework (ex-post) [11]. In this philosophy, formal properties informing linguistic acts are put in connection with the reality (be it physical, mental, or social) in which agents interact with each other, and even for authors accustomed to rephrasing natural sentences to highlight underlying onto-logical forms, language is in order as it is 8 . On the other hand, the concrete use of ontologies in information technology is often normative, or at least revisionary: developers are conveyed into mutually consistent interpretations by sticking to stipulated (ex-ante) meaning postulates, or suitably adapting their prior conceptualizations. For sure, if meaning agreements in information systems were based on wellestablished and widely accepted universals, the task of sharing business conceptualizations would be greatly facilitated, which motivates the interest of applied ontologists in descriptive metaphysics. However, in information sciences and practices, as well as in the real life of socio-technical systems, such description turns out to be very difficult to attain in a transparent and critical way. Instead, it remains implicit in out-of-the-box industry models, de facto standards, and a variety of other monolithic conceptual artefacts.

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3. Semantic agreements Any information system of minimum complexity yields a conceptual model in the community of agents that make use of it. These models take shape in the construction, the maintenance, and the exploitation of many kinds of knowledge corpora embodied in structured, unstructured or semi-structured data, as well as in interactions schemas such as searches and transactions. The aforementioned knowledge-based activities can be regarded as linguistic processes grounded in huge amounts of speech and interpretation acts, such as database updates and queries. In this respect, despite their formal apparatus, information systems look like natural languages: the kind of acts at their basis may be regarded as linguistic games in which designers and users are continuously involved. However, these linguistic games do not always look like those whose rules are equally and creatively brought into existence by players, as the ones Wittgenstein beautifully described. Instead, the way meaning stipulations take place is generally governed by organized activities, either normative, descriptive, or both. Depending on socio-systemic architectures, linguistic games run under defined rules, or anyway require managed elicitation workflows. In any case, the common recognition of intended models, which would 8 Ludwig

Wittgenstein, Philosophical Investigations (1953).

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Systems Mapping

Centralized Decentralized Centralized Data Integration Service Bus Distributed Knowledge Graph Semantic Web Table 1. Models of semantic integration

result from the specification of ontological commitments, requires conditions which appear to be very difficult to meet. Given an ontology, a meaning stipulation amounts, for agents, to adopting the same interpretation function over a shared domain. As easy as it may sound, achieving these stipulations is indeed far from trivial. Philosophers of language have studied the problem extensively9 , without reaching broad consensus about the general requirements of mutual understanding, and even on the possibility of such understanding [12]. Anyway, as artificial devices, information systems feature specific linguistic games, thus calling for some special kind of meaning theory, which however is still to be extensively investigated. Assuming that formal ontology could provide a basis for such investigation, we could nevertheless observe how the concrete use of ontological specifications would significantly vary across the spectrum of architectures and use cases that modern information systems display. In general, information integration appears to be dependent upon architectural geometries: • Centralized systems: a single system owns or controls resources and information flows; • Decentralized systems: resources are distributed and nobody fully controls informations flows.

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Orthogonally to architectural geometries, semantic integration follows two basic models: • Distributed mapping: each system has its own ontology and maps with ontologies of any other agent; • Centralized mapping: each system uses the same ontology by mapping it to local information resources. Examples of how these dimensions may combine in information technology semantic integration models are given in Table 1 [13]. Through this spectrum, a number of human and social factors impact the concrete ability of users, developers, content providers and stakeholders alike to reach consensus about intended models of any conceptualization whatsoever. These factors include: • • • • •

Epistemic: accessibility of truthmakers (facts that make propositions true); Hermeneutical: availability of explicit interpretation criteria; Pragmatical: operative purposes, e.g. normative or descriptive; Organizational: presence of organized and coordinated workflows; Socio-cultural: impact of collective specificities such as linguistic habits and trust attitudes; • Political: influence relationships among individuals and groups.

9 For

a survey of theories of meaning see https://plato.stanford.edu/entries/meaning/

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In the following sections we will discuss, as thoroughly as possible within the limits of the present contribution, how these factors may impact the attainability and practical use of formal ontological specifications in semantic integrations scenarios.

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3.1. Centralized systems The key feature of centralized systems is the presence of controlling authorities which provide conceptual schemas or otherwise regulate semantic stipulations within managed communities. Social networks, e-commerce platforms, corporate information systems, even if contributed by multiple sources as Knowledge Graphs [14], are examples of such kind. Most often, knowledge repositories of centralized information systems are databases where semantics is embedded in a combination of relatively stable logical schemas and lots of unconstrained (sometimes ephemeral) access and manipulation procedures. Database conceptual schemas, if present at all, are usually design-time artefacts which serve documentation purposes in the system’s life-cycle. In many cases, however, semantics is embedded in hidden procedures whose functioning is barely documented10 . In these cases, rather than promoting meaning agreements, centralized systems hypostasize the owners’ semantics, even in implicit and uncontrolled ways. In typical centralized scenarios, benefits of using ontologies may be found at both development and operative stages. At development time, ontologies serve as auditable conceptual models for engineers and stakeholders, who can therein express a system’s semantics in a declarative way. Under this respect, ontologies are the modern instantiation of software and data modelling tools, such as ER and UML. The ontological level, as characterized by Guarino, would improve the process of building and using such models. When they become operative, information systems should benefit from good conceptualizations both for users interactions (Business-to-Consumer) and third-party interoperability (Business-to-Business). Generally, when conceptualizing their business, centralized organizations keep epistemic and hermeneutical issues within the borders of operative departments, which therefore act (often implicitly) as “semantic authorities”. Semantic aspects of user interactions are otherwise addressed in non-functional analysis, including marketing and communication demands. The quality of meaning stipulations is largely addressed in software development activities, which are managed by strongly interconnected, mostly co-localized teams. In these activities, the need of a meta-level characterization of software artefacts such as database schemas or object models does not emerge, probably due to the ease of annotating them with natural language descriptions (e.g. API documentation). 3.2. Decentralized systems Decentralized systems are those in which there are no central nodes or controlling authorities, at least at a certain operational level. The original design of the World Wide Web is the paradigmatic example of such systems, as it has been conceived as a network of peer nodes (http servers). Distributed Ledgers (e.g. blockchains) are prominent instances of decentralized systems at the present time. Basically, the Semantic Web implements a distributed integration model. Although the W3C allows individuals and organizations to populate a namespace of Universal 10 In

popular culture, also known as “algorithms”.

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Resources Identifiers (URI)11 , the Consortium, by policy, does not dictate, recommend or overtly endorse any coherent and comprehensive collection of general ontologies. Google’s Knowledge Graph, in contrast, features a centralized integration pattern, because it assumes the worldwide adoption of a single conceptual model. The value of ontologies in decentralized models is universally acknowledged. All the Semantic Web endeavour, be it successful or not, revolves around sharing, or anyway manifesting, conceptual models called this way. Industry models developed within business communities12 , are nothing but “ontologies” specified by languages other than Description Logic. These shared conceptualizations (e.g. the United Nation’s models for the Coordination of Humanitarian Affairs13 ) are those that could most benefit from formal ontology, under the assumption that meta-properties such as rigidity or dependency can provide compelling guidance for the interpretation of the concept. The lack of formal characterization of shared conceptualizations of any kind (including those called “ontologies”) is probably due to trusting natural language more than intensional reasoning as a guarantee for the correct interpretation of predicate symbols. Moreover, since English has emerged as a sort of Western lingua franca, predicates of business information systems tend to melt into a specific natural semantics. The faith in English as a source of “universal semantics”, other than coarsely ethnocentric, would be utterly wrong, since vagueness and indeterminacy affect languages inherently and internally. In any case, if the need of characterizing concepts like student or person in a formal way is so rarely felt, this may be the consequence of a naive reliance on the binding force of linguistic meanings.

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4. Discussion If we read Quine’s famous definition to be is to be the value of a variable [15] as an equivalence between existing and being a distinguished subject of predication, and agree with it, then we could consider everything an information system quantifies on (e.g. by querying it) as, ipso-facto, an entity. This “logical point of view” (which is normally associated to relativism [16]) is probably the most popular one among information systems’ designers. In this view, ontological commitments taken by designers amount to a number of practical decisions on what is to be represented and handled. These decisions are then instantiated in database tables, nodes in knowledge graphs, classes in objectoriented systems, concepts in description logic terminologies, and software data structures in general. For instance, committing to universals like “redness”, which are shared by all the red things, rather than individual properties (tropes) such as “colour” which may possibly assume a distinct value in the region of “red” [17], is a matter of designing how the system is supposed to work with colours: whether individual chromatic qualities are to be represented, different nuances of the same colour are to be distinguished, and so on (see Figure 1). These practical representational choices, which meet a system’s functional requirements, have to be dealt with by users within information ecosystems. However, the possibility to set up hermeneutical assessments to make sure that users understand the concep11 https://www.w3.org/TR/xml-names11/ 12 e.g.

https://www.ibm.com/analytics/industry-models https://www.unocha.org

13 OCHA,

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Car

Red Thing

Car

Colour Property

Car

Red

My car

255,0,0

has-colour

My car

My car

Colour Value

has-colour

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Figure 1. Committing to colours

tualization the exact way it is intended by designers is problematic. In centralized systems, the intended meaning of predicate symbols and individual names may be dictated, enforced or at least supervised by systems’ designers. Users and content providers are supposed to understand them, or at least recognize all misunderstandings. In decentralized systems, on the other hand, ontologies supply shared conceptual vocabularies whose extensional semantics is established at the level of local interpretations, for instance by mapping legacy databases [6]. In either case, the inscrutability of reference [18] is lurking: even in ideal settings, ensuring the very same interpretation of constants and predicates by every involved agent faces epistemic limits and hermeneutical indeterminacies, as many philosophers have pointed out in the historical debate about skepticism [19]. For sure, generally viable socio-technical processes to make generative or interpretative acts transparently auditable by any communicating agent in every condition have never been experimented with yet. Imagine an Inuit e-commerce site which sells white shirts described on the basis of native capability of discriminating white nuances14 . Most probably, Inuit designers would consider mapping their rich “whiteness language” to a simpler, internationally standardized (English) one. Still, they could hardly figure out heuristics to make sure that their mapping extensionally runs worldwide: will customers in Kenya, for instance, be calling “ice white” colour nuances in the very same spectrum as them? Thanks to their informative power, a number of centralized systems technically actualize “Foucaultian conditions”, i.e. forms of authoritative control of the public discourse which may influence (or even determine) meaning formation processes by shaping the “informative environment” and thus constraining people’s choices [20]. Decentralized systems, on the other hand, require social semiotic deals, but, as a matter of facts, they operate on the basis of radical translations [18], i.e. arbitrary interpretations of others’ statements, driven by specific practical purposes and affected by mistakes or biases of any kind. In this picture, ontologies should help centralized systems who try to meet users’ semantic habits, as well as decentralized systems who strive to moderate the radical arbitrariness of each others’ interpretation. But by virtue of what, exactly? The use of formal ontology in information systems involves a sort of descriptive metaphysics15 , that is, a second-order account of linguistic (in the broad sense of socially grounded) conceptualizations. The vision that, when used outside the boundaries where it has been conceived, such a formal characterization would make a software conceptual model interpretatively cogent, can be enrolled in the realistic vein of the analytic tradition [11]. Basically, the idea is that linguistic concepts are bound to essences which lie beyond 14 After Franz Boas famous studies on American Indian languages (1911), scientists discovered that lexical competences about snow of native Americans were also somehow related to specific cognitive capabilities. 15 The definition comes from Strawson [7].

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language, and this binding (adaequatio rei et intellectus) has a definite direction: interpretation should eventually conform to reality. However, even accepting realism without qualms16 , when it comes to be put into practice, this conformance proves to be at least problematic. Even the core notion of rigidity, empirically assessed in cognitive sciences and linguistics [22], requires non-obvious choices when applied to information systems. In the next section, the problem of applying formal ontological analysis to conceptualizations is discussed in the specific case of (so called) “linguistic ontologies”. While these ontologies represent a niche, they paradigmatically exhibit problems that affect any common sense (i.e. non-scientific) conceptual model which may be used by agents operating in different contexts.

5. Linguistic knowledge In [3], a group of ontologists including Guarino revised WordNet’s “top level” in the light of OntoClean’s methodology. Among other problems, the revision spotted violations of the rigidity subsumption constraint17 : for instance, the lexical concept of Person (utterly rigid) was subsumed to Causal Agent (allegedly non-rigid).

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Someone could argue that every person is necessarily a causal agent, since agentivity (capability of performing actions) is an essential property of persons. Causal Agent should therefore be intended as a synonym of intentional agent, and considered as rigid. But, in this case, it would have only hyponyms denoting things that are (essentially) causal agents, including animals, spiritual beings, the personified Fate, and so on. Unfortunately, this is not what happens in WordNet: Agent, one of Causal Agent hyponyms, is defined as: “an active and efficient cause; capable of producing a certain effect; (the research uncovered new disease agents)”. Causal Agent subsumes roles such as Germicide, Vasoconstrictor, Antifungal. Instances of these concepts are not causal agents essentially. This means that considering Causal Agent as rigid would introduce further inconsistencies. Observe how the authors maintain that nouns such as germicide denote roles instead of substances. No one doubts that this is ontologically sound, since these nouns refer to the way certain substances (say, sodium hypochlorite) are usually, but not necessarily, employed. Still, since WordNet’s main purpose is to represent linguistic knowledge and support language processing, it may be useful (or at least tempting), to account for statements like: sodium hypochlorite is a germicide

(2)

so as to have the definiendum as a good subject filler for agentive verbs, as in: sodium hypochlorite killed all the germs.

(3)

Thanks to some common-sense reasoning, in fact, the sentence can be readily intended as 16 Influential 17 A

realistic positions are those of Barry Smith [21]. non-rigid concept can be subsumed to a rigid one, but not the other way around [9].

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someone or something caused sodium hypochlorite to kill all the germs

(4)

thus justifying the “ontologically coerced” (metonymic, in this case) use of the noun. Ontologists recommend removing WordNet’s subsumption of essential properties to non essential ones (roles), but of course this may lead to significant information losses. At first sight, the problem here is at least twofold: on the one hand, in sentences like (2), is a is read as a categorizing copula; on the other hand, categorization takes the logical form of an inclusion axiom. Most probably, in statements like (2), the verb to be should be intended in a telic sense, specifically in relation with the semantic field of USAGE:

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sodium hypochlorite is used as germicide.

(5)

This way, the substance-role inclusion would actually disappear, as requested by formal ontology, but a material relation (is used as) would take its place. Of course, this is not the only option. For instance, one may adopt a weaker logical interpretation of the hyponymy relation by resorting on typicality logics [23]. In this case, sodium hypochlorite could be seen as a typical germicide, without breaking OntoClean rules. The pervasive use of the verb to be18 is a source of troubles when modelling linguistic knowledge with logical devices, and has been subject of classic, extensive studies [24]. Likewise, ontologizing linguistic senses requires special attention, since, as linguists have always pointed out, lexical semantics cannot straightforwardly be reduced to mappings words with extensionally interpretable predicates [25]. Semiotic approaches to lexical concepts are accounted for in various formal models [26]. Also, standardization proposals developed by the W3C OntoLex community19 [27,28], as well as language specific initiatives such as Senso Comune (“Common Sense”) [29], developed models in which ontological categories are kept separated from linguistic meanings. Basically, in these models, meanings and categories are different kinds of entities, connected by a material relation (i.e. a first-order binary predicate subject of interpretation) which expresses the fact that words used in a certain sense typically refer to entities of a given category. In Senso Comune, this relation is called characterization, to recall the constructive import of linguistic practices, and is defined on the class of lexical meanings (linguistic senses) and a small set of ontological categories. For instance, Sodium Hypochlorite characterizes either a Substance or a Causal Agent, or both: Sodium Hypochlorite  ∀characterize.(Substance Causal Agent)

(6)

. Similarly to formal qualia of generative lexicon [30], to which Senso Comune is indebted, these relations bring ontology into semiology. However, as lexical concepts, meanings are not supposed to have any direct interpretation on extra-linguistic entities. Instead, they capture the fact that using certain expressions with specific purposes in given contexts presupposes the existence of entities belonging to distinguished categories. The list of such categories represents, strictly speaking, the very ontological commitment behind linguistic senses. The extensional separation of meanings and categories in fact reflects Quine’s distinction of ideology from ontology [31,32], insofar it acknowl18 “Being

is said in many ways” (Aristotle).

19 https://www.w3.org/2016/05/ontolex/

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edges the separation (and yet the relation) between “what is there” and how we talk (or even think) about it. How and to what extent formal ontology can help filling an appropriate list of such categories is an open philosophical question. In any case, when adopting a sort of modified nominalism as in [29], which consists in considering universals as a minimal set of theoretical constructions, the scope of formal ontology becomes limited to the realm of (hypothetical) categories of being, instead of spreading through the whole inventory of linguistic concepts. The case of linguistic knowledge suggests that, when dealing with socially constructed conceptualizations, formal ontology may help understanding problems, but does not offer, per se specific solutions. In this respect, it appears to be a “negative discipline”. On the other side, top-level ontologies play a crucial role by providing perspicuous semantic primitives. However, compiling such ontologies requires investigations that have been going on for centuries, often failing under discredit.

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6. Conclusion Ironically, ontology has gained a broad acceptance by information system developers, but mostly at a linguistic level. Does it mean that formal and metaphysical notions do not matter at all in information technologies? This brief note about the question has focused on attempts to turn lexical resources like WordNet into ontologies. But remarks presented here can be to some extent generalized, since a wide array of information systems, implemented under many different socio-technical conditions, deal with representational structures that are intimately connected to linguistic mediations. The conclusion is that, for these systems, formal ontology may certainly apply to core categories, wherever they are in place. However, in many scenarios and for most ordinary concepts, its scope is limited by the inscrutability of local interpretations, especially for decentralized systems and distributed mappings, as in the case of Semantic Web applications. Information systems based on highly formalized knowledge, on the other hand, inherit ontological commitments from scientific theories (e.g. biology or physics) they are built upon. There’s no doubt that, under the pressure of digital transformations, ontological analysis may play a role in revising scientific terminologies in many fields20 , but this specialist work is apparently feasible without the support of featured ontology devices, such as (real) ontology languages and development environments. This conclusion seems to be quite negative about the “proof of facts” that formal ontology, as a tool for information technology, has been going through in the last two decades. Conversely, the relevance of material ontologies seems to have a positive outlook in the future AI. In fact, large-scale research of data-driven approaches to knowledge construction, mostly based on unprecedented machine learning capabilities, is increasingly aware of how hard it is to acquire “common sense” knowledge from text sources [33] just relying on statistical methods. Data scientists using Machine Learning techniques, along with their customers, are starting to take model interpretability quite seriously [34], and this will unavoidably raise ontological questions. Rather than “the end of theory”, Big Data are accentuating the need for more effective and comprehensive theories on “what there is” and how to conceptualize it. In this scenario, formal ontology, as a descriptive metaphysics, has a rosy future as one of the most fundamental tools. The 20 e.g.

The Open Biological and Biomedical Ontology (OBO), http://www.obofoundry.org

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conceptual models needed to make sense of statistical outcomes will primarily focus on material aspects. Nonetheless, as Achille Varzi has written: the idea that material ontology and formal ontology could be worked out separately is either illusory or doomed to yield pretty poor theories on each side. [35] In building ontologies, formal and material plans (i.e. roughly, meta-level and objectlevel) are intertwined, since choices on the one level are reflected on the other one. The reason why formal ontology enters the process of building high quality material ontologies, however, has probably little to do with the mutual acknowledgement of intended interpretations for predicative symbols by communities of agents. Such diffuse, critical use of metaphysics is absolutely commendable, but finds its limit in the inscrutability of implementation practices, especially, but not exclusively, in decentralized settings, thus proving hardly feasible in most architectures and common socio-technical conditions. As a matter of facts, ontologies are mainly used to assert specific views on reality, which are functional to purposes and interests. It is a political question to make these purposes and interests transparent to communities of users and societies in general. Formal tools, if properly used, will make these views more sound and empirically effective, thus improving transparency and interoperability. Coming to the point of telling why formal ontology has not yet fully entered the information technology industry, the first and foremost reason seems to be the confusion, and indeed the collapse, of ontology and lexical semantics (or, to use the Quinean terms, ontology and ideology), not only in linguistic resources but in most business conceptualizations. Setting (always hypothetical) categories of being apart from socially mediated concepts, and then putting the two layers in the proper relation, seems to be a crucial move for making further steps towards better conceptual models in information systems, along the way Nicola Guarino has opened.

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References [1] [2]

[3]

[4] [5]

[6] [7] [8] [9]

N. Guarino. The Ontological Level. In: Casati, R., Smith, B., and White, G., editors, Philosophy and the Cognitive Science, pages 443–456. H¨older-Pichler-Tempsky, 1994. N. Guarino. The Ontological Level: Revisiting 30 Years of Knowledge Representation. In: A.T. Borgida, V.K. Chaudhri, P. Giorgini , and E.S. Yu, editors, Conceptual Modeling: Foundations and Applications. Lecture Notes in Computer Science, vol. 5600, pages 52-67. Springer, 2009. A. Gangemi, N. Guarino, C. Masolo, A. Oltramari, and L. Schneider. Sweetening ontologies with DOLCE. In: A. G´omez-P´erez, V.R. Benjamins, editors, Knowledge Engineering and Knowledge Management: Ontologies and the Semantic Web, EKAW 2002. Lecture Notes in Computer Science, vol. 2473. Springer, 2002. G. Guizzardi. Ontological foundations for structural conceptual models. Telematica Instituut / CTIT, 2005. R. Gupta, A. Halevy, X. Wang, S. Whang, and F. Wu. Biperpedia: An Ontology for Search Applications. Proceedings of the 40th International Conference on Very Large Data Bases (PVLDB), pages 505–516, 2014. M. Lenzerini. Ontology-based data management. In: Proceedings of the 20th ACM international conference on Information and knowledge management, pages 5–6, 2011. P.F. Strawson. Individuals. Methuen, 1959. D. Wiggins. Sameness and Substance. Blackwell, 1980. N. Guarino, and C. Welty. Evaluating Ontological Decisions with OntoClean. Communications of the ACM, 45(2):61–65, 2002.

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[29] [30] [31] [32] [33]

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N. Guarino, D. Oberle, and S. Staab. What Is an Ontology? In: S. Staab and R. Studer, editors, Handbook on Ontologies, International Handbooks on Information Systems, pages 1–17, Springer-Verlag 2009. J. Dejnozka. The Ontology of the Analytic Tradition and its Origins: Realism and Identity in Frege, Russell, Wittgenstein, and Quine. Rowman and Littlefield Publishers, 1996. T.J. Taylor. Mutual Misunderstanding: Scepticism and the Theorizing of Language and Interpretation. Duke University Press, 1992. G. Vetere and M. Lenzerini. Models for semantic interoperability in service-oriented architectures. IBM SYSTEMS JOURNAL , 44(4), pages 887–903, 2005. J.Z. Pan, G. Vetere, J.M. Gomez-Perez, and H. Wu, editors. Exploiting Linked Data and Knowledge Graphs in Large Organisations, Springer 2017. W.V.O. Quine. On What There Is. The Review of Metaphysics, 2(5):21–38, 1948. W.V.O. Quine. Ontological Relativity and other Essays, Columbia University Press,1969. C. Daly. Tropes. In: D.H. Mellor and A. Oliver, editors, Properties, pages 140–159, Oxford University Press, 1997. W.V.O. Quine. Word and Object, MIT Press, 1960. P. Klein. Skepticism. In: E. N. Zalta, editor, The Stanford Encyclopedia of Philosophy, Stanford University, 2015. M. Foucault. Discourse on Language (L’Ordre du discours), Gallimard, 1971. B. Smith. The Benefits of Realism: A Realist Logic with Applications. In. K. Munn and B. Smith, editors, Applied Ontology: An Introduction, Ontos, 2008. E. M. Markman. Categorization and naming in children, MIT Press, 1989. D. Lehmann. Stereotypical reasoning: logical properties. Logic Journal of IGPL, 6(1):49–58, 1998. R. Jackendoff. Semantics and Cognition, MIT Press, 1983. C.K. Ogden and I.A. Richards. The Meaning of Meaning: A Study of the Influence of Language upon Thought and of the Science of Symbolism, Harcourt, Brace and World, 1923. J.A. Bateman. Upper Modeling: organizing knowledge for natural language processing. Proceedings of the 5th International Natural Language Generation Workshop, 1990. J. McCrae, J. Bosque-Gil, J. Gracia, P. Buitelaar, and P. Cimiano. The OntoLex-Lemon Model: development and applications. s://john.mccr.ae/papers/mccrae2017ontolex.pdf, 2017. P. Buitelaar, P. Cimiano, J. McCrae, E. Montiel-Ponsoda, and T. Declerck. Ontology lexicalisation: The lemon perspective. WS 2 Workshop Extended Abstracts, 9th International Conference on Terminology and Artificial Intelligence, TIA, 2011. G. Vetere, A. Oltramari, I. Chiari, E. Jezek, L. Vieu, and F.M. Zanzotto. Senso Comune, an Open Knowledge Base for Italian. Traitement Automatique des Langues (TAL), 52(3), 2011. J. Pustejovsky. The Generative Lexicon, MIT Press, 1995. W.V.O. Quine. Ontology and Ideology. Philosophical Studies, 2(1), 11–15, 1951. L.B. Decock. Trading Ontology for Ideology: The Interplay of Logic, Set Theory, and Semantics in Quine’s Philosophy, Springer 2002. X.L. Dong, E. Gabrilovich, G. Heitz, W. Horn, N. Lao, K. Murphy, T. Strohmann, S. Sun, and W. Zhang. Knowledge Vault: A Web-Scale Approach to Probabilistic Knowledge Fusion. Proceeding of the 20th ACM SIGKDD international conference on Knowledge discovery and data mining, KDD ’14, pages 601–610, 2014. F. Doshi-Velez and B. Kim. Towards A Rigorous Science of Interpretable Machine Learning. arXiv:1702.08608, 2018. A.C. Varzi. On the Boundary between Material and Formal Ontology. In B. Smith, R. Mizoguchi, and S. Nakagawa, editors, Interdisciplinary Ontology, Vol. 3, Keio University, 2010.

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IV. Ontological Categories and Relationships

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Guarino’s Possibilism Antony GALTON 1 Department of Computer Science, University of Exeter, UK Abstract. In this paper I examine Guarino’s recent tensed account of the semantics of ongoing and future occurrence identifiers, with an emphasis on placing his proposals in the context of the doctrines of eternalism, possibilism and presentism that have been variously espoused by philosophers of time.

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Keywords. events and processes; ongoing and future events; philosophy of time

§1. How do we refer to events which have not yet happened, or which are in the process of happening but not yet finished? This question is the focus of an extremely interesting recent paper by Nicola Guarino [1], which engages with some of the profoundest questions in the philosophy of time while at the same time having an immediate practical bearing on formalising the ontology and semantics of information systems which require reference to future or ongoing events. Such systems include, to cite Guarino’s own examples, management systems for such diverse topics as flight reservations, football matches, news, business processes, and financial risk. In relation to the first of these examples, the flight reservation system, Guarino considers the properties associated with a particular flight. To be concrete, let us take the Emirates flight EK778 from Dubai to Cape Town, scheduled to depart at 10.25 from Terminal 3 on 16th September 2018, and to arrive at 18.10 (local time) the same day. At the time of writing, this flight has not yet occurred; but because it is scheduled to occur, we naturally refer to it as a future event. But when the time comes, this flight might be delayed or cancelled. If it is delayed then some of its actual properties—such as the departure time—may differ in point of detail from its scheduled properties; and if the flight is cancelled then there will be no actual event corresponding to the scheduled event, and the unique identifier associated with the latter will turn out to be an empty name. But by the time this article is published, it will be known whether or not the scheduled flight occurred, and if it did, all the detailed properties of the actual occurrence will be known, or at least knowable in principle: in any case, regardless of what we know, there will be a fact of the matter as regards each of these properties. As Guarino notes, these properties include ‘local’ properties such as the speed at any particular moment during the flight, ‘cumulative’ properties such as the distance covered so far at each moment, ‘contextual’ properties such as the weather during the flight, and ‘modal’ properties such as “the possibility, for an ongoing trip, to miss the next connection”. In our everyday understanding of time we tend to think of most of these properties as somehow ‘fluid’, meaning that they are not fixed in advance but are subject to the vagaries of ‘how things turn out’. This way of thinking about the future is clearly in accordance with brute epistemic uncertainty, the fact that at a given time we 1 E-mail:

[email protected]

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do not know, and seemingly cannot know, exactly what the future holds. But by refining our understanding of the causal order of things, and our ability to observe in sufficient detail the minutiae of the present situation, we can improve our predictive capabilities to the point where many more future events become known to us with certainty or at least with a high degree of probability. From the fact that we can often predict future events with a remarkable degree of accuracy, one is easily tempted to suppose that future events are in some sense already fixed, and that it is only our limited ability to know them which leads us to believe that at least some future events are intrinsically undetermined before they occur. This doctrine of determinism has, of course, been vigorously disputed for many years. It is generally claimed that science supports it, not only by uncovering ever more causal laws underlying the observed phenomena, enabling ever more accurate forecasting, but also because it seems hard to reconcile the idea of a genuinely open future with well-established tenets of the Special Theory of Relativity. On the other hand science is also claimed to refute determinism as a result of the inherently probabilistic nature of Quantum Mechanics. §2. It is natural to align these two points of view—the fixed future of determinism, and the open future of the opposing doctrine—with the philosophical positions of eternalism on the one hand, and possibilism (or, more extremely, presentism) on the other. The eternalist holds that all of time in some sense ‘already’ exists, and that the distinctions we draw between past, present, and future are purely subjective and do not correspond to any features of objective reality. The possibilist holds that, on the contrary, this distinction is real, that only the past and present already exist, and that the future is, as it were, up for negotiation. The presentist narrows the scope of what exists still further: only the present exists, the past having no more reality than the future—or rather, such reality as may be ascribed to the past belongs solely to the traces that it has left manifest in the present.2 At first sight it may seem that the eternalist must also be a determinist, but depending on exactly how the latter doctrine is interpreted this may not be quite right. The determinist, as usually understood, believes that all events are completely determined by earlier events in accordance with binding causal laws; but an eternalist who wishes to repudiate determinism could claim that an event might be timelessly fixed without this being so by virtue of causal relations it exhibits to preceding events. Again, the assumption that all events, past, present, and future, are in some sense fixed does not necessarily mean that the distinction between past, present and future is purely subjective. The ‘moving spotlight’ theory of time holds that although the course of time is fixed, successive portions of it become fleetingly present (as if ‘lit up’ by a spotlight), and, on at least one version of the theory, this transient presentness is perfectly objective (see, for example, [3]). Guarino’s paper, however, is premised on the assumption of possibilism: past, present and future are objectively meaningful categories, and whereas the content of the past and present are fixed, the content of the future is not, or not entirely. On this view 2 The terms “eternalism” and “presentism” are well-established, and there is a reasonable degree of consensus as to what doctrines they refer to [2]; I have the impression that “possibilism” is less widely used, and that there is less agreement as to what it means. It can be used to denote the antithesis of determinism, or of actualism, and, outside philosophy, in various other ways. The sense intended here could be called “past-and-presentism”, contrasting the reality of the past and present with the unreality of the future; it is often known as the “growing block” theory. This view is not incompatible with determinism, but is unlikely to hold many attractions for the determinist, and it is clearly to the non-deterministic version that the term “possibilism” is most appropriate.

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time really does pass—this is not just a metaphor from our subjective experience. It is often said that as time passes, successive portions of the future become present and then past (i.e., ‘passed’), and that in passing from future to present, events and their properties become fixed. But this does not seem right: on a truly possibilist perspective, the future simply does not exist. As time passes, what is present becomes past, to be replaced by a succession of entirely new presents—these have not ‘come from the future’ since there is no future for them to have come from. When we talk about future events, what we are referring to are hypothetical constructs, built on the basis of our abilities, such as they are, to predict what new presents there will be, or our propensity to make plans, to hope, and to fear. In the flight reservation system, on a possibilist view, the future flight for which you book a seat is not a flight existing in reality, but only the idea of such a flight, an item in the airline’s schedule, its reality comprising not the physical movement of an aircraft but a commitment on the part of the airline to initiate such movement. Now imagine you are in mid-flight, somewhere over Africa. Does the flight exist now? Is it a real entity you can robustly refer to, more than the mere idea it was before? Part of the flight— from take-off to your present position—is certainly real, for the possibilist at least. It has definite attributes (the exact course taken, the speed and heading at each moment, the meteorological conditions encountered—and all the activities of crew and passengers), and these are forever unalterable, inalienable properties of the flight as a chunk of spatiotemporal reality. But so far it is an incomplete flight: while we think we can be reasonably confident of what will happen next, at least in rough outline (for only on that basis would we venture to board any flight at all), we believe, if we are possibilists, that the remainder of this flight does not yet exist as part of reality, and that therefore all of its properties are as yet indeterminate. In this situation, the flight is an ongoing event, and Guarino’s paper, as well as addressing the puzzle of what it means to refer to future events, also grapples with the way in which we refer to ongoing events, and what we can legitimately say about them. §3. In order to help us understand how we can refer to future and ongoing events, Guarino introduces a distinction between episodes and processes as two distinct kinds of event. Here it is necessary to sound a note of caution: the terms ‘event’, ‘episode’, and ‘process’ have all been used in various ways as terms of art by different authors, and it is therefore incumbent on any author who uses these terms to declare how they intend them to be understood. Guarino himself is fully alive to the necessity of this, as he informs us in his footnote 1, where he also tells us that he is using ‘event’ “as a synonym of ‘occurrence’ ”—in other words as a generic term to cover anything that can be said to take place in time. On this understanding, events include processes and perhaps even states as well. This is opposed to a stricter sense that is also current, by which events are contrasted with states and processes. For this narrower notion of event, the one that contrasts with, rather than includes, processes, Guarino uses the term ‘episode’, which he defines as “an event that requires completion” (i.e., a telic event, as opposed to atelic events such as he takes processes to be). For Guarino, episodes and processes differ in the way in which they become present. Processes, he tells us, “become present as soon as their first temporal part is present, and they remain present for an extended interval by embodying new temporal parts that accumulate Ontology Makes Sense : Essays in Honor of Nicola Guarino, IOS Press, Incorporated, 2019. ProQuest Ebook Central,

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with the previous ones so that processes are bearers of cumulative properties that may change over time.” [1, p. 483, italics original] By contrast, while like processes they “become present as soon as their first temporal part is present”, episodes remain only partially present until becoming fully present when their culminating part becomes present. This is in contrast to processes, which “are always fully present, since, whenever they are present, they have no parts that are not present yet”. Let us apply these ideas to the example of the flight considered earlier. Here it is useful to distinguish the flight, as an episode in Guarino’s terminology, from the process of flying. Guarino notes that

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“there is an important relationship between episodes and processes: for an episode to be present at t, there must be a corresponding realization process present at t. We shall say that an episode is gradually embodied by a process. When the embodiment is complete, the episode becomes fully present, so that we may say it is constituted by a process that is temporally co-located with it.” [1, p. 484, italics original] Thus when flight EK778 takes off, a flying process comes into being that is fully present from the moment of take-off for as long as the plane remains airborne. The flight itself, which is the episode ultimately constituted by that process, becomes partially present at the moment of take-off, and then becomes gradually embodied by the ongoing flying, all the while remaining only partially present, until the moment of landing, at which the flight becomes fully present. What is not clear from Guarino’s paper is what happens after that: after the plane has landed, the flying process ceases to be present, and presumably this is also the case with the flight itself, which is now past. If this is right (as seems plausible), the flight is only fully present at the moment of completion, as the plane lands. Guarino cautions us not to confuse the term “fully present” with the more widelyused term “wholly present”. The latter is most often encountered in the context of the distinction between continuants (such as ordinary objects) and occurrents (i.e., events, processes, etc). Continuants are said to be “wholly present” at each moment of their existence, whereas occurrents—other than instantaneous ones, if such there be—have ‘temporal parts’ and are therefore never present as a whole at any moment. As Guarino puts it, the distinction between “wholly present” and “fully present” is that the former means that “all the parts are present” while the latter means that “there are no parts yet to be present (although some parts may be past)”. §4. Does this notion of full vs partial presence stand up to scrutiny? Consider first the flying process. At each moment when it is present at all, according to Guarino, this process is fully present, meaning that it has no parts that are yet to be present, although some parts may be past. Let us focus on two distinct moments during the flight, say t1 , when exactly one hour has elapsed since take-off, and t2 , when two hours have elapsed. Then on Guarino’s scheme we can say that at t1 the flying process is fully present, consisting of a present part—the flying at t1 —and indefinitely many past parts, namely the flying at each moment that one can pick out between the time of take-off and t1 , for example the flying that is present half an hour into the flight. What about the flying that is present at t2 ? Na¨ıvely one might suppose that at t1 this is a future part of the flying process, that is, a part that is yet to be present, but Guarino cannot allow this: since the flying is fully present at t1 it has, at t1 , no parts yet to be present.

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This need not be as crazy as it sounds; to make sense of it, recall my earlier characterisation of possibilism as holding that the future does not exist. Successive presents come into existence rather than being recruited from a pre-existing future. Thus we can say that the flying process continuously acquires new parts but at any given time the parts that will subsequently be added do not exist and hence cannot be said to be ‘yet to be present’. This means that qua process, the flying is at every stage already complete, being mostly past, with a present ‘leading edge’. By contrast, the flight remains incomplete until the final moment of touchdown. This is because this particular flight is defined as an episode, constituted by the flying taking place over a particular interval, that begins with take-off from Dubai and ends with landing at Cape Town. Both the take-off and the landing, and every stage in between, are essential parts of the flight, without which it would not be that flight. At t1 and t2 the flight is only partially present because although some of its parts are past or present, it has parts which are yet to be present—future parts—including in particular the culminating part which is the landing in Cape Town. In saying that at t2 it has future parts, we must not be understood as saying that there exist parts which it has yet to acquire, but rather something more like this: in order to become fully present the flight must acquire new parts, of a specified type, that do not yet exist. §5. Let me now summarise my understanding of Guarino’s proposal as I have expounded it so far. Entities extended in time are called events; these may be divided into episodes, which are telic, meaning that they come with an inbuilt notion of completion, and processes, which are atelic, lacking any notion of completion. Of these, processes are the more fundamental, since episodes are constituted by processes. The occurrence of an episode may be likened to the enactment of some at least partially pre-ordained script, the parts of which, initially existing only in schematic form as abstract ideas, become successively realised in the medium of some ongoing process or processes. If the whole script is enacted, then the episode is said to be completed; but this is not inevitable, and an episode might remain forever incomplete because some end portion of it fails to be realised by any process (this would be the case, for example, if a flight crashes before reaching its destination3 ). Guarino likens a future episode to an empty lake-basin, devoid of water. The enactment of the episode corresponds to the gradual filling of the basin with water; the continuously-increasing quantity of water in the lake at any time corresponds to the growing process which, when complete, constitutes the episode. He admits that the analogy is not strict: in the case of the lake, once it is full, the water is all present in the lake at the same time; whereas the parts of the process that “fill” the episode are present only successively, each at a different time. And a lake, once filled, can dry up again, and then become filled for a second time; whereas an episode, once it has occurred, is forever “frozen” and cannot be repeated—although of course a different, but similar, episode could occur, corresponding to the filling of a different, but similar, lake basin. Guarino borrows the notion of “variable embodiment” from Fine [4] and Moltmann [5], noting that ongoing events “change by embodying temporal parts as time passes by” and conceiving of future events as “empty embodiments”. 3 But see also footnote 6. Happily, I can report that for the flight we are considering this did not occur: I was on that flight and arrived safely in Cape Town.

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It seems to me that there is much to commend in Guarino’s account; yet at the same time it is in some respects problematic. In the remainder of this paper I shall adopt a more critical attitude, pointing out what I believe to be flaws in the account, and suggesting revisions in order to overcome them. §6. The lake-basin analogy seems particularly apt for events which are scheduled to occur at a particular time—the lake-basin, which fixes a particular spatial location for the lake, is like a fixed slot in the calendar marked out for an episode to occur in. Some of Guarino’s examples of episodes are of this type—as well as the flight, for example, he mentions “a future football match”, presumably one scheduled to occur at a particular time and place. But he gives other examples of episodes which do not fit so well into this mould: a run to the station, running for an hour, or just sitting for an hour (the last of these illustrating the fact that an episode need not be dynamic). These last two examples, it seems to me, should give us reason to draw the distinction between processes and episodes differently from how Guarino does it. If Nicola says “I shall run for an hour” and does so, then afterwards I can say that he ran for an hour, and in this case we do have the enactment of a preconceived plan, where the completion is as it were scheduled from the start, making the event telic; as such, this running for an hour should count as an episode for Guarino, and is appropriately included amongst his examples. But suppose instead that Nicola simply starts running with no thought for how long he is to continue; if he stops running after an hour I can again say that he ran for an hour, in this case without there being anything by way of a schedule or plan in accordance with which exactly this occurred. At the end of an hour there is a cessation of running, but it does not seem appropriate to call this cessation a completion, since no termination conditions have been in any way laid out in advance. In this case, therefore, the hour of running cannot be called a telic event and therefore in Guarino’s scheme should not qualify as an episode. And yet, viewed from the outside, with no knowledge of Nicola’s intentions, the two cases are indistinguishable. For Guarino, it seems, the planned running-for-an-hour is an episode, whereas the unplanned one, being atelic, must be a process—just a running which happens to last an hour. But both cases involve the process of running: in Guarino’s account, the runningfor-an-hour episode is embodied by the process of running: there is an hour’s slot marked out in time from the point at which Nicola first starts running with the intention of continuing for an hour, and as the hour elapses this slot is cumulatively “filled”—or “embodied”—with actual running. The only difference in the atelic case is that the timeslot is open-ended: it is not completely specified from the start. But again we have a durative event, with a beginning and an end, which is constituted by the process of running. §7. In the light of this, it seems that Guarino’s use of the term “process” to denote an atelic event should be set alongside an alternative notion of process that is in an important sense more fundamental. A process in Guarino’s sense is similar to a telic event, or episode, except that its termination is not understood to count as the completion of anything. A typical example of such a process might be an hour’s worth of running by Nicola; with this conception of process, it makes perfect sense to speak, as Guarino does, of “temporal parts” of a process. The more fundamental notion of process I alluded to above picks out, not the hour’s worth of running, but running itself, that activity of which the atelic event is equated to an hour’s worth. For this notion of process, which seems to be missing from

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Guarino’s account, it does not make sense to refer to temporal parts. To see this, we can revert to the lake analogy, where it clearly makes sense to speak of the parts of a body of water such as a lake, but it does not make sense to speak of “parts of water”. If anyone asked me what the parts of water are, I could only make sense of this as an inquiry into its chemical composition, the parts of water in this sense being hydrogen and oxygen. The distinction being drawn here is thus between a body of water, which clearly has parts (these are spatial rather than temporal parts), and water, which designates a type of matter, to which it does not make sense to attribute parts in this sense. Analogously, then, we should distinguish between a bout of running, which has temporal parts (e.g., the first, middle, and last third), and running, which designates a type of activity, which does not.4 And just as a body of water is made of water, so a bout of running is “made of” running—that is, it exists by virtue of running occurring over the duration of the bout. This contrast between the two senses of process—Guarino’s and mine—is reflected in the use of the expressions “constituted by” and “made of”. Just as we might say either that a vase is constituted by a certain quantity of clay, or, simply, that it is made of clay, so we might say, following Guarino, that a particular flight is constituted by an hour-long flying process, or, following me, that it is “made of” flying. And just as the notion of clay is surely more fundamental than that of a quantity of clay—since the latter can hardly be defined without making use of the former—so, analogously, the notion of flying is more fundamental than that of a bout of flying. I used the word “bout” to describe a stretch of time filled with a particular activity, but this is perhaps not the most felicitous choice of word for this. A more appropriate word to convey this idea, it seems to me, is “episode”, but in the present context I hardly dare court confusion by using this, since not all episodes in this sense would count as episodes in Guarino’s sense, lacking the defining property of telicity. Having duly noted this, however, I shall from now on depart from Guarino’s usage and use the terms “process”, “episode”, and “event” in the following senses. A process is an ongoing activity, wholly present from moment to moment for as long as it persists; as such, it does not have temporal parts, any more than a person or a building does.5 An event is something that happens: it has a beginning and an end (which in the exceptional case of instantaneous events coincide), and the time of the event is the interval spanned by these. For a process P, an episode of P is an event consisting of P’s starting, persisting for a while, and then stopping, without prejudice as to whether the stopping occurs in accordance with some pre-existing plan, schedule, or intention. Look at the world, and whatever you see going on is a process: but very often we describe what is going on in terms of some event which that process contributes to the realisation of. During the flight, what is going on is flying. But if I say that I am flying from Dubai to Cape Town, then I am characterising the flying that is currently going on as contributing to the realisation of a flight from Dubai to Cape Town, which, when 4 But again, by analogy with the chemical composition sense of “part of water”, the “parts of running” could be construed to mean, e.g., a forward movement of the left leg, a forward movement of the right leg, and any other bodily movement involved in the activity of running—note that these parts are as much spatial as temporal. 5 It is this—admittedly non-standard—notion of process that I have advocated elsewhere, in publications such as [6,7]; see also [8,9,10] for a similar view, and [11] for a (partial) critical rebuttal. In more recent publications [12,13] I have toyed with alternative notions of process, which are, however, no closer to Guarino’s; here I must confess that I do not yet have a “final” account of what processes are, and my view on the matter continues to evolve.

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completed, is an event.6 Note that one and the same episode of flying might be described as realisations of different event types, such as a flight from Dubai to Cape Town, a 7600 km flight, a nine-hour flight, someone’s first flight, or their last flight, or the second leg of a journey from London to Cape Town. Each of these descriptions picks out an event type, which may have any number of distinct instances constituted by different episodes at different times; an event token, that is, a fully particularised individual event, is an episode which answers to the description of some event type. §8. With this understanding of these terms, let us see how much we can retrieve of Guarino’s notion of events being “fully” or “partially” present. Regarding processes, ‘present’, as Guarino notes, essentially means ‘going on’ (or ‘ongoing’).7 This applies to processes in both Guarino’s and my senses, modulo a somewhat different understanding of what is meant by ‘ongoing’. In either case, a ‘past process’ can therefore only be understood as a process that was going on at some past time (with, perhaps, a strong suggestion that it is no longer going on), and similarly with future processes. For me, since a process is not the sort of thing to which it makes sense to attribute temporal parts, it makes no sense either to distinguish between full and partial presence of a process. A process just goes on; it is wholly present whenever it is present, and not by virtue of any past or future going on of the same process. With events it is different. Like processes, events can also be said to be going on. This is, perhaps, the prototypical use of the progressive aspect in English: “John is making a cake”, “Nicola is running for an hour”. What this means in each case is that, as regards some telic event type E, there is some ongoing process which has so far generated an incomplete episode which, given suitable future continuation of that process, could form an initial temporal part of some episode or set of episodes constituting an occurrence of E, and the circumstances are such as to lead one reasonably to expect that such continuation will occur, leading to a completed occurrence of E. I have elsewhere [14] discussed the kind of circumstances which can give rise to a “reasonable expectation” of such completion. The prototypical case is where the event in question is the intentional act of some agent; in that case it is the apparent or inferred existence of the intention that constitutes the relevant circumstances. But causality, or perhaps other factors, can take the place of intention here (for a discussion of some possibilities, see [14, chapter 7]). To be going on is one way for an event to be present; for Guarino, when an event is going on, it is ‘partially present’. Only at the moment of completion does it become ‘fully present’. Arguably, though, at the moment of completion the event becomes fully past. There is nothing wrong with Guarino’s intuition here: but his terminology is confusing. It would be better, I think, to use his idea of embodiment rather than presence and say that an ongoing event is partially embodied, and when it reaches completion it becomes fully embodied. A fully embodied event is thus necessarily in the past. The moment of completion is precisely the moment at which the event ceases to be ongoing (and thus in some sense present) and becomes wholly past. Instead of ‘embodied’ we could equally well say ‘realised’. 6 Indeed, should it not be completed, by termination in an unexpected way—e.g., the flight is diverted to Durban, or crashes—that too is an event, but not one answering to the description of “flight from Dubai to Cape Town”. 7 In fact, he puts it the other way round: “for processes, being ongoing is just synonym of being present” [1, p.484].

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What can we say about future events? Sometimes we can have a reasonable degree of certainty that some event will occur, even though we may be uncertain about exactly how it will occur. The failure of a predicted eclipse might require radical revision of our astronomical theories; our failure to see it because of unexpected cloud is much less drastic. Here we are dealing with events governed by the laws of physics; whether or not all future events are fully determined, many can be known with a high degree of confidence, justifying us in saying that such-and-such an event will occur, even that it will occur at a precisely specified time. With events governed by human plans, schedules, or intentions, there may be more or less certainty, but in practice we are often sufficiently certain of future events to allow them considerable influence in regulating our lives. But unless we are eternalists, we still believe that there is a difference between a past event that we have strong grounds for believing to have occurred and a future event which we are highly confident will occur. The former, we believe, is in the domain of the real (i.e., the realised); the latter does not yet form part of reality. We believe that there is something special about the present—“the now, the here, through which all future plunges to the past”8 —because it is where the embodiment or realisation of events happens. A future event, however much it is known, even in fine detail, is, precisely because it is future, unembodied. For the possibilist, this process of embodiment is an essential, objective feature of reality, and any account of the nature of time that fails to include it is necessarily incomplete. For the eternalist, on the other hand, embodiedness is a subjective feature: from the standpoint of an individual at a particular point in space and time, some events are embodied, others not, but this says nothing about the events themselves, only about the individual whose standpoint it is. The appearance of objectivity, on this view, is an illusion fostered by the fact that many individuals share similar standpoints: our timelines do not intersect, but remain close together, so we can agree about what is past, present and future. But note that it is I now who agree with you now: there is much less agreement between me now and you in ten years’ time. §9. It is, I believe, very difficult to characterise adequately this distinction between the past and future other than by gesturing towards our common experience of time; and such gesturing does not amount to a conclusive argument. For this reason, anyone seeking to develop a truly objective, scientific account of time feels a pressure to reject the distinction as some kind of subjective illusion, alien to the “true nature” of time itself. What objectively exists, on such a view, might be characterised as a “block universe” comprising innumerable spatio-temporal locations, at some of which there exists conscious awareness on the part of a given subject—here glossing over the difficulties of defining “a given subject”. The awareness that exists at a given location L encompasses sensations of both memory and expectation, where the former sensations for the most part bear a specific causal relation to the contents of awarenesses existing at locations in the backward-pointing portion of the light-cone centred on L, while the latter bear a rather more complex relation (involving beliefs, desires, intentions, hopes, fears, etc) to locations in the forward-pointing portion. On this view, the subjective impression of the passage of time is merely a consequence of the existence of such timeless relations between the contents of one’s awareness at different points in one’s history. In many information systems, the only difference between a record of a past event and a scheduled future event is that the former has a timestamp that denotes a time earlier 8 James

Joyce, Ulysses.

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than the time registered on the clock, whereas the timestamp of the latter denotes a later time. This fails to capture the idea, rejected by eternalism but embraced by possibilism, that the future is not yet fixed and that therefore the relation represented by associating an event with a future time differs fundamentally from that represented by associating it with a past time. Accounting for this difference is undoubtedly one of the prime motivations for Guarino’s paper. Guarino speaks of the “freezing” of events as they become embodied, reflecting the irreversibility of time. This notion, that the future remains fluid whereas the past is frozen, is central to possibilism. Traditional information systems, in line with the eternalist view, cannot make this distinction, instead effectively treating all of time as “frozen”. Guarino’s final rallying cry—“Let’s defrost events!”—calls, in effect, for information systems to embrace a possibilist view of time. The implied research programme involves the design and development of technical tools to support such a view. My philosophical instinct is to support this, but I believe the technical difficulties may be formidable.

Acknowledgments I should like to express my gratitude to the three anonymous reviewers of this paper, whose comments led me to think more carefully about some of the issues discussed here. As a result, I believe that the paper in its present form is a substantial improvement over the original submission.

References [1]

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[2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]

[13] [14]

N. Guarino. On the semantics of ongoing and future occurrence identifiers. In H. C. Mayr, G. Guizzardi, H. Ma, and O. Pastor, editors, Conceptual Modelling, Proceedings of the 36th International Conference, ER 2017, Valencia, Spain, November 6-9, 2017, pages 477–490. Springer, 2017. D. Ingram and J. Tallant. Presentism. In E. N. Zalta, editor, The Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University, spring 2018 edition, 2018. R. P. Cameron. The Moving Spotlight: An Essay on Time and Ontology. Oxford University Press, Oxford, UK, 2015. K. Fine. Things and their parts. Midwest Studies in Philosophy, 23(1):61–74, 1999. F. Moltmann. Variable objects and truthmaking. In M. Dumitru, editor, Metaphysics, Meaning, and Modality. Oxford University Press, Oxford, UK, 2014. A. Galton. Experience and history: Processes and their relation to events. Journal of Logic and Computation, 18(3):323–340, 2008. A. Galton and R. Mizoguchi. The water falls but the waterfall does not fall: New perspectives on objects, processes and events. Applied Ontology, 4(2):71–107, 2009. R. Stout. Processes. Philosophy, 72:19–27, 1997. R. Stout. The life of a process. In G. Debrock, editor, Process Pragmatism: Essays on a Quiet Philosophical Revolution. Rodopi, Amsterdam/New York, 2003. R. Stout. The category of occurrent continuants. Mind, 125(497):41–62, 2016. H. Steward. Processes, continuants, and individuals. Mind, 122(487):781–812, 2013. A. Galton. The dynamic present. In P. Hasle, P. Blackburn, and P. O. hrstrøm, editors, Logic and Philosophy of Time: Themes from Prior, Volume I, pages 167–187. Aalborg University Press, Aalborg, Denmark, 2017. A. Galton. Processes as patterns of occurrence. In R. Stout, editor, Process, Action, and Experience. Oxford University Press, Oxford, UK, 2018. A. Galton. The Logic of Aspect: an Axiomatic Approach. Clarendon Press, Oxford, 1984.

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Processes Endure, Whereas Events Occur Gilles KASSEL MIS Laboratory, Jules Verne University of Picardie, Amiens, France [email protected]

Abstract. The objective of the present essay is to clarify the nature of so-called ‘occurrences’ by attributing distinct modes of existence and persistence to processes and events. In doing so, we break away from the perdurance theory claimed by DOLCE’s authors, and we distance our self from mereological analyses (such as those recently used by Guarino to distinguish between ‘processes’ and ‘episodes’). In line with the work of Stout and Galton, we first draw a parallel with how processes and objects endure by proposing that processes have a dynamic presence (contrasting with a static presence for objects). Next, we give events the status of abstract entities by identifying them with objects of thought (by individual or collective subjects). This allows one to distinguish between the existence and occurrence of events. We therefore define the latter as psychological or even social endurants, which may occur contingently. Keywords. Process, event, object, fact, endurance, occurrence, occurrence-maker fact, intentional ontology

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1. Introduction Over the last few years, several new analyses of ‘occurrences’ (i.e. entities that are said to ‘happen’) have been reported in the field of Formal Ontology. Occurrences (also referred to as ‘perdurants’ and ‘eventualities’) correspond to entities that are just as diverse as processes, events, states, and changes of state. According to Antony Galton [1], these efforts are warranted; even today, the literature contains as many classifications as there are researchers. The problem is less our choice of the criteria but rather our imperfect understanding of the nature of ‘occurrences’. Significant work on clarifying the nature of processes was performed independently by Rowland Stout [2,3] and Galton [1,4] in the late 1990s and early 2000s. These researchers suggested a new conception of processes (which they likened to objects with regard to how they endure in time) that are ‘wholly’ present at every moment of their lives. This proposal is subject to debate. An important issue (in the eyes of the debaters) is whether or not processes are entities extended over time, having temporal parts. If they are, Helen Steward [5,6] suggests that processes should remain ‘occurrences’ that share some features of continuants (such as being able to change their properties over time). If not, Stout [7] suggests that processes should be ‘dynamic’ continuants. More specifically, for Stout [7], what matters is whether processes (like objects) have properties at times or atemporally. Nicola Guarino is also researching the nature of occurrents. As a co-author of DOLCE, Guarino’s analysis of occurrences was based on perdurance theory [8]. Recently, by building on his work with Giancardo Guizzardi and João Paulo Almeida

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concerning the conceptual modeling of business processes [9], Guarino proposed a refined mereological theory of DOLCE perdurants [10]. The objective was to better characterize two categories of occurrences: ‘processes’ and ‘episodes’ [10]. For our part, we recently tackled this topic by developing an ontological framework that is strongly inspired by Stout and Galton’s proposals [11]. The novel aspect of our proposal relates to our conception of events: whereas the event is conventionally (according to Donald Davidson [12]) conceived to be a concrete particular (and Guarino agrees with this conception), we consider events to be abstract entities by assimilating them to mental and even social entities. Historically, this point of view was defended in the 1970s by philosophers like Roderick Chisholm [13] and Neil Wilson [14]. More recently, Kathleen Gill argued that the only way to distinguish between processes and events in an ontological inventory was to consider abstract events [15]. Fundamentally, we consider that the value of this conception is its ability to distinguish between two frequently confused notions: the existence and the occurrence (in the sense of realization) of events. In this essay, we elaborate on our ontological framework whose basic commitments and main primitives are described in Sections 2 and 3, respectively. Our intention is to show that it is possible – and even preferable – to seek to clarify the nature of occurrences while disregarding the mereological dimension (following the option chosen by Stout [7]). In Section 4, we will focus on processes and events. With regard to processes, we will account for their endurance via the notion of a ‘dynamic’ physical presence (vs. the ‘static’ presence of physical objects). With regard to events, we will distinguish between the notions of logical existence and occurrence in order to describe them as psychological (or even social) endurants, which can occur contingently. To formulate these proposals, we will position ourselfs with respect to DOLCE and Guarino’s recent analyses.

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2. The basic commitments As a starting point, we adopt Strawson’s [16] use of descriptive metaphysics to account for “the actual structure of our thought about the world.” The objective is thus to establish categories and notions that reflect how we conceive the world.1 By adopting a contemporary perspective of ontology, we consider that the world is primarily structured by three types of reality: physical, mental and social. This division of reality is based on the recognition of distinct modes of existence, and prompts us (in our commitments) to carefully follow the border between facts and interpretations, as Maurizio Ferraris suggested [17, pp.72-74]: “Therefore, the point is not to claim that there is a discontinuity between facts and interpretations but rather to understand what objects are constructed and what ones are not. (...) This work consists in distinguishing carefully between the existence of things that exist only for us, that is, things that only exist if there is a humanity, and things that would exist even if humanity had never been there.”

1

In this respect, we agree with the direction also taken by the authors of DOLCE. However, we will see later (in Section 4) that the need to assign properties to ‘nonexistent’ entities will lead us to go beyond a simple ‘cognitive bias’ and to opt for an intentional ontology exclusively composed of intentional mental entities.

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Figure 1. The distinction between experiential and historical entities (from [1])

This meticulous investigative work takes us into the field of occurrents. An important first step, for us, is Galton’s proposal of replacing the conventional ‘continuant’ vs. ‘occurrent’ distinction by the EXP vs. HIST distinction (Fig. 1), i.e. a distinction between the world as it unfolds and its history [1, p.323]: “(…) processes differ markedly from events in their relation to change. Whereas events are fixed items of history which cannot be described as undergoing change, processes are more like ordinary objects in that they can be directly present at one time and can undergo change as time proceeds. This leads to a fundamental ontological distinction between EXP, the dynamic experiential world of objects and processes as they exist at one time, and HIST, the static historical overview populated by events that are generated by the ongoing process in EXP.” According to Galton, this distinction between processes and events comes down to an ontological distinction between two categories of entities populating the physical world; both entities are concrete individuals, as confirmed by Galton and Mizoguchi’s [18] support for the thesis in which events are constituted by processes. On the contrary, we intend to contrast the physical world with the mental and social worlds and, more precisely, to position events conceived as historical entities within the mental and social worlds [11]. Our ontological commitment can be summarized as follows: the history of the physical world consists of how the world evolves over time; to identify change (or, on the contrary, stability) requires the adoption of a viewpoint outside the physical world, and this is what subjects do, thanks to their memory and cognitive abilities; events are psychological and social constructs that enable subjects to interact with their environment.

3. Our ontological framework in a nutshell In this section, we provide an overview of our main ontological primitives2. To set the scene, we will pursue the following sequence: • The physical world is populated with substances – objects and processes – that (by enduring) ensure its stability and dynamicity (Section 3.1). 2

Due to space limitations, we have not justified the choice of these primitives, and just provide an inventory. Readers interested in justifications and positioning vis-à-vis alternative ontological commitments may refer to [11].

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•

•

Given that substances temporarily bear properties and maintain relationships with other substances, they have a life consisting of facts that exist in the physical world (for brute facts) and that may exist in the mental and social worlds (for social facts) (Section 3.2). Cognitive subjects are immersed in the physical world; through events, they represent the past, present and future history of the world, and interact with it (Section 3.3).

3.1. Substances

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To begin our inventory, we adopt a classic conception of the physical object as something that: (o_i) wholly exists at instants; (o_ii) has properties (e.g. color, odor, mass, and volume) at instants; (o_iii) may change over time. These properties express the conception of an entity that ‘wholly’ exists (i.e. through its full identity3) at instants and endures over time with properties that can vary over time. The properties (o_ii) and (o_iii) characterize the physical object’s life; we shall return to this aspect in Section 3.2. By extension, examples of physical objects are maximally connected objects, whether inert (e.g., a stone, an apple detached from the tree, a molecule of water and a planet), animated-alive (e.g., a human being, a flower and a tree) or artifactual (e.g., a chair, a clipboard and a television). We will see in Section 3.2 that artifacts are considered to be physical objects simpliciter endowed with a social life. The characterization of physical processes that we give below is largely based on the idea of dynamic continuants developed mainly by Stout [2,3], Galton [1,4], and (to some extent) by Galton and Riichiro Mizoguchi [18]. A physical process is something that: (p_i) wholly exists at instants; (p_ii) has properties (e.g. direction, speed of execution, sound level, and spatial amplitude) at instants; (p_iii) may change over time; (p_iv) is enacted by a physical object. The properties (p_i), (p_ii), and (p_iii) are the same characterizations as for the physical object – in other words, that of a substrate that bears properties. By extension, examples of physical processes include the movement of a physical object leading to the displacement or rotation of an object, the growth in size of a physical body, a person’s life process, the ripening of a fruit, the oxidation of a metal object, and the melting of a glacier. Property (p_i) is a strong commitment to the full existence of processes, in the sense of having a full identity. It is expressed by Stout [2, p.26]: “The phrase, ‘What is happening now’, is naturally taken to denote a whole process; and we do want to claim that what is happening now is literally identical with what is happening at some other time – the very same process.” 3

In Section 4.1, we return to the meaning of the term ‘wholly existing’. However, it should be noted here that the term is devoid of any mereological significance, be it spatial or temporal.

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This commitment is based on a specification concerning the nature of the process; the latter is a causal process in which properties are transformed. When an object changes location, this change results from movement of the object – the process.4 According to Stout, the endowment of a process with causal power is necessary to refute the Russellian conception of a movement as a series of successive states [3]: “[The] motion should not be understood in Russell’s way as the arrow being in one state and then in another and in the meantime being in all the intervening states. The arrow’s motion is what gets it through this continuous series of states – it effects the transition.” The properties (p_ii) and (p_iii) follow on logically, and continue to liken processes to objects, as Galton puts it [4, p.6]: “Like objects, processes can change: the walking can get faster, or change direction, or become limping. All around us processes undergo changes: the rattling in the car becomes louder, or change rhythm, or may stop, only to start again later. The flow of the river becomes turbulent; the wind veers to the north-west.”5 To conclude (for the moment) this characterization of physical processes, let us mention a last ontological commitment – property (p_iv). Namely, a process is not a continuant that floats in the air; it is necessarily ‘anchored’ in a support object: this is the movement of an arrow, the ripening of a fruit, the melting of a glacier, etc. To account for this strong constitutive link, we borrow the enaction relationship introduced by Galton and Mizoguchi [18]. According to the latter researchers, saying that an object ‘enacts’ a process amounts to saying that an object carries an ‘external’ process or a ‘behavior’ [18, p.94]: “The key notion is that an object, considered from a particular point of view, is characterized in terms of the processes it enacts. These are what we call the external processes or behavior of the object. This behavior arises as a result of various internal processes which causally contribute to it.” This enaction relation establishes an existential dependence between the process and the object. As we will explain below, enacting processes is part of an object’s contingent life.

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3.2. The life of substances At this point, our ontological inventory is composed of substances – physical objects and processes. Since these substances are entities that persist in time without losing their identity, they exist at different instants – prompting one to speak of their ‘life’. Intuitively, this term denotes what happens contingently to a substance between the moment when it acquires an existence and the moment when it ceases to exist. The properties (o_ii) and (p_ii) respectively characterize the basic bricks of the life of objects and processes. It must be noted that this presumes the existence of properties. 4

For further details on the nature of the process, we refer the reader to Carol Cleland’s [19] dispositional analysis. In this reference, Cleland’s contribution is to mobilize the physical sciences to give an explanation of the ‘real’ and continuous change and to justify, by the same, that a ‘causal process of transformation of properties’ finds a place in our ontological inventory. 5 This rapprochement was recently questioned by Thomas Crowther [20]. He considers that when a person starts to walk faster, we are dealing with a person with different walking speed properties at two distinct instants, rather than a temporal change in a walking process. This position is explained by Crowther’s denial of a process’s ability (p_i) to fully exist at times; he thus likens the process to a change that cannot itself change. The reader will note that we have chosen to identify the process as an entity causally responsible for a change, rather than a change per se – thus avoiding the risk of infinite conceptual regression.

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To bring them into our inventory, we will provide some details about their nature. Moreover, the brick itself expresses a temporal fact. In line with a conception that is now well established in metaphysics, we also add this primitive to our inventory. Lastly, what we refer to as the ‘life’ of a substance corresponds to the facts that accumulate during the substance’s existence. Let us start with properties, and with a terminological clarification: the term ‘property’ is commonly used to denote the universals (types) and tropes (instances) that characterize substances on one hand [21], and the concepts or categories that structure our representations and theories of the world on the other [22]. To distinguish between these two situations, we will use the terms ‘physical property’ and ‘conceptual property’, respectively. These properties have different modes of existence and attribution. As we will see later, the coherence of our ontological framework requires one to consider both categories of properties. In particular, for the notion of life that interests us in this paragraph, the distinction between these two categories of properties makes it possible to distinguish between a substance’s ‘physical’ life and its ‘social’ life. We will firstly consider physical properties whose existence is independent of human thought – an extensive account of these properties is covered in chapters 2 and 3 of reference [21]. In agreement with Peter Hacker [23], we consider that objects and processes bear different properties. The ‘way of being’ of a physical object (a person, for example) corresponds to properties/relations like ‘being anxious’, ‘being next to Mary’, and ‘walking’.6 For a process, examples of properties are ‘being fast’, ‘being noisy’, and ‘slowing down’. Secondly, we also identify conceptual properties whose existence depends only on human thought [24]. Typically, these properties correspond to functions that one assigns to physical objects (e.g., ‘being a table’ or ‘being a paperweight’) or processes (e.g., ‘being an endorsement’ or ‘being a threat’).7 We will now see that the distinction of modes of existence among properties is reflected by distinct modes of existence among facts. Having introduced properties, we will continue to expand the inventory by considering facts. The thesis whereby these entities exist (put forward by many philosophers, including Kit Fine [26] and David Armstrong [21]) complements the real existence (i.e. the ‘physical existence’) of properties: the simultaneous existence at a given instant of the substance ‘Paul’ and the property ‘being anxious’ does not mean that the substance ‘Paul’ exemplifies the property ‘being anxious’ at that instant. The same holds true for the substance ‘Paul’ and the relation ‘being next to Mary’. A fact (or ‘state of affairs’, to use Armstrong’s term, or still ‘circumstance’, to use Fine’s term) corresponds to this internal link that unites (at a given instant) the substance and the property/relation in an entity. The main argument for the existence of facts is that they are truth-makers, i.e. something that makes propositions like ‘Paul is anxious’ or ‘Paul is beside Mary’ true in the world [21]. It will be noted that time is a constituent of our facts, which are thus considered to be tensed facts. This is consistent with the properties (o/p_ii), which assert that objects and processes bear properties at instants. However, this choice has an impact on the facts’ mode of existence. Indeed, facts only 6

In fact, the latter property is a relational property – that of enacting a walking process. We consider that such a process is expressed by the substantive ‘walk’, as in ‘Paul’s walk’. 7 The processes in question may be a head movement and a fist movement, respectively. In line with Amie Thomasson [25], we assimilate artefactual (or at least functional) objects and processes to ‘concrete social’ entities, i.e. physical entities to which a social function has been attributed.

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exist at times at which (a) their constituents exist and (b) their constituents are bound by the relation expressed in the fact; hence, they only exist at the instant corresponding to their temporal constituent (e.g., at the instant ‘Now’ in the fact ). These are states of affairs that ‘obtain’ (or ‘are actual’) at this instant; they do not endure in time. In line with our distinction between physical and conceptual properties, we distinguish between ‘physical’ facts (or ‘brute’ facts, to use Searle’s terminology) and ‘social’ facts. The former are independent of all human thought towards them: the fact that ‘Paul is next to Mary now’ has a physical reality, independently of what Paul or Mary might think. In contrast, the latter are human constructs. The association of a conceptual property with a substance corresponds to a human stipulation that can be based on a social convention. In line with Searle’s analysis and its use of the term ‘count as’ to denote the result of this stipulation [24]: a piece of paper counts as ‘being a 10 euro banknote’ (for an agent or a community of agents, under certain circumstances), and a pebble counts as ‘being a paperweight’. The literature contains various analyses of social facts (e.g., [25]). Searle’s analysis is cited here as an example. Most importantly, we wish to emphasize that the life of a substance is not limited to its physical life but that it also involves (for cognitive subjects) a social life. Before ending this section on facts, and in view of the forthcoming discussion on the notions of occurrence and event, let us consider two categories of brute facts related to the dynamics of the world. We have already mentioned the first category, where property (p_iv) indicates that every process is enacted at every instant of its lifetime by an object. These process enaction facts are as much as part of an object’s ‘processual life’ as they are of a process’s ‘objectual’ life. The second category of facts more specifically concerns the life of a process; processes can perpetuate each other through the propagation of causation. In this respect, we have adopted a relation identified by Galton in his inventory of causal-like relations between processes and events [27]. For example, a moving mass of air can ‘perpetuate’ the movement of a leaf, and the movement of a person’s arm can ‘perpetuate’ the movement of his/her wristwatch. By participating in the dynamics of the world, the enactions and perpetuations of processes can be said to ‘occur’. It should be noted that these enactions and perpetuations are not usually included in inventories of occurrences because they are neither processes, events, states, nor changes of states. The role of enactions and perpetuations in explaining the dynamics of the world is, in any case, an additional argument in favor of their existence (completing the ‘truth-maker’ argument). 3.3. The life history of substances By evoking social facts, we began to sort out the world of mental and social constructs. In this section, we will continue in this direction by focusing on a specific category of constructs: the life histories of the substances (objects and processes) populating the physical world. The main ontological category to be added to our inventory is the event category. In the 1970s, researchers such as Chisholm [13] and Wilson [14] suggested that events are abstract entities. However, the metaphysics of states of affairs was in its infancy at that time, which explains the limitations of their suggestions. We have leveraged progress in this field (notably with regard to the ontology of facts) to propose a more robust theory.

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We consider that an event is something that: (e_i) exists for a given subject at instants; (e_ii) may occur; (e_iii) has properties at instants; (e_iv) may change over time. Before discussing these properties, we must by extension characterize the class of events. Events are diverse because of the number of substances involved and the variable length of the substances’ lives taken into account. Basically, conceiving a substance’s life history amounts to considering a slice of its life bounded in time. This mechanism has been described by Galton and Mizoguchi, with the aim of distinguishing between processes and events [18, p.75]: “We maintain, on the contrary, that so far from being a mark of short duration, boundedness is a precondition for the assignment of any definite duration: processes endure, but only once we have assigned bounds to them can we speak of duration, and the act of assigning bounds means that we have switched our attention from the process to an event.” For a process of running (for example), a slice of life could be ‘the first 10 seconds of Paul’s run’. For a person, one could cite ‘Paul’s childhood’; we commonly refer to many slices of people’s lives, e.g., adolescence, youth, retirement, and old age. By focusing on the history of a particular substance, one can see that another category of events concerns the way in which a substance’s aspect changes (or does not change) over time. States express stability over time, e.g. ‘Paul’s tiredness this morning’ (for an object), and ‘Paul’s slow pace during the first 5 minutes of his run’ (for a process). In contrast, changes reflect a change in an aspect of a substance, e.g. ‘Paul’s journey to the station this morning’ (for an object), and ‘Paul’s blazing acceleration over the last 100 meters of his run’ (for a process). Lastly, and again by extension, some events concern the life of a large number of objects and processes, such as: ‘the assassination of Julius Caesar on March 15, 44 BC’, and ‘the sinking of the Titanic in the night on April 15, 1912’. Some events (such as the ones just mentioned) have a social dimension, whereas others have a more private dimension (such as ‘my last bike crash’). As these examples show, some events are intentional and others are not. In [28], we argued that the actions we plan and (in some cases) realize constitute an important class of events. This class includes individual actions (e.g., ‘my writing of this essay’) and collective actions (e.g., ‘the FOIS 2018 conference’). Let us now turn to the properties characterization of our events, and firstly the thesis (e_i) whereby events are abstract entities. The weaker thesis (i.e. in which certain events are mental constructs) appears to be easily justified. This argument focuses on the importance of distinguishing between existence and occurrence (or realization): a football game (like a conference) cannot be improvised; these events must be socially planned in advance if they are to occur. This means that the events must be thought out, and therefore exist for subjects, so that they can be realized (the realization of a conference corresponds to the activities of its participants). Although we have just mentioned social events realized by collective activities, this also applies to events corresponding to an individual activity, for example: my journey to work tomorrow. The stronger thesis (i.e. in which no event is concrete) is more difficult to justify. In the absence of a sole, decisive argument, we will put forward two reasons: (i) given the lack of examples not covered by our current primitives, and applying the principle of parsimony, it does not seem appropriate to

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broaden our inventory further by considering two categories of events (abstract and concrete), especially since (ii) it should be noted that our category of ‘brute fact’ already makes it possible to account for the dynamics of the world, e.g. with facts like process enactions by objects and process perpetuations (see Section 3.2).8 We will continue our characterization of events by referring to a property that usually qualifies them as ‘occurrents’, namely the fact that they may ‘occur’ or ‘happen’ (e_ii). Intuitively, saying that an event ‘occurs’ means that something happens that consists in the realization of the event. The occurrence of a football match consists of two teams playing on a pitch under the control of a referee. More formally, this property is defined as follows:

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Let e be an event that exists for a subject s at a time t; the event e ‘occurs’ at a time t' if the facts whose history is related by e exist at time t'. The occurrence property of events can be considered to be analogous to the truth property of propositions [29]: the existence of facts conditions the occurrence of the event, just as it conditions the truth of a proposition. By analogy with the term ‘truthmaker’, we suggest using ‘occurrence-maker’. A person’s displacement occurs when a series of ‘occurrence-maker’ facts corresponds to a succession of different locations for the person. The order relationship between t and t' in the definition determines whether the history is past, present, or future (we will develop these points in Section 4). Let us now consider how events bear properties. As Guarino recently reminded us, the current point of view is that events carry their properties timelessly; for some researchers, this characteristic even distinguishes processes from events [10, p.477]: “According to the standard wisdom, all temporal occurrences are considered as ‘frozen in time’. This means that all their properties are fully determined, and they can’t change.” Yet, as Guarino also notes [10, p.477], “This is certainly true for historical occurrences, but, at least in the ordinary language, ongoing and future occurrences seem to admit the possibility of change: the score of an ongoing match may change in time, and a future trip may be delayed.” Our view (bearing in mind properties (e_iii) and (e_iv)) is that the properties of events are tensed – meaning that all events can change. This position will be justified in Section 4; here, I merely present the general idea. These properties are conceptual properties, and their attribution to events at given times corresponds to a judgment. When a judgment relates to a past event, the judgment is well established and is unlikely to change (unless new historical elements lead us to review our judgment). Descriptions of past events do not therefore depend on time. In contrast (and we agree with Guarino in this respect), things are different for current (and even future) events. The reason is that judgments made about an ongoing event may depend temporarily on how the event is performed: a football match that is boring at an instant t (because the opposing teams are sizing each other up in the early stages of the match) can become exciting at a later instant t' (when the players have freed themselves of their initial stress, and the match has truly ‘taken off’). Before we look at the existence and persistence of processes and events, Fig. 2 summarizes the progress made since Galton’s [1] experiential-historical distinction that served as our starting point. Our ontological framework applies to a physical world 8

Of course, we have considered only two examples of fact that accounts for the dynamics of the world. The consolidation of this second argument requires these dynamics to be characterized more fully. In particular, we have ignored the births and deaths of objects and processes that participate in the dynamics of the world.

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populated by enduring substances, namely (static) objects and (dynamic) processes, whose instantaneous life consists of facts that obtain at instants.9 The history of the world consists of psychological and social constructs that account for the world’s changes (as well as its stability) over time.

Figure 2. An overview of our ontological framework

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4. Processes’ and events’ modes of existence and persistence In this section, we will specify the modes of existence of physical processes and events; this leads us to specify (review) the notions of endurance and perdurance. Before turning our attention to these entities in particular, it should be noted that our ontological framework classifies both concrete and abstract entities. This raises the question of which type of ontology should be adopted, in the perspective of a formalization: an extensional ontology (in the sense of extensional semantics), an intentional ontology (in the sense of intensional semantics) or a mixed ontology? In Section 4.1, we give some background that argues in favor of an intentional ontology, and prompts us to specify the notion of endurance as applied to physical objects. 4.1. Logical existence, physical presence, and endurance As a starting point, let us return to physical objects, which constitute the paradigmatic figure of continuants. These objects are said to ‘wholly exist at any time of their existence’, an expression used by Stout (as we have seen) to characterize physical processes. We adopted it ourselves for properties (o_i) and (p_i). However, this expression can be ambiguous, depending on the meaning we attribute to the verb ‘exist’ and, hence, the meaning given to the adverb ‘wholly’: does it have mereological significance or does it qualify (as we have heard) a full identity? Firstly, we resume 9

This vision contrasts with Galton’s recent proposition [30]. Our disagreement (corresponding to the debate mentioned in the Introduction) concerns the nature of processes, which Galton considers to be extended entities [30, p.167] “(...) processes, being inherently temporally extended, can only exist over intervals, not at instants.” More precisely, the question concerns the ontology of time, of which Galton described different aspects in [30]. I shall simply state here that I conceive instants to be indivisible entities that nevertheless have a duration; in my opinion, this reduces the extent of our disagreement.

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Fine’s [31] analysis of this expression. His analysis is advantageous in that it is independent of any mereological discussions; this will prove to be important for our characterization of process endurance. Secondly, we distinguish between two notions of existence, namely that of physical presence and that of existence for a subject, in order notably to clarify the latter to which we refer for events. According to Fine [31], the meaning of the expression ‘o is wholly present’ (in the case where o is a physical object) is based on two different notions: the fact of existing and thus that of occupying a spatial region.10 Fine further considers that an object’s existence is not a matter of degree – an object exists or it does not – but that its spatial extension can be quantified: one can thus consider that o wholly occupies the spatial region in which it extends, while only partially occupying parts of the region. The expression ‘o is wholly present’ is therefore to be understood in the sense of ‘o exists and o is extended in space’, while leaving implicit the adverb ‘wholly’. Leaving aside – for the moment – the notion of spatial extension, we will now specify the notion of existence.11 In the literature, many notions of existence have been proposed; in any case, several terms are used: ‘logical existence’, ‘ontological existence’, and ‘physical presence’. In DOLCE (taking its new kernel DOLCE-CORE revised by Borgo and Masolo as the benchmark [32]), logical existence is granted to temporal entities. In addition to physical objects, the domain of quantification includes abstract entities, such as regions of magnitudes of qualities and concepts; these abstract entities are considered to possess a life by being created, modified, and abandoned. Discourses about entities include those relating to an entity’s period of life: ‘Paul lived from 1925 to 2008’, for example (time is also part of the discourse domain). This presence is represented by means of the predicate PRE(x,t) used to identify the times t at which the entity x is present. This predicate makes it possible to say that Paul was present neither in 1920 nor in 2015 but that he was present in the years between 1925 and 2008. The presence of an object at different times – e.g.: PRE(Paul,T1) ∧ PRE(Paul, T2), where T1 and T2 are between 1925 and 2003 – reflects the object’s endurance over this period12. By using a general formula F(x, t), Borgo and Masolo refer to the meaning proposed by Trenton Merricks [33]: “x exists at t and it has the property F when t is (was, will be) present”. Since the subexpression ‘x exists at t’ is synonymous with ‘x is present at t’, the following axiom is assumed: F(x, t) → PRE(x, t). These ontological commitments create several problems. One problem (highlighted by Guarino [10]) is that we cannot assign properties to x at times t at which x is not present. According to Guarino [10, p.481], this possibility is necessary for events (italics original) “For instance, if x is an event that occurs at t0 (say, a person’s birthday), it may be expected at a time t1 < t0 only if x is not present at t1, and remembered at a time t2 > t0 only if x is not present at t2, since we can’t expect nor remember something that is present.” It is as much for physical objects [10, p.481] “Similarly, a person can have various properties, such as being admired or being the 10

In the reference [31], Fine defends a 3D theory of the physical material object, denying it the fact of having temporal parts. Although we sympathize with this thesis, we do not seek to discuss it here. Recall that we want to identify notions that are free of any mereological dimension. 11 In [7], Stout regrets that Fine leaves us with an ‘abstract’, undefined notion of existence. 12 Indeed, the dissectivity of the predicate PRE(x, t) posed by the axiom PRE(x, t) ∧ P(t',t) → PRE(x,t') (where the predicate P(x,y) holds for ‘x is a part of y’) ensures that Paul is present at all times between T1 and T2 .

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mother of somebody, also when she is not present anymore since she is died.” A more general problem (albeit related to the previous one) concerns the absence of a distinction between logical existence and ontological existence (taken in the sense of physical presence). This distinction is critical for our ontology of events, which are identified as abstract objects. DOLCE-CORE’s strategy is to admit abstract objects into the domain of quantification, alongside concrete objects. The objects therefore enjoy a logical existence and, as such, belong to the domain of the predicate PRE(x, t). The problem is that this predicate, whose role is to locate entities in time, is problematic for events. For events, we intuitively need to account for two levels of existence and location. Firstly, the fact that they are thought by subjects makes them exist as temporal entities, and causes them to possess a first temporal location. Secondly, when facts exist which make events occur (we named them ‘occurrence-maker’ facts), this realization/occurrence has a different temporal location.13 For physical objects, and to resolve the problem raised by Guarino, we affirm that it is also appropriate to distinguish between two types of entities (abstract and concrete), each of which having a different mode of existence. To meet these needs, our proposal is firstly to consider that our domain of quantification is populated only by objects of thought.14 In the domain of semantics, this amounts to the adoption of cognitive semantics [37] that are able to speak of entities that ‘do not exist’.15 On the ontological side for physical objects, this leads one to distinguish between the object of thought PaulOoT and its physical correlate PaulPO – namely, the physical thing to which the object of thought refers.16 Note that in the case of objects that ‘do not exist’ (like Sherlock Holmes, for example), only the object of thought exists. Events are precisely objects of thought with no physical correlates (more specifically, occurrence-maker facts are correlates of events when the latter occur). To make it possible to speak about the presence of a physical object’s correlate (and in addition to the predicate PRE(x, t) that continues to locate objects of thought in time), we propose introducing a new predicate PC_PRE(x,t) having for domain objects of thought referring to physical things, and having for significance: ‘the physical correlate of x is present at time t’. In this way, the physical endurance of a physical object is represented by the fact that its correlate is present at different times, for example: PC_PRE(PaulOoT, T1) ∧ PC_PRE(PaulOoT, T2). On this basis, let us complete our theory of physical endurance. We now wish to clarify the meaning that we give to our properties (o_i) and (o_iii) when we assert that a physical object (o_i) wholly exists at times and (o_iii) may change over time. 13

For the sake of completeness, we should add that this relation between occurrence-maker facts and events cannot correspond to a classification of instances by concepts – even when indexed by time. 14 In Section 2, we indicated that we intended to develop a descriptive ontology, as defined by Strawson. Our choice of intentional ontology is a step in that direction. It should be noted that historically (and for reasons similar to those mentioned in the previous paragraph), this type of choice was made by Castañeda [34] (with his ‘epistemological’ ontology) and by Chisholm [35] (with his ‘intentional’ ontology). Our objects of thought can be likened to not only Castañeda’s individuals but also Edward Zalta’s abstract individuals [36]. 15 Discourses can relate to Paul’s house, even though it does not yet exist (e.g. ‘the house that Paul is going to have built will have a large patio’) or no longer exists (e.g. ‘the only thing left of Paul’s house is a brick wall likely to collapse’). 16 We thank an anonymous reviewer for having drawn our attention to the fact that the foundational ontology GFO [38] distinguishes between these two levels of entities. In GFO’s theory of continuants, a continuant is a purely cognitive entity constructed on the basis of mind-independent physical entities called ‘presentials’.

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Let us start with the property (o_i). As we have just pointed out, we exclude the mereological interpretation of the adverb ‘fully’ and will stick to a ‘full identity’. To characterize the identity of the physical object, we again call upon Fine, but this time with his theory of embodiment [39]. In his [39], Fine aims to account for the notion of whole, for physical objects composed of parts. Fine defends the thesis according to which the standard mereological theory is insufficient to account for this notion of whole, and that it is necessary to add an intensional or conceptual component: this component makes it possible, for example, to attribute to a sandwich an identity largely independent of the states in which its material components – two slices of bread and a slice of ham – are found. We find our object of thought and its physical correlate. By transposing Fine’s conception and expanding it, this amounts to saying that the physical object consists both of the object of thought and its physical correlate. Physical identity is therefore partly a human stipulation, even when we attribute physical properties to the object. Let us continue with the property (o_iii). This property amounts to admitting that the same physical object o can be F at t and not F at t'. On the contrary, some researchers (like David Lewis [40]) hold that it is impossible for a physical object to endure. According to Merricks [33] and other researchers, the objection rests on the fact that identity implies indiscernibility. The argument is as follows: “If some object O, which exists at t is F, persists until t*, at which time it is not F, then it would seem that there is a property that O at t has but O at t* lacks; therefore, O at t and O at t* are not indiscernible. But if O at t and O at t* are not indiscernible they are not identical.” We have just seen that we base our concept of identity partly on psychological criteria. It is clear, then, that the argument of the opponents on endurance does not hold and that we can produce many counterexamples. These counter-examples correspond to Fine’s [39] notion of variable embodiment according to which physical objects can see their material manifestation change while still being considered to be the same object: my car, leaving the garage with a new carburetor, remains my car. At the extreme, we can even rely on a purely intensional identity in the absence of any physical correlate. 17

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4.2. Physical processes endure Let us now seek to characterize how physical processes exist and persist. In Section 3, we saw the role we attribute to a process in the conceptualization of change. To be precise, a process is a concrete particular at the origin of the change over time in a physical object, this evolution corresponding to a series of facts; the series can be observed and conceptualized as a change. Let us again consider Stout’s thesis for an object’s change of location; when a person moves while walking, a walking process is ‘wholly present’ at all instants during the displacement, provided that the latter is uninterrupted. This ‘whole’ presence can be likened to that of physical objects at all instants of their existence. Just as we did for objects, we adopt Fine’s strategy to distinguish between physical existence on one hand and the resulting spatio-temporal occupation on the other. Regarding physical existence, in order to differentiate between an object and a process, we propose distinguishing between a ‘static’ presence for objects and a ‘dynamic’ presence for processes. In order to represent this dynamic presence in a 17

Note that this strategy is followed by Guarino [10] when defining ‘future’ events. Guarino calls on Fine’s [39] notion of variable embodiment to define events that do not yet have manifestations.

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commonly used terminology, we introduce the predicate OPE(x,t), which means that ‘x operates (or is active) at time t’ (given that we are talking more specifically about the physical correlate of x). A process’s endurance is therefore rendered by the fact that the ‘same’ process operates at different times (e.g., OPE(WLK1,T1) ∧ OPE(WLK1,T2) for a walking process, where WLK1, T1 and T2 are objects of thought referring to physical entities). According to our characterization of processes, any operating process is enacted by an object that is statically and concomitantly present – constituting a physical existence dependence. Conversely, Peter Simons’ theory of the endurance of physical objects [41] holds that all objects depend on processes. According to Simons [41, p.70]: “for a human being or other animal the relevant processes are those which are vital to it, which are a (probably not exactly delimited) collection of occurrents in its life, involving respiration, blood transport, nutrient breakdown and the chemical reactions within the cells. These are all processes which have to go in order for an animal to continue to exist.” In the case of an inert object (e.g. a stone) [41, p.71], “The widespread cohesion of the crystals in the rock which hold it together as a mechanically unified mass depend on chemical bonds among atoms.”18 According to this conception, processes and objects are dependent on each other for their physical existence. We interpret this mutual dependence as a sign of the same notion of presence, which specializes as static and dynamic. It should be noted that this conception of presence (on which we base our theory of endurance for the physical objects and processes) does not require a mereological analysis of these entities.

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4.3. Events endure logically and occur contingently Let us now consider events. Since our theory of events is not conventional (because it does not coincide with the dominant (Davidsonian) thesis of concrete spatiotemporal individuals), we cannot expect our characterization of their modes of existence and persistence to be any more so. To be more precise, we started to explain in Section 3.3 that events exist and persist logically. Concerning the link between the events and the physical world, differently from objects and processes that are physically present in it, events occur in it. This occurrence corresponds to the notion of physical realization by facts. Events are objects of thought, and therefore enjoy a logical existence and identity. They exist at times for subjects, although this time is distinct from the times of the physical presence of the objects and processes of which they relate the history.19 In fact, events can be past, ongoing or to come, relative to the time at which they are thought of. Their identity is determined and maintained by stipulation by individual or collective subjects.20 One can speak of their endurance. Thus, the community of philosophers of 18

Galton and Mizoguchi have also proposed a similar analysis [18, p.101]: “Although a simple rock may seem inert and lifeless, in fact it exhibits some remarkable behavior. If you live it alone, it will just sit there – but significantly, it stays in one piece. The maintenance of the rock’s integrity is a process: from the point of view of the rock, it is an internal process enacted by the constituent grains of the rock (…) whose mutual cohesion holds the rock together.” 19 Events may also involve fictional objects, such as those corresponding to Sherlock Holmes’ reported exploits. 20 For reasons of space, we have not discussed the distinction between a psychological identity and a social identity. The reader may consider that a social identity is constructed from psychological identities according to a collective recognition mechanism (as described by Searle [24]).

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action has become accustomed to perpetuating the event in which Brutus stabbed Caesar. The latter is an example of an event with exceptional longevity. Events corresponding to actions that we carry out on a daily basis (e.g., the fact that ‘Paul has buttered his toast this morning’) have a shorter life span. Endurance causes events to change because they bear opposing properties at different times: an event expected at a time t may no longer be expected at a time t' – especially if it has occurred in the meantime. Perdurantism is usually put forward to account for the persistence of events. The reader will have understood that the logical persistence mentioned above does not take account of a mereology of events. Furthermore, logical persistence is unrelated to an entity’s existence through its temporal parts alone and its persistence through the accumulation of parts (i.e. the foundation of perdurantism). However, perdurantism contains a relevant intuition that we wish to maintain – namely that an ongoing event ‘exists only partially’. The idea is that when an event is in progress (for example, a football match that has started), each moment of the event constitutes only a ‘part’ of the event’s existence; past parts of the event no longer ‘exist’, whereas other parts are yet to come and do not ‘exist’ yet. We consider that this intuition is important to maintain, and so we have linked it to our notion of occurrence. Our interpretation of an ongoing event is that the event ‘is realized, but only in part’. The notion of a part of an event must therefore be elucidated. Firstly, saying that an event is ongoing at a time t is equivalent to saying that facts realizing the event exist. In Section 3.3, we named these facts as ‘occurrence-makers’, by analogy with the term ‘truth-maker’. Let us return to our example of the football match. When the event is in progress, it exists socially for both the players and the spectators. The match existed long before the kick-off, in as much as the players were getting ready and the spectators were preparing to travel to the stadium. The match’s occurrence corresponds to the teams’ presence on the pitch because many ongoing processes are generating ‘occurrence-maker’ facts. With regard to the question ‘which facts realize an event?’, one should note that the same event can be realized by very different facts. In our example of a football match, the realizing facts will depend on how the game unfolds. In some matches, a tied score after the ‘normal’ duration of 90 minutes may result in extra time being played. More fundamentally, one should note that because an event is a social entity, its definition necessarily includes social uncertainty: in particular, does a football match start at the first kick-off or when the spectators enter the stadium? In this sense, we agree with Achille Varzi that an event is a largely indeterminate entity [42]. Furthermore, a ‘partially’ realized event is an event of which only a ‘part’ is realized. The notion of part, in the case of physical objects, is based on a notion of spatial inclusion: a part of an object occupies a spatial region included in that occupied by the object as a whole. The notion of inclusion can also apply to events. However, the temporal dimension must be taken into account, and one must consider that the spatiotemporal region concerned is that occupied by facts: a part of an event is such that the facts realizing it are within the spatiotemporal region occupied by the facts realizing the global event. Examples of parts of events are slices of life of substances over interlocking periods: a person’s childhood and adolescence are parts of his/her life. Other examples of parts of events are provided by intentionally realized events (actions) for which a plan (i.e. a structure of sub-events) is specified. A football match is therefore a conventionally structured event; two periods of play are separated by a half-time break. At half-time, one can say that the match is only ‘partially’ realized.

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When specifying the criteria for the unity of events, we must generally expect to encounter the same difficulties as for physical objects.

5. Conclusion At the end of reference [10], Guarino’s maxim ‘Let’s defrost events!’ emphasizes that ongoing and future events should be considered as first-class citizens. The conception of the events presented above leans in this direction; by assimilating events to abstract entities, we give the former (whether past, current or future) the same mode of existence. In this regard, it should be noted that attributing events with the status of objects of thought does not make them second-class citizens – in contrast to some philosophers’ arguments (Joseph Melia’s attempt [43] to eliminate the events from his ontology is an example of the latter). The idea that human actions correspond to events (an idea only mentioned briefly in the present text and defended in [28]) seems to us to be a sufficient argument. In conclusion, and in order to summarize the general principles of our ontology of ‘occurrent’ entities, we will add two slogans à la Guarino: (i) ‘Let’s substantiate physical processes!’ (thus granting them the same mode of endurance as physical objects) and (ii) ‘Let’s make events abstract!’ (making it possible for them to both occur and exist)21.

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References [1] A. Galton, Experience and History: Processes and their Relation to Events, Journal of Logic and Computation 18(3) (2008), 323-40. [2] R. Stout, Processes, Philosophy 72(279) (1997), 19-27. [3] R. Stout, The life of a process, In G. Debrock (ed.), Process Pragmatism: Essays on a Quiet Philosophical Revolution, Rodopi (2003), 145-57. [4] A. Galton, On What Goes On: The ontology of processes and events, In R. Ferrario and W. Kuhn (eds.), Proceedings of the 4th International Conference on Formal Ontology in Information Systems, IOS Press (2006), 4-11. [5] H. Steward, Processes, Continuants, and Individuals, Mind, 122(487) (2013), 781-812. [6] H. Steward, What is a continuant?, In Proceedings of the Aristotelian Society, Supplementary Volume LXXXIX (2015), 109-23. [7] R. Stout, The category of occurrent continuants, Mind, 125(497) (2016), 41-62. [8] C. Masolo, S. Borgo, A. Gangemi, N. Guarino, A. Oltramari and L. Schneider, The WonderWeb Library of Foundational Ontologies and the DOLCE ontology, WonderWeb Deliverable D18, Final Report, vr. 1.0, 2003. [9] G. Guizzardi, N. Guarino and J.P.A. Almeida, Ontological Considerations About the Representation of Events and Endurants in Business Models, In M. La Rosa, P. Loos and O. Pastor (eds.), Business Process Management (BPM 2016), Springer, 20-36. [10] N. Guarino, On the semantics of ongoing and future occurrence identifiers, In H.C. Mayr, G. Guizzardi, H. Ma and O. Pastor (eds.), Conceptual Modeling, Proceedings of the 36th International Conference ER 2017, LNCS (Springer) (2017), 477-490. [11] G. Kassel, Processus, événements et couplages temporels et causaux. Revue d’Intelligence Artificielle, 31(6) (2017), 649-79. 21

I would like to warmly thank three anonymous reviewers whose comments enabled me to significantly improve a first version of this essay. Furthermore, I also wish to thank David Fraser for copyediting my imperfect English and thus making it readable. Above all, I would like to thank Nicola Guarino and his LOA group for introducing me to the field of applied ontology and giving me the opportunity to write this essay.

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[28]

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D. Davidson, Events as Particulars, Noûs 4(1) (1970), 25-32. R.M.. Chisholm, Events and Propositions. Noûs 4(1) (1970), 15-24. N. Wilson, Facts, Events, and Their Conditions, Philosophical Studies XXV (1974), 303-321. K. Gill, On the Metaphysical Distinction Between Processes and Events. Canadian Journal of Philosophy, 23(3) (1993), 365-84. P. Strawson, Individuals. An Essay in Descriptive Metaphysics, Methuen, London, 1959. M. Ferraris, Manifesto of New Realism, State University of New York Press, 2014. English translation by S. De Sanctis of Ferraris (2012): Manifesto del nuovo realismo. A. Galton A. and R. Mizoguchi, The water falls but the waterfall does not fall: New perspectives on objects, processes and events, Applied Ontology 4(2) (2009), 71-107. C.E. Cleland, The Difference Between Real Change and Mere Cambridge Change, Philosophical Studies 60 (1990), 257-280. T. Crowther, Processes as Continuants and Process as Stuff, In R. Stout (ed.), Process, Action, and Experience, Oxford University Press (2018), 58-81 D.M. Armstrong, A world of states of Affairs, Cambridge University Press, 1997. E. Margolis and S. Laurence (eds.), Concepts: Core readings. MIT Press, 1999. P.M.S. Hacker, Events and Object in Space and Time, Mind 91 (1982), 1-19. J.R. Searle, Making The Social World: The Structure of Human Civilization, Oxford University Press, 2010. A.L. Thomasson, Foundations for a social ontology, Protosociology 18 (2003), 269-90. K. Fine, First-Order Modal Theories III – Facts, Synthèse 53 (1982), 43-122. A. Galton, States, Processes and Events, and the Ontology of Causal Relations, In M. Donnelly and G. Guizzardi (eds.), Proceedings of the 7th International Conference on Formal Ontology in Information Systems, IOS Press (2012), 279-92. G. Kassel, Ontologie de l’action et formes logiques des phrases d’action : de nouvelles perspectives. In T. De Lima et S. Doutre (eds.), Proc. of the 12th Journées d’Intelligence Artificielle Fondamentale, (2018). A. Iacona, Are there propositions?, Erkenntnis 58(3) 2003), 325-51. A. Galton, The Dynamic Present, In P. Hasle, P. Blackburn and P. Ohrstrom (eds.), Logic and Philosophy of Time: Themes from Prior, Aalborg University Press (2017), 167-187. K. Fine, In Defense of Three-Dimensionalism, The Journal of Philosophy, 3(12) (2006), 699-714. S. Borgo and C. Masolo, Foundational choices in DOLCE, In: S. Staab and R. Studer (eds.), Handbook on Ontologies, Springer Berlin (2009), 361-381. T. Merricks, Endurance and Indiscernibility, Journal of Philosophy, 91 (1994), 165-184. H.-N. Castañeda. Thinking and the structure of the world, Philosophia 4(1) (1974), 3-40. R.M. Chisholm, Person and Object: A Metaphysical Study, London: Allen and Unwin, 1976. E.N. Zalta, Abstract Objects: An Introduction to Axiomatic Metaphysics, Dordrecht: D. Reidel, 1983. P. Gärdenfors, Some Tenets of Cognitive Semantics, In J. Allwood and P. Gärdenfors (eds.), Cognitive Semantics: Meaning and Cognition, John Benjamins Publishing Company (1999), 19-36. H. Herre, General Formal Ontology (GFO): A foundational ontology for conceptual modelling, In R. Poli, M. Healy, and A. Kameas (eds.), Theory and Applications of Ontology: Computer Applications. Heidelberg: Springer (2010), 297–345. K. Fine, Things and Their Parts, Midwest Studies in Philosophy XXIII (1999), 61-74. D. Lewis, On The Plurality of Worlds, Oxford: Blackwell, 1986. P. Simons, Continuants and Occurrents, In Proc. of the Aristotelian Society 74 (2000), 59-75. C.A. Varzi, Events, Truth and Indeterminacy, The Dialogue, 2 (2002), 241-264. J. Melia, Continuants and Occurrents, In Proc. of the Aristotelian Society 74 (2010), 77-92.

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Ontology Makes Sense S. Borgo et al. (Eds.) IOS Press, 2019 © 2019 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-61499-955-3-194

Towards a New Foundational Ontology of Properties, Attributives and Data Heinrich HERRE IMISE, University of Leipzig

Abstract. In this paper we outline a foundational ontology of properties, attributives, and data. This paper takes up ideas in [1] and presents a new ontology of attributes, data and properties. This ontology was motivated by the need to contribute to the theoretical foundation for the evolving data science. The current situation of data overload is caused by lack of methods for abstraction and interpretation of data, but also by an insufficient understanding of the relation between data and knowledge. There is a need for an ontological foundation of these notions which provides a framework for the integration of the manifold of types of data. The first version of this ontology was presented in [2]. In the current paper further details of this theory are elaborated and applied to various ontological regions, taken from physics, biology, and agent-driven process generation. Keywords. Ontology, Attributives, Properties, Data Semantics

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1. Introduction In the seminal paper [1] Nicola Guarino and Christopher Welty established a metaontology of properties, including, among others, rigidity, identity, and dependency. Furthermore, a classification of several kinds of properties was discussed, which are called categories, types, formal roles, and attributes. According to the principles of DOLCE [3], there are three different options to represent properties. The first option considers properties as extensional predicates, based on the model-theoretic semantics of the First order logic. The second option specifies properties as concepts, being entities of its own. The third option of a property relies on the notion of individual quality, quality type and quality space; for each individual quality there exist a uniquely determined individual in which this quality inheres. In the current paper we take up ideas in [1] and in DOLCE [3], and investigate the third option of properties in more detail. The current investigation is a continuation of [2]; it is intended to contribute to a further clarification of basic notions and provides a novel approach for a classification of attributes and properties. This approach is conducted by a classification of the bearers on which the properties existentially depend. Furthermore, the relation between qualities, properties and data is investigated. The motivation for the current approach is the development of an ontological foundation for the newly evolving data science. We are living in the age of big data. Data are collected about anything which has a mode of existence; this can be objects, processes, pictures, verbal reports, and many other types of things. The final aim of data is not to collect more data but to transform data in relevant applications. For this aim there is a need to transform data into knowledge which is the basis for a manifold of applications.

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The current situation of data overload is caused by lack of methods for abstraction and interpretation of data, but also by an insufficient understanding of the relation between data and knowledge. There is a need for an ontological foundation of these notions which provides a framework for the integration of the manifold of types of data. From this need various tasks can be derived. Firstly, we must clarify what data are, how they can be classified, and how they are related to attributives and properties (semantic problem), secondly, we need methods to acquire data (acquisition problem), thirdly, we need means to correctly represent data in a formal framework (representation problem), and, finally, we need methods to evaluate and use these data (utilization problem). Currently, there is a tendency to collect, acquire, measure, observe and store huge volumes of data, though, the interpretation of these data is weakly founded. Any of these procedures is directed to certain entities to be processed. These entities have a mode of existence which is independent of these procedures. The semantic problem concerns the elucidation, interpretation, and understanding of these entities at which the procedures are directed. The current paper is devoted to the semantic problem of data science, a solution of which should be built upon an expressive ontology of data. This paper is organized as follows. In section 2 we summarize the basics of GFO which is used as a framework for the subsequent investigation. Section 3 outlines and refines a top-level ontology of attributive and data, presented in [2] and called GFO-Data. This ontology provides a semantic basis for data. Furthermore, axiomatic fragments of this ontology are presented. In section 4 the ontology of data elements is expounded. Section 5 contains an overview on related work and in section 6 various applications are collected. Section 7 selects some open problems and outlines future research on the ontology of properties.

2. GFO – The Analytical Framework

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The investigation is carried out in the framework of the Top Level Ontology GFO (General Formal Ontology) [4, 5], the basics of which are summarized in this section. 2.1. Basic Categories of GFO and Basic Axioms The term entity refers to anything which has a mode of existence. Entities are classified into categories and individuals. The basic entities of space and time are chronoids and topoids; these are considered as individuals which are instances of the categories time and space. The ontology of space and time of GFO is inspired by ideas of Franz Brentano [6]; this theory is presented in [7] and in [8]. Individuals are divided into concrete and abstract ones. Concrete individuals exist in time and space, whereas abstract individuals are independent of time and space. According to their relations to time, concrete individuals are classified into objects, presentials and processes. Processes happen and evolve in time and are said to have a temporal extension whereas objects persist through time and have a lifetime. The lifetime of an object obj, denoted by lft(obj), and the temporal extension of a process p, denoted by tempext(p), are both chronoids. Presentials can be informally understood as snap-shots of objects. Objects are considered in this paper as material objects, which occupy space and possess matter. The arguments of predicate MatOb(x) are material objects, which are in some top-level ontologies called continuants or endurants.

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A material object exhibits at any time point of its lifetime a uniquely determined entity, being a presential, which is wholly present at this time-point. For the sake of formalization we introduce the relation exhib(x, t, y) with the meaning: the material object x exhibits at time-point t the presential y. The notion of ‘being wholly present at a time-point’ is a metaphysical condition, which can be grasped by a form of introspection, which is called reine Anschauung1, following Kant [9]. The existence of such entities is postulated by an axiom. If an entity is wholly present at a timepoint t then the genuine properties of this entity are likewise wholly present at t. Examples of material objects are this ball and this tree, being persisting entities with a lifetime, whereas examples of presentials are snapshots of this ball and this tree, any of them being wholly present at a certain time boundary t. Hence, the specification of a presential additionally requires the declaration of a time point. In contrast to a presential, a process cannot be wholly present at a time point. Examples of processes are a particular tossing of a ball, a 100m run as well as a surgical intervention, the conduction of a clinical trial, etc. For any process p having the chronoid c as its temporal extension, each temporal part of p is determined by taking a temporal part of c and restricting p to this sub-chronoid. The relation temprestr(x,y,z) has the meaning: “x is the restriction of the process y to the chronoid z, being a temporal part of the temporal extension of x”. Similarly, p can be restricted to a time boundary t, belonging to p’s temporal extension. The resulting entity is called a process boundary, which does not fall under the category of processes. The relation procbd(x, t, y) has the meaning: “x is a process and y is the process boundary of x at time-boundary t.” The integration axiom of GFO postulates a basic relation between a material object and a corresponding process. Integration Principle. For every material object x there exists a process p such that the presentials, exhibited by the object x, equals with the process boundaries of x; formally:

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‫׊‬x(MatObj(x) ՜ ‫׌‬y(Proc(y) ‫ ר‬lft(x)ൌtempext(y) ‫׊ ר‬tz(exhib(x, t, z) ՞ procbd(y, t, z)))) The integration principle distinguishes GFO from the available 3D and 4D top level ontologies in various aspects. Any foundational ontology should postulate the existence of objects and processes and should explicate how objects and processes are related. In 4D-ontologies there are only processes, whereas objects are considered as particular processes [10]; hence, there is no integration problem. In some 3D-Ontologies, notably for BFO [11], processes depend on objects, they are – so to say – attributives of objects. In DOLCE a mutual existential dependency between object and processes (called in DOLCE events) is postulated which is realized by a participation relation PC(x, y, t), having the meaning that the object x participates in the process y at time t. Axiom A41 in [3] is a weak form of an integration axiom; it postulates that for every object Obj which exists at time t there exists an event Ev (process) at time t such that Obj participates in Ev. The ontology of properties and attributives, as expounded in the current paper, cannot be reconstructed within the DOLCE-framework, unless DOLCE is essentially extended. Another dimension for classification of concrete individuals is their complexity and degree of existential autonomy. We hold that the higher the degree of the existential autonomy of an individual is, the more complex it is. In this sense, an object can be informally understood as a bundle of attributives. Objects are combined to facts by using relators, and facts are embedded into situations. In the current paper we do not consider 1

The term ‘reine Anschauung’ has no adequate translation into English.

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the general theory of situations but restrict our investigation to relational facts and the corresponding relational propositions. Furthermore, we use the dependency relation and the degree of independency in an informal manner because philosophers and formal ontologists did not yet achieve a consensus on the precise meaning of these notions. We hold that any theory of existential dependency must take into consideration the seminal work of Roman Ingarden [12]. 2.2. Attributives, Properties, and Property Values 2.2.1. Attributives The term attributive denotes in GFO an individual which depend on a bearer, hence an attributive has no autonomous existence, it occurs only together with other entities. Similar notions used in the literature are individual property, moment, quality, or attribute. There is no general precisely specified category which covers all the heterogeneous types of attributives, and there is no general consensus reached about the exact meaning of this notion. Attributives include entities as diverse as qualities (as colors, size, weight), functions, dispositions, relators, roles and many other dependent entities. Hence, we understand the class of attributives as an incompletely specified category, stipulating only sufficient conditions for being an attributive. At several places of the paper we use the term quality in the sense of attributive because of its widespread usage.

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2.2.2. Properties and Values Properties are the abstract side of attributives, they are in the terminology of GFO categories. Hence, a property has instances, being attributives. According to the different types of attributives we distinguish, among others, quality-properties (or intrinsic properties) and role-properties (extrinsic properties), and the role-properties are classified into relational role properties (abr. relational properties) and social role properties (social properties), see [13]. For any type T of attributives we introduce the term T-property. Phenomenal attributives are closely related to the senses which form an interface between the mind and the independent reality. The instances of a property can be further partitioned in sets, called values. Sometimes properties and their values are called determinates and determinables, see [14]. Determinates and determinables are relative notions which depend on the granularity of the specification. An example is the property weight W the instances of which are individual weights. The extension of W equals the set of instances of W, denoted by Ext(W). By a measurement process the weights of two persons P resp. Q, w resp. v can be specified as having equal values. This condition defines an equivalence relation which partitions the set Ext(W) into equivalence classes. These equivalence classes can be identified with the values of the property W with respect to a certain granularity. A refinement of the values can be introduced by defining scales between the values, for example a linear ordering. In our approach a property is specified by three components (ECat, P, R), where ECat is a category of entities, P is a property the instances of which are connected to the instances of ECat by the relation R. A typical example of such a relation is the inherence relation, which satisfies the non-migration principle. The triples PFrame = (ECat, P, R) are called property frames; these were introduced in [15].

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2.3. The Integrative Realism of GFO The integrative realism of GFO is characterized by the following features. The whole world is divided into four ontological regions, the region of ideal entities, being independent of the mind and independent of time and space, the psychological region which contains those entities which are internal parts on the mind, the material region which is related to the material entities being the research objects of the natural sciences (physics, chemistry, and biology, including mixed fields), and finally the region of sociosystemic entities. The organization of the world into ontological regions, as adopted in GFO, use ideas of Hartmann [16], Poli [17], and Ingarden [12]. Examples of entities of the ideal region are mathematical entities, including numbers, geometric objects, and pure sets. The psychological region contains phenomena of the mind, including, among others, perceptions, emotions, consciousness and intentionality, whereas the region of socio-systemic entities covers a manifold of entities of social systems, including social roles, organizations, class structures, and economical entities. The integrative realism stipulates certain basic relations between these ontological regions, notably between the mind and the material region. We distinguish at least three kinds of categories: universals, concepts, and symbol structures. We hold, that any fully developed foundational ontology must include all these three types of categories2. Universals are constituents of the real world, they are associated to invariants of the spatiotemporal real world, they are something abstract that is in real things.3 Concepts are categories that are expressed by linguistic expressions and which are represented as meanings in someone’s mind. Symbols are signs or texts that can be instantiated by tokens. There is a close relation between these three kinds of categories: a universal is captured by a concept which is individually grasped by a mental representation, and the concept and its representation is denoted by a symbol structure, being an expression of a language. Texts and symbolic structures may be communicated by their instances that are physical tokens. The integrative realism is concerned with the relation between the mind and the mind-independent entities. The elaboration of the approach of integrative realism is a longstanding research program, the present stage of which is focused on the interrelation between the mind and the real material world. The interface between these two worlds are perceptual processes the results of which – the percepts, the sense data – are organized within sense-data spaces. There is a relation between the subjective phenomena of percepts and the mind-independent entities of the material world. The mind-independent material entities possess a type of dispositions which are transformed by the perceptual processes into mind-inherent percepts. For example, electromagnetic waves of a certain frequency are transformed by a perceptual process in the quale red which is a part of the mind. Hence, this electromagnetic wave possesses a disposition which unfolds in a mind as a quale red. We distinguish at least two types of concepts, according to the entities they capture. Sense-data-concepts are built upon sense data spaces whereas Platonic-based concepts capture entities of the region of ideal entities, for instance mathematical entities. Communication between individual minds are based on concepts inhering in these minds. 2 This approach is defended by Jorge Gracia in [33]. We emphasize the relevance of Gracia’s theory for establishing a Top Level Ontology. 3 There are at least two basic types of universals, those which are in the real (material) things, and those which are independent of the mind and of the material world, called Platonic universals.

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The communication between individual minds needs a spatiotemporal material process which generates material tokens being instances of symbolic structures. These material tokens encode concepts and other mind-inherent entities which are decoded by the communication-partner. The elucidation of the relations between the mind and the mind-independent ontological regions, but also the relation between the region of ideal entities and the material world, exhibits unsolved problems and mysteries. E. P. Wigner observed in [18]4 that the mathematical structure of physical theories often directs the way to further research in that theory and even to empirical theories. The idea of the integrative realism was influenced by the philosophy of G. W. Hegel [19], by ideas of N. Whitehead in Process and Reality [20], and by the Chinese philosopher Zhang Dong Sun [21].

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3. A Foundational Ontology of Properties and Attributives We hold that the semantics of a datum is provided by an attributive. More precisely, the attributives represent the individual data and the corresponding properties provide an understanding, an interpretation of this datum. We consider as an example the weight and the color of an object, say a red ball B of weight of 1kg. The entity B is an individual in which inhere an individual red r and an individual weight w, both being attributives. The understanding of these individuals r and w is established by the properties Red and Weight of which r and w are instances. Another aspect of a datum is its syntactic representation by a token which itself is an instance of a symbolic structure. Attributives depend on bearers, and we assume for the current version that the bearers are concrete individuals. Attributives are classified with respect to three aspects, which are specified by the bearer and connecting relations (1), by the level of abstraction (2), and by complexity (3). 5 The dimension of complexity of an attributive is not considered in the current paper6; we restrict our investigation to the aspects (1) and (2). In the present version of the ontology we distinguish three levels of abstraction: the phenomenal level, the relational level (including relations, relators, functions, and roles of various types, see [13]), and the propositional level, restricted to the case of relational propositions. 3.1. Phenomenal Attributives (of Material Entities) The elementary form and the origin of these attributives are sense data, but also data which can be measured by instruments. With respect to the bearers we distinguish between object-attributives and processual attributives. The term phenomenal attributive has its origin in the theory of phenomenalism. Phenomenalism defends the view that whatever is finally meaningful can be expressed in terms of our own sense experience; hence, reference to objects is always finally a reference to sense experience. 4 “The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve.” 5 There are other principles for classification of attributives and properties. DOLCE, for example, uses a meta-classification by stipulating certain meta-properties for properties. 6 The investigation of the complexity of attributes, and of the corresponding properties, is a research field of its own. This concerns the question how attributives are composed of other attibutives, and whether there are atomic components. Some ideas on this topic are discussed in [35].

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3.1.1. Object-Attributives Presentic object-attributives. A genuine attributive of an object, considered at a timepoint of the object’s lifetime, is wholly present at this time point 7. Categories of objectattributives are: visual data, forms, color, material boundaries etc. Others are captured by measuring instruments, for example weight and size. The term ‘presentic’ has its origin in the view that the actual presence has no temporal extension, hence it exists at a time-point. A presentic entity exists wholly at a time-point. Global object-attributives. Any object has a life time of non-zero duration. Formally, we could consider the life time of an object as a quality of it; another example is an electrocardiogram of a patient. We assume that genuine attributives of an object are wholly present at every time-point of the object’s life time. In some 3D-Ontologies, notably for BFO, processes depend on objects, they are – so to say – qualities of objects. This approach leads to various difficulties. First of all, the notion of an object, being an enduring entity which is the bearer of processes, leads to inconsistencies, see [22, 23]; secondly, global processual properties are incompatible with the presentic nature of the object’s qualities, and, finally, a description of processes in the framework of a 3Dontology, which takes into account all relevant features of processes, seems to be impossible. In the GFO-approach, based on the integration law, for any object O there exists a process Proc(O), which is closely related to O. Then, we hold that the global non-presentic qualities of an object O should be associated to the underlying process Proc(O) and, hence, are borrowed from it. 8 Hence, global attributives of objects are inherited from processes in which the object participates, the are – so to say – disguised process properties. We restrict the object qualities to the presentic ones, and classify all global properties under processual properties.

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3.1.2. Processual Attributives The bearers of processual attributives are processes. Processual attributives are classified into presentic and global ones. Presentic attributives are wholly present at a time-point of the process’ temporal extension, whereas for global attributes it does not make any sense to be wholly present at a time-point. Presentic processual attributives. These are attributives, existing at process boundaries. They are wholly present at time points. The isolated presentic attributives of process boundaries do not need any reference to a process. They can be completely reduced to object qualities. These are typically qualities of objects, participating in the process. For example, consider the movement of a thrown red ball. Any boundary of this process contains a presentic red ball, and this quality red can exists at a time-point without reference to a process. Such object-qualities are, so to say, independent of the process in which the ball participates. Non-isolated presentic attributives of a process are associated to the process boundaries and cannot be separated from the process itself. Investigating, for example, the movement of the red ball B, we may consider the velocity of B at a time-point t. This 7 “To be wholly present at a time-point” is a mode of existence that cannot be explained by other ontological notions. 8 We emphasize that the object is not the same entity as the underlying process. This point was extensively discussed in [34].

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quality cannot be specified without a preceding process, it cannot exist without a process. Hence, such qualities are called presentic non-isolated. Other examples are qualities of presentic events9 which always refer to processes. For example, if a train comes to an end; this can be understood only if there was a movement, i.e. if there was a preceding process. Discrete changes within a process also belong to this kind of processual attributives, see [7]. Other types of such qualities can be found in physics, for example in fluid or aero-dynamics.

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3.1.3. Global Processual Attributives The global attributives of processes form the richest class of attributives of processes. The main feature of them is that it does not make any sense to specify them at a process boundary. One type of such qualities is abstracted from time series. Time series can be understood as selections of qualities of process boundaries, linearly ordered by time. We may consider the values of a fixed property, say the temperature of a patient. Since the patient P himself can be associated to the process Proc(P), according to the integration axiom, the temperature can be measured at selected time-points and the corresponding set of values can be transformed into a curve. Such curves can be evaluated to draw conclusions, for example, that the fever curve is typical for the disease Malaria. Other examples are electro-cardiograms, or a long- term blood pressure measurement. Such curves are global qualities of the underlying process which are abstracted from a set of presentic values of a property. The visualization of the pattern is an indirect global property, associated to the process. Time series are used in diverse fields, as in statistics, patterns recognition, and in any domain of applied science and engineering which involves temporal measurement. Such time-series are underpinned by a process, and usually express global properties of this process. Another example of extracting temporal structures from processes is presented in the seminal paper by Yuval Shahar [24]. On ontological top level of a process’ property some basic patterns can be established in GFO, see [4]. These include continuous changes, discrete change, states, and a manifold of combinations constructed out of them. There are many other global attributives of a process which are not derived from time series. Examples are the duration of a process, its temporal extension, or its occupied space. Physics provides many examples of this kind. For example, the average velocity of a moving body is associated to this process as whole (as completed), but it does not make any sense to say that the process has an average velocity at a certain time-point. Other examples pertain to the geometric form of the movement’s path, for example the circularity of this path. A further example is the physical work associated to a moving object along a path which can be calculated by an integral ∫ F* v dt. A systematic investigation and classification of global processual attributives is work in progress. 3.2. Relations, Functions and Roles Relations, functions and roles provide a new type of properties and attributives, the bearers of which are objects or processes. A relation is a category, the instances of which are relators. A relator is an attributive which is composed of (relational) roles. Throughout this section we use an illustrating example, the expression G := “John’s 9

In GFO, events exist at temporal boundaries of a process; they occur instantaneously at a final timeboundary of a process.

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drinking a beer”. The sub-term ‘drink’ denotes a relation, denoted by Rel(drink). Let p be an instance of Rel(drink), which is called a relator. From this relator we may derive two roles, the role q1 of the drinker, and the role q2 of the drunken. John plays the role of the drinker and the beer plays the role of the drunken. These constituents are composed to a complex entity, a relational fact, expressed by “John`s drinking a beer”; the fact, denoted by this expression G, is denoted by Fact(G). The bearers of a relator are determined/specified by the players, which play the corresponding roles. The roles themselves occur as unary attributives, though, they cannot be separated from the relator of which they are a part [13]. Relators, roles and functions belong to a level of abstraction which is higher than the level of phenomenal attributives. In particular, they cannot be perceived by our senses and cannot be measured. We may see the drinking John, but we cannot see the role of a drinker which John plays. Other examples are provided by social roles. The role of a teacher cannot be perceived or measured. Roles, relators, and functions are cognitive constructions which are used to structure the world, and to achieve an understanding and interpretation the world. These attributives do not belong to the physical level; there is no physical description of them. The relation, connecting the roles to the players, is the inherence relation. Functions exhibit a similar behavior as roles and relators; they are localized at the same level of abstraction. Function are cognitive constructions, which are ascribed to entities by an actor. A stone, for example, may be used in the function of a hammer; hence the function to drive nails can be ascribed to stones. We hold that roles and functions of processes are always global attributives. A typical example is the function to achieve a certain goal, which might be ascribed to a process. If the goal is achieved at the end of this process then the ascribed function must be, obviously, a global attributive.

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3.3. Relational propositions We hold that propositions are localized at higher level of b abstraction than facts, roles or functions. We restrict this question to what we call elementary relational propositions. Elementary relational propositions correspond to relational facts. We hold that the bearers of propositions are parts of the world which act as truth-makers. Let us consider the fact Fact(G), associated tot the expression G := “John’s drinking a beer.” By an operation of abstraction, the mind transforms the fact Fact(G) into the proposition Prop(Fact(G)) := “John is drinking a beer.” The modes of existence of Fact(G) and Prop(Fact(G)) are different: Fact(G) is a part of spatiotemporal reality, whereas Prop(Fact(G)) is an abstract entity the relation of which to reality is indirect, mediated by the corresponding fact. Propositions can be satisfied or disproved, hence, they can be true or false. Relational propositions can be made true by corresponding relational facts. If we consider the truth-makers, being facts, as bearers of proposition, then relational propositions cannot be directly attributed to objects or processes. Relational propositions are at the interface between data and knowledge. To achieve a full picture about the ontology of data, we need an understanding about the relation between data and knowledge. The investigation of this topic is a research field of its own, and we believe that this topic is one of the big challenges of the future. Figure 1 summarizes the system of basic categories of a Foundational Ontology for attributives and the corresponding properties.

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Attributive

Phenomenal Attributive

Relational and Functional Attributive (relator, function)

Object Attributive

Presentic Isolated Attributive

Relational Propositions

Processual Attributive

Presentic Non-isolated Attributive

Global Processual Attributive

Figure 1. Categorial basic structure of attributives.

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3.4. Axiomatic Foundations In this section we present the first step towards an axiomatic core for the formalization of the considered categories. We must distinguish the following three components for the specification of a property: (1) the property P, (2) a class C of bearers (assumed to be material entities, processes and objects), (3) a binary relation, connecting the instances of P with the instances of C, summarized by PF = (P, C, R). We call such a triple a property-frame. Property-frames capture the semantic part of data elements, investigated in the next section. They are called nexus in [15]. All the axioms are formalized within the FOL (first order logic). Further categories to be used, Attr(x) stands for “x is attributive”, Ind(x) for “x is an individual”, Proc(x) for “x is a (material) process”, and Mat(x) for “x is a material object” (in the sense of continuant). We stipulate that certain basic axioms should be true. ‫׊‬x(P(x) ՜ Attr(x)) ‫׊‬x(P(x) ՜ ‫׌‬y(C(y) ‫ ר‬R(x, y))) (any instance of P is connected to an object of C by the relation R). Depending on the relation R, further axioms can be added, for example R can be a one-to-one relation (injective), or many-to-one, etc. We may postulate that R satisfies the condition of a partial ordering (in case that R is a part-of-Relation). If R is the inherence relation, then it satisfied the non-migration axiom: ‫׊‬xyz(P(x) ‫ ר‬C(y) ‫ ר‬C(z) ‫ ר‬R(x, y) ‫ ר‬R(x, z) ՜ y ൌ z) We may consider a list of property-frames, PF1, …, PFn, called property-system, with the corresponding signature ∑ = (R1, …, Rl, P1, …, Pm, C1, …, Cn). Then arbitrary formulas over this signature can be formulated within the FOL. The axiomatization for Ontology Makes Sense : Essays in Honor of Nicola Guarino, IOS Press, Incorporated, 2019. ProQuest Ebook Central,

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such a signature – still a work in progress – will be elaborated following the ontoaxiomatic method explained in [7].

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4. The Ontology of Data Elements We hold that the semantics of data is established by attributives and properties. The communication, storing and processing of attributives need syntactic representations, being tokens of symbol structures. The meaning of data cannot be stored in a data base, but only their representations. Often, we know only a token, denoting a datum, for example the binary representation of a real number; though, the exact meaning, the semantics, remains unclear. In general, the semantics of data is provided by a system of inter-related concepts which is the basis for grasping the meaning, for interpretation, and for understanding. We hold that the notion of data or datum should be established upon the notion of a data element, described in the standard ISO-11179. A data element is a complex structure which integrates all relevant aspects and components of a datum. An ontological analysis uncovers the essence of the notion of data element, see [15]. A data element has two constituents/components, a semantic one, called data element concept, and a syntactic one, called representation. Since the data element itself is a category in GFO we must clarify how its components relate to the whole. For this sake we introduce a suitable partof relation, called constituent-part. Data elements are GFO-categories with certain constituents. A data element concept DEC includes an object class ObC(DEC) and a property P(DEC). An object class is a category whose instances are entities of the real world. The property, being a constituent of the data element concept (DEC), can be attributed to all instances of the class ObC, i.e. every instance of ObC(DEC) has the property P(DEC). To a data element concept there is associated a uniquely determined conceptual domain. This conceptual domain is a set of entities which serve as the value meanings of the property P. At this place we must clarify what value meanings of a property are. Let us consider as an example the property weight denoted by W. The instances of this property are qualities being individual properties that inhere in objects which are instances of ObC. We may partition the instances of W by a measure, say, g, kg. Then, for example, 70 kg represents an equivalence class which exhibits the set of all instances of W which are measured as 70 kg. Hence, W(70kg) may be considered as a sub-property of W. But, the main point is that by using a measuring process we get a natural partition of the instances of W into equivalence classes. The value domain is the most important part of the representation. A value domain is a set of permissible values that are represented by relators consisting of value meaning/value-pairs. The values denote the value meanings. We consider now in more detail the relations between the conceptual domain and the value domain. A conceptual domain may be represented by different/several value domains whereas every value domain represents a uniquely determined conceptual domain. Hence, if we introduce a relation Repr(VD, CD) with the meaning that VD represents CD than this relation is a many-to-one relation, i.e. for every VD there exists exactly one CD. Furthermore, there is also another relation repr(x, y), where x is an element of VD, and x represents an element y of CD. The relation between value meanings and values can be ontologically specified by using the notion of the relator. We introduce a (value, meaning)-relation, briefly denoted

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by Rmv, whose instances are relators. The relators of Rmv are individuals with two parts, called roles, the value-role and the meaning-role. These roles inhere in the players, and the player of the meaning-role is a member of the conceptual domain, and the value-role is played by tokens. A token is an instance of a symbol structure.

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5. Related Work on Properties There is an extensive philosophical literature on properties; questions about the nature and existence of properties are as old as philosophy itself. Philosophy is one of the roots of formal ontology, being an evolving new science. Other roots are artificial intelligence and formal logic. According to the approach of GFO, formal ontology is aimed at developing formalized axiomatic systems for describing various domains of different extents and levels of abstraction. With this respect formal ontology provides methods for developing knowledge systems in the sense of artificial intelligence. We hold that the used methods of formal ontology and the resulting knowledge systems represent the modern form of the field of knowledge representation. In the current section we overview only such fields which have a relation to formal ontology, omitting the huge philosophical literature. To the best of our knowledge, we did not find in the literature an approach for studying properties of entities, which is similar to the method presented in the current paper. Subsequently, the ontology proposed in the current paper is referred to GFO-Data. DOLCE provides an extensive theory on properties which uses classification principles, different from the approach of the present paper. DOLCE’s theory of properties (and predicates) differs in many aspects from the foundational ontology GFO. In [1] and [25] a set of meta-properties is elaborated, and it is shown how these metaproperties impose constraints to the subsumption between properties. The aim of this approach is to develop better taxonomies and ‘to clean’ existing taxonomies. OntoClean is a methodology for validating the ontological adequacy of taxonomic relationships. The purpose of the ontology in the present paper is different, namely, to develop an ontology of properties which contributes to a foundation of data science. This goal lead to novel classification principles and establishes a link to the notion of data element of the standard ISO-11179. DOLCE admits, in contrast to BFO, properties for events, including, for example, be sudden, fast or slow, etc. GFO-Data includes these properties as special cases and provides a much broader framework. In [26] the main topic are measurement and measurement systems. In Masolo’s paper, DOLCE’s theory of qualities is grounded on the measurement theory of [27]. The ontology of measurement is an important topic for data science, though, measurement is not in the focus of the ontology, presented in the current paper. In [28], an ontology is outlined which investigates observations and measurement of data. Kuhn’s paper studies processes which are realized by observations and measurements. In contrast, the current paper is directed at a semantic classification of those entities which are to be observed and measured. Hence, the aims of these papers are different. The paper by Florian Probst [29] is devoted to the topic of observations, and of measurements. This paper partly addresses problems which are relevant for the semantics of data, though, his main focus is directed at observations and measurements. Furthermore, the classification principles of Probst’s work and GFO-data are different.

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Summarizing different approaches and goals for properties and data, one may distinguish pure ontological questions about the mode of existence of data and their classification, from the topic of acquiring data by perception, measuring, observation, and questioning. An expressive ontological theory of data, attributives and properties is an inevitable basis, on which theories of acquisition of data are grounded.

6. Applications and Examples In this section we consider some applications and examples of the presented theory. The purpose is to exemplify and check the theory in various domains. The first domain is Physics, the processes of which are governed by physical laws without interventions of human beings. The second domain is biology of cells in which new phenomena arise which cannot – we believe – completely reduced to physics. The third domain is medicine, focused to the field of surgical interventions. In the latter field, humans play an active role, they create these processes by activities, which cannot be understood on the basis of physics and biology alone. The areas of biology and psychology can be clearly separated from physics. Processes in which human actors are involved contain components of non-physical nature, these processes exhibit phenomena as relations, functions, and goals. 6.1 Waves and Particles Physics

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6.1.1. Waves We hold that waves are global properties of processes, being themselves processes. That means, that there are processes, which depend on certain basic processes. Subsequently we make a difference between a wave, being a property of a process, and the process which is the bearer of the wave. In all these cases we may distinguish a basic process on which the waves occur. For example, an electrocardiogram can be understood as a visualization of a global property of the process of heart activity. The heart activity can be presented as the basic process which is associated to the heart In physics, a wave is a disturbance that transmits energy through matter or space, with little or no mass transport. There are different kinds of physical waves, we consider in the sequel mechanical waves, electromagnetic waves, matter waves and gravitational waves. Mechanical waves propagate through physical matter, the substance of which is deformed by forces, restoring forces then reverse the deformation. The alternation of deformation and its reversing at different spatial locations through time is the basic process upon a wave occurs. Since a wave is a global attributive of a process, it inherits basic features of a process, particularly it cannot be wholly present at time-points and it evolves through time. Hence, a wave is itself a process, though it has no autonomous existence, it depends on a basic process with higher degree of autonomy. We essentially agree with the approach of [30] that conceives waves as processes which are not composed of moving material objects, and where waves cannot be identified with its medium. An electromagnetic wave consists of two waves that are oscillations (alternations) between the electric and magnetic fields. An electromagnetic wave moves in a direction that is at right angles to the oscillation direction of both fields. Again, these waves can

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be understood as global attributives of a basic process which consists of changes of the field forces at different localizations of the electro-magnetic field. Gravitational waves are disturbances in the curvature of spacetime, generated by accelerated masses, that propagate as waves outward from their sources at the speed of light. As objects with mass move around spacetime, the curvature changes to reflect the changed locations of those objects. The basic process is the change of the curvature of spacetime, caused by accelerated masses, upon which gravitational waves occur. These gravitational waves are global attributives of the basis process.

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6.1.2. Wave-particle Duality The wave-particle duality is a concept in quantum mechanics. It postulates that every particle or quantum entity may be partly described in terms of particles, but also in terms of waves. It expresses the inability of the classical concepts of particle or wave to fully describe the behavior of quantum objects. Current scientist holds that all particles exhibit a wave nature. There are various views on the wave-particle duality. For the both-particle-and-wave view there is no duality, but rather a system which exhibits both particle properties and wave properties simultaneously. An example are the matter waves which are attributed to particles, and de Broglie postulated that all particles with momentum have a wave of a certain wave length. The wave length λ is determined by the formula λ = h/p, where h is the Planck constant, and p the momentum of the particle. The wave only view proposes to analyze the behavior of particles in terms of wave functions, and attributes the apparent particle-like behavior to quantization of effects and eigenstates. There is further the particle only view, but also the neither-wavenor-particle view, arguing that there are never exact particles or waves, but only some compromise or intermediates between them. From the ontological point of view, the particle-wave duality can be interpreted on the basis of the integration law of GFO. The waves observed for material objects (as in the case of matter waves) are global attributives of the process underlying the material object. In this interpretation the duality between wave and particle remains and can be generalized to a universal duality principle of the material spatiotemporal world which is – finally – based on a complementary duality between the behavior of objects and those of processes. 6.2. Cellular Genealogies and Processes in Biology We consider the problem of modelling of processes, applied to the domain of stem cells. Let C(0) be a stem cell at the time-point of its birth, i.e. after division of a preceding cell. C(0) is the initial point of a cell tree process. C(0) persists through time till a division event occurs which yields a branching point and generates two new distinct cells. This process continues and the whole complete process is denoted by GenTree(C(0)) which is called the full genealogical tree of C(0). Cells C may be classified with respect to their genealogical trees GenTree(C). There is a starting cell C(root) of the whole organism, and for every cell C the process GenTree(C) is a closed sub-tree of GenTree(C(root)). The tree GenTree(C) contains many sub-trees whose ontological classification are of relevance for a deeper understanding of the development of cells. For this sake GenTree(C) must be annotated by suitable properties, which are assigned to the tree’s components. The basic components of the genealogical tree are determined by the following views.

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Firstly, any cell C at a time-point t, denoted C(t), is completely/wholly present at t and has no temporal parts; furthermore, C occupies space because it has a certain (inherent) extension space, has a morphology and natural boundaries. C(t) is called a presentic cell. Secondly, any cell C persists through time, that means if this cell C is considered at two different time-points t1 and t2, which yield two snap-shots C(t1), C(t2), then these two entities, though different, belong to the same C. Hence, a cell satisfies the conditions of a material object. Thirdly, any cell is a process, being a temporal part of GenTree(C(0)) which has no branching point. Further, the whole entity GenTree(C) forms a process with branches. There is a manifold of properties which can be attributed to GenTree(C) and its components. Properties can be assigned to continual cells (objects) and to processual parts of GenTree(C). GenTree(C) is the structurally richest entity associated to C which allows an integration of knowledge on the single cell level. An important property of a cell is stemness. In [31] it is stated that stem cells are defined in terms of their functional capabilities which can only be verified if the full genealogical tree is developed. At present it seems to be impossible to find a presentic attributive of a continual cell which implies that the full genealogical tree verifies the stemness of the cell. This kind of uncertainty principle is based on the complementary duality between presential and process.

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6.3. Processes with human agents Processes in physics can be described by physical laws without interventions of human agents, whereas processes in biology and in social systems need further components and notions to achieve a complete understanding. An example of such processes are business processes. They are distinct from processes in physics and in biology, because the human agents participating in the process play a fundamental role. Here, new phenomena occur which cannot be reduced to physical or biological notions alone. The new aspects are presented by such entities as roles, functions, aims, and teleological aspects. Another example of non-physical processes are surgical interventions. An activity in surgery is a processual segment which has a function, which is a non-physical attributive. The various levels of surgical interventions are studied in [32]. A surgical intervention is a process the temporal extension of which can be subdivided into activities and phases. Activities are certain temporally extended actions, they are considered as atomic components of the whole process. Such a process cannot be understood within purely physical notions because here occur attributives which have a cognitive nature, namely relators and functions. A cut, for example, is an activity with a physical basis, though it is augmented with a function, an aim. Furthermore, these activities are carried out by a surgeon, a human, and there is no physically determined causal relation between subsequent actions.

7. Conclusions and Further Research. In this paper we outlined a foundational ontology of properties, attributives, and data which is intended to contribute to the foundation of an integrated data semantics. Properties and attributives are classified with respect to different axes. One axis is the classification with respect to the properties’ bearers, which yields a particular rich

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ontology of processual properties. Another axis of the classification of attributes pertains to the level of abstraction. In contrast to phenomenal attributes, which can be perceived or directly measured, relational and functional attributives do not possess this feature. These are cognitive creations of the mind, which are assigned to bearers. Relational and functional attributives play a role for objects, created by humans, and for processes in which human actors participates. We collect some research topics which might be relevant for the future. There is a need to further developing a top-level ontology of attributives, properties, and data. The current GFO-Data presents only a first version of such an ontology, which must be refined and completed in various directions. In particular, we need a framework for the establishment of axioms for property-frames and property-systems. A challenging problem is the development of an ontological framework which may serve as a unifying theory of data and knowledge. Furthermore, we expect applications in the field of natural science.

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Ontological Dependence, Spatial Location, and Part Structure Friederike MOLTMANN1 Centre National de la Recherche Scientifique

Abstract. This paper presents new observations about ontologically dependent objects which cannot have a host-independent spatial location or a physical part structure, namely disturbances (holes, folds, scratches), tropes, and attitudinal objects (claims, thoughts, promises, requests). It proposes an account of such attributively limited objects in terms of Fregean abstraction, which has so far been applied only to abstract objects. Keywords. Ontological dependence, spatial location, part structure, abstraction, disturbances, tropes, attitudinal objects

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1. Introduction Applied ontology, natural language ontology as well as the metaphysics of ordinary objects generally recognize that their domain of entities comprises a great range of ontologically dependent, minor entities. Such entities include what are called disturbances (entities of the sort of holes, folds, faults, and scratches) and tropes (particularized properties or features). A general approach to such entities is to take them to be ontologically derivative, introduced by an ontological operation from more basic entities or conditions, an operation which one may consider an operation of reification. There are two important operations of reification that have been discussed in the literature. One of them introduces an entity on the basis of the truthmaking relation [1,2,3,4,5]. The other operation is more familiar from the philosophy of mathematics, namely abstraction in the Fregan sense [6,7,8]. In this paper, I argue that certain ontologically dependent entities, including disturbances and tropes, should be viewed as entities introduced by a combination of truthmaking and abstraction. This is needed in order to order to account for both their concreteness and a surprising lack of specification for certain types of properties. It is a standard view in contemporary metaphysics that concrete objects come with a spatial location and a physical part structure. This view faces a serious challenge from our intuitions about the spatial location and the part structure of certain ontologically dependent concrete objects. Those ontologically dependent objects, it appears, simply lack a non-relative spatial location (a location not just relative to another object) or the sort of part structure they are expected to have as concrete objects. I will call objects of this sort attributively limited objects and their peculiarity attributive limitation. Attributive limitation is more familiar from abstract objects as 1

Friederike Moltmann, IHPST, 13 rue du four, 75006 Paris, France; E-mail: [email protected].

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entities introduced by a form of Fregean abstraction, such as numbers or directions on the Fregean account. This paper will suggest that the attributive limitations of the relevant class of concrete objects be accounted for by a form of abstraction as well. It will do so by drawing on a notion of an abstract state that is already an entity somewhat between abstract and concrete, and arguably plays a significant role in the semantics of natural language. I will first present standard assumptions regarding the distinction between concrete and abstract objects as well as particular views about the inheritance of properties of objects from more fundamental ones. I then present the central issue of the paper, intuitions about the spatial location and part structure of certain ontologically dependent concrete objects. Finally, I will suggest a way of applying an abstractionist account to the relevant types of ontologically dependent concrete objects.

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2. The abstract-concrete distinction The distinction between abstract and concrete objects is a central distinction in metaphysics, and according to the standard view, concrete objects and abstract objects are distinguished by different sorts of properties they may have, without there being agreement as to what sorts of properties best characterize the distinction. Properties that have been proposed as characteristic of abstract objects are properties such as being non-mental, being nonphysical, being causally inefficacious, and not having a spatiotemporal location [9]. Whether abstract objects have a temporal duration is a matter of controversy: abstract artifacts are abstract in the sense of not being physical, but they come into being at some point in time and may go out of being at some point in time as well. Having a spatial location, by contrast, is a less controversial characteristic that concrete objects are taken to have and abstract objects are taken to lack.2 While the distinction between abstract and concrete objects is generally based on general conditions on what sorts of properties concrete and abstract objects may have, there is also an approach according to which certain types of objects do not come to bear properties directly, but derivatively, by inheritance from more fundamental entities [10,11]. This particularly applies to material objects and the material that constitutes them. Entities individuated, at least in part, by their shape such as artifacts, inherit, on that view, color, texture, weight from the material constituting them [10,11]. Also the spatial location of artifacts can be considered inherited from the spatial location of their material manifestation at a time. Fine [12] applies property inheritance to another relevant case, qua objects (which includes non-basic actions). A qua object such as John qua father is an object individuated by particularly restricted condition of property inheritance from its base (John). John qua father inherits only those properties from John that John has while being a father [12] or, better, that John has in virtue of being a father [13]. John qua father thus comes out as an attributively limited object, displaying a lack of specification for all properties that are not based on John being a father. Making use of property inheritance conditions thus deviates from the standard view according to which all concrete objects by nature come with the same types of characteristic properties.

2

There is some controversy, though, regarding the spatial location of sets of concrete objects [9].

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3. The intuition about some ontologically dependent entities

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3.1. Spatial location We can now turn to the central issue of this paper, intuitions about the spatial location and part structure of ontologically dependent concrete objects. Let us first consider entities like holes, folds, flaws and scratches. Entities of this sort are based on regular or irregular gestalt conditions in material objects, and are generally called disturbances [14,15,16]. We clearly treat disturbances as entities: they generally are countable and come into existence and go out of existence at particular points in time. Thus, we can say that a hole, fold, flaw, or scratch exists or no longer exists, and that there are several of them. Disturbances are ontologically dependent objects par excellence. They exist only if the object which hosts them (their base) exists. Also, for their identity, they require the identity of the object that hosts them. They are thus ontologically dependent in the sense of existence dependence and identity dependence [17,18]. Linguistically, the ontological dependence of disturbances is reflected in the applicability of the have-construction, which can be used to express ontological dependence: the bag has a hole, the cloth has a fold, the paper has a flaw, and the surface has a scratch. Disturbances have a location relative to the object on which they depend, requiring a suitable spatial preposition such as in or on, as in the hole in the bag, a fold in the cloth, a scratch on the surface. The prepositions in and on in fact may also convey the dependence relation of a disturbance to the host itself, permitting a further specification of a location of the disturbance within the host, as in the hole in the bag is near the handle or the scratch on the surface is close to the edge. Now what is remarkable is that disturbances do not have a spatial location that is not relative to their host. Thus, if the hole is in the bag and the bag is in the drawer, it does not follow that the hole is in the drawer. In fact, the hole can only be in the bag and located within the bag; it lacks a location that is independent of the bag.3 Similarly, a fold cannot be on the table even if the cloth is that has the fold. The fold is nowhere in fact but in a particular place in the cloth. A scratch on the screen is not on the table even if the screen is; the scratch is nowhere in fact but in a particular place on the screen. Disturbances do not inherit their location from the object on which they depend: they do not have a location that is not relative to their host. Disturbances also cannot move, even when the object on which they depend moves. If the flag has a hole and the flag moves in the wind, the hole would not move in the wind. The hole cannot move, unless it does so within the object that has it If the surface has a scratch and the surface moves, the scratch does not move (it can be said to move only when it is not clear that it is something on a particular surface). Mary may put away the dress, but she thereby would not put away the fold in the dress. Tropes display the same sort of behavior as disturbances with respect to a spatial location. Tropes in twentieth century one-category reductionist ontological theories are considered entities more fundamental than individuals and properties, coming with two fundamental relations: similarity and co-location [21]. On such a view, tropes would not be ontologically dependent, but rather individuals and properties would be constituted by tropes. However, on the older, Aristotelian tradition, tropes (or 3

See [19] and [20] for observations about the non-monotonicity of is in for holes.

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‘accidents’) are ontologically dependent objects par excellence. A trope exists only if its bearer exists and a trope is identical to another trope only if their bearers are identical, or so the standard view maintains. Again the ontological dependence of tropes is reflected in the applicability of the have-construction, though when conveying the ontological dependence of tropes on their bearers the have-constructions imposes particular restrictions: Socrates ‘has’ wisdom, the painting ‘has’ an unusual quality, though the apple does not really ‘have’ redness, and the pillow does not really ‘have’ softness. Clearly, tropes clearly do not inherit a location from their bearer. If Socrates is in Athens and Socrates has wisdom, Socrates’ wisdom is not in Athens. The painting may be on the wall and there may be an unusual quality in the painting, but the unusual quality of the painting is not on the wall. If the stone has an enormous weight (a quantitative trope), and the stone is on the table, the enormous weight of the stone is not on the table. Tropes have no bearer-independent location. Moreover, a great range of tropes cannot even be attributed a bearer-dependent location. Despite locutions Aristotle may have used, Socrates’ wisdom is not ‘in’ Socrates, Socrates just has it. The weight of the stone is not ‘in’ or ‘on’ the stone, the stone just has the weight. Not all ontologically dependent objects, though, behave that way with respect to their spatial location. Shadows, for example are generally considered ontologically dependent on the object throwing the shadow, but they can be attributed a location independently of the object on which they depend as well as movement. (The shadow may be here and there and moves across the wall etc.). What then are the conditions on entities unable to have non-object-relative locations? The condition appears to be that such entities need to be constituted by features of the base object whose location is properly included in that of the base object.4 This condition is not satisfied for the relation between material and the objects they constitute. A trope (such as the quality of the painting) need not be limited to a location properly included within the bearer (the painting). Thus, the relevant class of ontologically dependent objects should be characterized as those entities that have a location properly within the object on which they depend on or else are tropes. The attributive limitations of disturbances and tropes could not be accounted for by considering them qua-objects that fail to inherit a location from their bearer. Qua objects inherit whatever property they may have from their base. Disturbances and tropes are not individuated by restricted property inheritance from their base or bearer; rather, they are constituted by features of (part of) the object on which they depend, without themselves having such features (e.g. a roundness trope is not itself round). 3.2. Part structure There is another important case of attributive limitation that I want to mention, and that concerns the part structure of objects. Sometimes an object is expected to have part structures in different ‘dimensions’, but displays just a single part structure. Some objects come with a part structure based on partial content. Yet those objects may be physical objects at the same time and thus have two part structures, in two dimensions. An example is a book. A book is an entity that comes with two distinct 4

Note that the location of a hole is strictly speaking not included in the location of its host because where there is hole, there is no matter constituting the host, by the very definition of what a hole is.

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facets, as a material object and as an information object, and they involve two part structures. ‘Part of the book’ can mean a material part of the physical object or else a partial content.5 However, there are also physical objects that lack a physical part structure. Entities of the sort of claims, requests, and offers are of this sort, that is, the non-enduring products of illocutionary acts, illocutionary products [22,23,24,25].6 A claim can be overheard and cause uproar and it is made at a particular point in time, at a particular place. Thus a claim has a range of features of concrete objects. But part of a claim can never be a physical part, say a temporal part of an action of claiming. Part of a claim can only be a partial content. A claim, intuitively, has only parts that are partial contents of what is claimed. Thus, claims are peculiar in that they clearly display features of concreteness, but yet cannot have physical parts. They are thus what I will call mereologically restricted objects. Tropes in a way are also mereologically restricted. Tropes are particular property manifestations in objects, their bearer. Their bearer may have a spatial part structure, yet tropes will generally not inherit a spatial part structure.7 The parts of tropes can only be features constitutive of the (complex) trope or perhaps temporal parts. For example, part of John’s happiness can be features of John constitutive of his happiness or else a perhaps a period of his happiness. This is different for events [26,23]. Events may have several part structures in different dimensions at once, say a temporal part structure, a participant-related part structure, and a spatial part structure [13]. Part of the battle, for example, can be a temporal part of the event or a spatial part or a subevent constitutive of the battle at the time and place of the battle. Tropes are thus mereologically restricted in a way events are not.8

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4. Towards an account of attributive limitations of disturbances and tropes Disturbances and tropes thus are entities that are attributively limited. The question then is, how are such attributive limitations to be accounted for? I want to suggest an approach to the puzzle of attributive limitation by drawing a connection to one particular ontological theory about abstract objects, namely abstractionism, the theory of an object being introduced by a form of Fregean abstraction [6,7,8]. Frege proposed 5

As a referee has pointed out, a book in fact can have parts that themselves come with the two facets, such as a chapter: one can read a chapter or tear off a chapter from a book. 6 See [23,24,25] for arguments that nouns like claim, request and offer are not ambiguous standing either for acts or events or else contents, as the standard view would have it, but rather always stand for entities of a third sort, illocutionary products. I argued that illocutionary and cognitive products belong to a broader class of attitudinal objects, which also include state-like objects of the sort of beliefs, intentions, and desires [23,25]. Offer and claim may also refer to modal objects, which unlike illocutionary products may endure past the illocutionary act that produced them [25]. 7 One might think that tropes based on a pattern or the shape of an object should inherit a spatial part structure, for example the triangularity of the figure. However, such tropes are in fact not generally treated as having a part structure that reflects the relevant spatial part structure of the base. Thus, part of the triangularity of the figure makes little sense. 8 One might also consider enduring material objects as mereologically restricted. Enduring material objects are in space and time, but have only a spatial part structure, according to our intuitive notion of them. Temporal stages of material objects do not intuitively count as parts of enduring objects. The part structure of enduring objects, however, is linked to their mode of persistence, to what is constitutive of their identity at a time. Enduring objects exist in time (or endure), which basically means they need to be (more or less) wholly present (present with all their parts) at each moment of the time at which they exist – at least according to one influential view of endurance.

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that numbers be introduced by the abstractionist principle below, which gives identity conditions for objects obtained by the abstraction function g from entities o and o’ that stand in some equivalence relation R: (1) For an equivalence relation R, for all o and o’, g(o) = g(o’) ↔ R(o, o’). Frege used (1) to introduce natural numbers as entities obtained by abstraction from concepts for whose extensions there is a 1-1 mapping. What is special about an abstractionist theory of an object type is that it introduces an object as an object that will have only those properties specified by the method employed for its introduction. Thus numbers introduced by the principle in (1) do not have other properties that could not be derived from the condition of their identity with other numbers introduced in the same way. The abstractionist account thus introduces a number as an object that is not specified as to whether it is identical to a non-number, say, the individual Caesar, or has any properties of concreteness. Abstractionist theories have not only been proposed for abstract objects in the context of the philosophy of mathematics. There is also an abstractionist theory of states (and of non-worldly facts).9 This is what Kim’s [27] account of events amount to. Kim’s account, it is generally agreed, is not an account of events, but of states, more specifically of ‘Kimean states’ as Maienborn [28] calls them or ‘abstract states’, as I prefer to call them [29,3]. Kim’s account is given below, now formulated as a theory of states (of a rather simple sort, consisting of a property holding of an object):

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(2) The Kimian account of states a. For a property P, an object o, the state s(o, P) obtains at a time t iff P holds of o at t. b. For properties P and P’ and objects o and o’, s(o, P) = s(o’, P’) iff P = P’ and o = o’. Kim’s account is an abstractionist account: (1) can be generalized to n-place abstraction functions applying to n objects that stand in respective equivalence relations to each other. Kim’s account then introduces states on the basis of a two-place abstraction function applying to objects and properties and the equivalence relation of identity. On the Kimian account of states, states will have identity conditions and a temporal duration, but no other intrinsic properties. Kimean or abstract states are not on a par with events ontologically. Events involve a particular manifestation and a spatial location, and they can act as relata of causal relations [2,3,28]. By contrast, states as entities introduced by abstraction as in (2) will carry only properties specified for them by the method of introduction. This means that they have a particular temporal duration and that their identity depends strictly on the property and object from which they are abstracted. But it also means that such states have no spatial location, won’t stand in causal relations, won’t involve a particular manifestation or particular manner, won’t be perceivable etc. They may act, though, as objects of mental attitudes and as relata of causal explanation [28]. States in that sense play an important role in natural language semantics, as Davidsonian, implicit arguments of stative verbs such as own, owe, know, weigh, 9

Frege also proposed an abstractionist account of directions (the direction of a is identical to the direction of b iff a is parallel to b).

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resemble, weigh, measure, have and be, or so it has been argued [28]. The states described by most stative verbs (including those just mentioned) accept only a very restricted set of adverbial modifiers. They resist in particular location modifiers, manner adverbials, instrumentals, and causal and perceptual predicates, representing just the sorts of properties that states introduced by abstraction as in (2) should not be specified for.10 If abstract states play a semantic role as implicit arguments of (most) stative verbs, this explains the resistance of stative verbs to adverbials of the relevant sorts. Abstract states also play a semantic role as referents of gerundive nominalizations of stative verbs such as John’s owning the house, Mary’s owing an amount of money, John’s knowing French, Bill’s weighing over 100 kilo, Socrates’ having wisdom, Mary’s being happy etc. Abstract states have a temporal duration and thus are in time, and they obtain (at a time) on the basis of what is going on in the world. Even though they do not contain the individual and the property from which they abstracted as parts, their identity and existence depends on them. Abstract states thus display some features of concreteness, yet they clearly show attributive limitations. I want to propose that ontologically dependent objects that are disturbances be viewed similarly, as entities obtained in a particular way by abstraction from relevant properties of their base. The abstraction principles however will be different from that of abstract states in that they should not involve a particular (possibly nonspecific) property, but rather a range of fully specific features of the base objects. Disturbances will be entities based on features of the base object that together meet certain gestalt conditions, a relation that can be viewed as a truthmaking relation. Disturbances will then be individuated as objects having only properties strictly pertaining to those features and their relation to the base object (in particular their location within the base object) and nothing else. Unlike abstract states, disturbances will involve a very particular manifestation of the particular gestalt conditions in question (truthmakers of the relevant gestalt conditions). But they will not be specified with properties in respects not strictly related to the manifestation of those gestalt conditions in the base object; and thus in particular they will lack an independent spatial location. Disturbances will then be fully specific in certain respects only, for example regarding the shape and size of a hole or fold as well as the location of the hole or fold with respect to the base object. Tropes have often been viewed as entities obtained by abstraction in a psychological sense, the act of attending to only one property of an object and abstracting from all others.11 But the relation between a trope and its bearer need not be understood in a psychological sense. It can be viewed rather in the same sense of a formal ontological operation of abstraction as in the case of disturbances. The relation of abstraction obtaining between the bearer and the trope involves two things. First, the trope will be based on features of the bearer fulfilling a particular condition, a relation that may be regarded as the truthmaking relation. Second tropes will have properties only pertaining to those features of the bearer and the bearer itself. Tropes will then lack a specification with respect to other types of properties such as that of an 10

This is known as the Stative Adverb Gap. Some researchers have taken the Stative Adverb Gap to mean that stative verbs lack a Davidsonian [30] event argument position, rather than having one filled in by abstract states [31]. 11 This is reflected in Campbell’s [32] term ‘abstract particular’ as an alternative term for William’s [21] term ‘trope’.

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independent spatial location. Like disturbances, tropes will be fully specific with respect to some types of property attributions, but lack other types of property attributions. Disturbances and tropes thus would be introduced by a combination of truthmaking and abstraction, a complex ontological operation that of course needs to be developed in much further detail formally. The mereological restrictions of illocutionary products would be accounted for in similar ways. Illocutionary products would be introduced as products of illocutionary acts with specific physical features, but yet at the same time as being specified for parthood only in one respect, that of content.

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5. Conclusion Entities like disturbances, tropes, and illocutionary products are ontologically secondary, derivative objects. Yet they play an important role for ontology, in particular applied ontology, natural language ontology, and just the metaphysics of ordinary objects. This paper has pointed out that entities of this sort are attributively limited and challenge standard ontological views about the spatial location and the physical part structure of concrete objects. Such attributive limitations could not be accounted for if the entities in question were just the result of reification based on truth making in Guarino and Guizzardi’s [4,5] sense. The paper rather argued that entities of this kind be viewed on a par with objects introduced by abstraction, mathematical objects as well as abstract states, entities which have some features of concreteness and play a particular role in natural language semantics. Disturbances, tropes, and illocutionary products, on that proposal, are introduced by abstraction, ensuring they lack certain property specifications; at the same time, they would be based on a fully specific manifestation of a condition or set of conditions, a truthmaker of sorts in the case of disturbances and tropes. The proposal was presented as a sketch, of course, and needs to be developed in much greater detail on another occasion.12 There are also further application of the proposal to be pursued, in particular to functional or nonexistent intentional objects, entities that arguably depend ontologically on (unsuccessful or pretended) acts of reference and are attributively limited to the extent to which those acts do not go along with attributions of particular properties [34].

Acknowledgments The paper has greatly benefited from comments on a previous version by Fabrice Correia, Kathrin Koslicki, Jonathan Schaffer, Achille Varzi, and three anonymous referees, as well as from conversations with Kit Fine. 12

The proposal bears some similarities to Guarino and Guizzardi’s [33] theory of relationships, where (reified) relationships are taken to be sums of ‘aspectual slices’ of the relevant relata and in that sense would involve abstractions over relational qualities inhering in the relata. For example, the marriage m between John and Mary is taken to be the sum of two entities: John-qua-husband-of-Mary and Mary-qua-wife-of-John, aspectual slice of John and Mary respectively.

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References [1] K. Mulligan, K., P. Simons, and B. Smith, Truthmakers, Philosophy and Phenomenological Research 44 (1984), 287–321. [2] F. Moltmann, Events, Tropes and Truthmaking, Philosophical Studies 134 (2007), 363-403. [3] F. Moltmann, Nominals and Event Structure, in R. Truswell (ed.), Oxford Handbook of Event Structure. Oxford University Press, Oxford, to appear. [4] N. Guarino and G. Guizzardi, Relationships and Events: Toward a General Theory of Reification and Truthmaking, in G. Adorni G., S. Cagnoni S., M. Gori, and M. Maratea (eds), Advances in Artificial Intelligence, Springer, Cham, 2016, 237-249. [5] N. Guarino, T. P. Sales, and G. Guizzardi, Reification and Truthmaking Patterns, inTrujillo J. et al. (eds), Conceptual Modeling, Lecture Notes in Computer Science, vol. 11157, Springer, Cham, 2018, 151165. [6] G. Frege, Die Grundlagen der Arithmetik: eine logisch-mathematische Untersuchung
ber den Begriff der Zahl, 1884, translated by J. L. Austin as The Foundations of Arithmetic. Blackwell, New York, 1950. [7] B. Hale, Abstract Objects. Blackwell, Oxford, 1987. [8] [C. Wright, Frege's Conception of Numbers as Objects, Aberdeen University Press, Aberdeen, 1983. [9] G. Rosen, Abstract Objects, in Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy (fall 2018 edition), , URL . [10] K. Fine, Things and Their Parts, Midwest Studies in Philosophy 23 (1999), 61-74. [11] K. Koslicki, The Structure of Objects, Oxford University Press, New York, 2008. [12] K. Fine, Acts, Events and Things, in Language and Ontology: Proceedings of the 6th International Wittgenstein Symposium, Hölder-Pichler-Tempsky, Vienna, 1982, 97-105. [13] F. Moltmann, Parts and Wholes in Semantics, Oxford University Press, Oxford, 1997. [14] T. Karmo, Disturbances, Analysis 37 (1977), 147–148. [15] P. Simons, Parts. A Study in Ontology, Oxford University Press, Oxford, 1987. [16] R. Casati and A. C. Varzi, Holes and Other Superficialities, MIT Press, Cambridge, MA, 1994. [17] K. Fine, Ontological Dependence, Proceedings of the Aristotelian Society 95 (1994), 269–290. [18] T. E. Tahko and J. E. Lowe, Ontological Dependence, in E. N. Zalta (ed.), The Stanford Encyclopedia of Philosophy (winter 2016 edition), URL= . [19] M. Aurnague and L. Vieu, A three-level approach to the semantics of space, in C. Zelinski-Wibbelt (ed.), Semantics of Prepositions: From Mental Processing to Natural Language Processing, Mouton de Gruyter, Berlin, 1993, 393–439. [20] A. Varzi, Reasoning about Space. The Hole Story, Logic and Logical Philosophy 4 (1995), 3-39. [21] D.C. Williams, The Elements of Being, Review of Metaphysics 7 (1953), 3-18. [22] K. Twardowski, Actions and Products. Some Remarks on the Borderline of Psychology, Grammar, and Logic, 1911, in J. Brandl and J. Wolenski (eds.), Kazimierz Twardowski. On Actions, Products, and Other Topics in the Philosophy. Rodopi, Amsterdam and Atlanta, 1999, 103-132. [23] F. Moltmann, F., Abstract Objects and the Semantics of Natural Language, Oxford University Press, Oxford, 2013. [24] F. Moltmann, Propositions, Attitudinal Objects, and the Distinction between Actions and Products, Canadian Journal of Philosophy 43 (5-6) (2014), 679-701. [25] F. Moltmann, Cognitive Products and the Semantics of Attitude Reports and Deontic Modals’, in F. Moltmann and M. Textor (eds.), Act-Based Conceptions of Propositions: Contemporary and Historical Contributions. Oxford University Press, Oxford, 2017, 254-290. [26] F. Moltmann, F., Degree Structure as Trope Structure A Trope-Based Analysis of Comparative and Positive Adjectives’. Linguistics and Philosophy 32 (2009), 51-94. [27] J. Kim, Events as property exemplifications, in M. Brand and D. Walton (eds.), Action Theory. Reidel, Dordrecht, 1976, 310-326. [28] C. Maienborn, On Davidsonian and Kimian States, in I. Comorovski and K. von Heusinger (eds.), Existence: Semantics and Syntax, Springer, Dordrecht, 2007, 107–130. [29] F. Moltmann, F., On the Distinction between Abstract States, Concrete States, and Tropes, in A. Mari, C. Beyssade, and F. Del Prete (eds.), Genericity, Oxford University Press, Oxford, 2013, 292-311. [30] D. Davidson, D., The Logical Form of Action Sentences, in N. Rescher (ed.), The Logic of Decision and Action. Pittsburgh University Press, Pittsburgh, 1967, 81–95. [31] G. Katz, Events as Arguments, Adverb Selection, and the Stative Adverb Gap, in E. Lang (eds.), Modifying Adjuncts, de Gruyter, Berlin, 2003, 455-474. [32] K. Campbell, Abstract Particulars, Blackwell, Oxford, 1990.

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[33] N. Guarino and G. Guizzardi, ‘We Need to Discuss the Relationship’: Revisiting Relationships as Modeling Constructs, CAiSE (2015), 279-294. [34] F. Moltmann, Quantification with Intentional and with Intentional Verbs, in A. Torza (ed.), Quantifiers, Quantifiers, Quantifiers. Springer, Dordrecht, 2015.

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V. Ontologies and Applications

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Taking It to the Next Level: Nicola Guarino, Formal Ontology and Conceptual Modeling Giancarlo GUIZZARDI a,b,1 , John MYLOPOULOS c a Conceptual and Cognitive Modeling Research Group (CORE), Faculty of Computer Science, Free University of Bozen-Bolzano, Italy b Ontology and Conceptual Modeling Research Group (NEMO), Computer Science Department, Federal University of Espírito Santo (UFES), Brazil c University of Trento, Italy

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1. Introduction This paper is dedicated to Nicola Guarino, on the occasion of his 65th birthday. Nicola has made seminal contributions to Conceptual Modeling that include some of the greatest advances in this field of research over the past thirty years. Nicola’s contributions include OntoClean [1,2], proposed jointly with Chris Welty, the first proposal of formal ontological analysis. This work has been widely cited, but is also used in academic and industrial settings around the world, thus having had tremendous impact. One of the OntoClean papers has had more than 1,000 citations (Google Scholar, October 2018) and won an “Thomson-ISI recognition of an "Emerging Research Front" award in 2004. Another seminal contribution of Guarino’s research is his work on the DOLCE foundational ontology, which has also had broad and deep impact in the field [3,4,5,6,7]. But by far his most significant contribution lies in his critique of conceptual modelling and knowledge representation languages for being ontologically neutral. Instead, he has argued convincingly that such languages should make commitments for the primitive concepts they offer on their ontological properties concerning existence, dependence, identity and rigidity. Such commitments reduce the space of possible interpretations for conceptual models and align them more closely to modeller intentions. This view that Conceptual Modeling Languages should break with ontological neutrality by committing to a suitable ontological theory strongly influenced the design of a next-generation of conceptual modeling approaches such as, for example, OntoUML [8,9,10]. The main objective of this paper is to present some of Nicola’s contributions and highlight their importance to Conceptual Modeling. To do so, we begin with an account of what is Conceptual Modelling (section 2), followed by the essential elements of the ontological framework proposed by Nicola (section 3). In section 4, we present the no1 Corresponding

Author: [email protected]

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tion of Ontology-Driven Conceptual Modeling and, in particular, how it has been implemented in the OntoUML program, with important direct contributions from Nicola. Section 5 presents some final considerations.

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2. Conceptual Modeling It is a foundational tenet of Cognitive Science and Philosophy of Mind that cognitive processes create, use and transform mental representations of the world. Such representations are “intentional" in the sense that they refer to, or are about something. Mental representations may be conceptual in the sense that they consist of concepts, such as thoughts, or non-conceptual, such as sensations. We call these conceptual mental representations conceptualizations. The field of research we call Conceptual Modeling aims to develop concepts, tools and techniques for building computational models of conceptualizations, to be used for purposes of understanding and communication. The same can be said for the related field of Knowledge Representation in Artificial Intelligence (AI). The difference between the two fields is that for Conceptual Modelling, these models are used to support the design of databases, software, business processes, enterprises etc., whereas in Knowledge Representation, these models (aka knowledge bases) are used to endow an intelligent computational agent with suitable knowledge for the performance of an intelligent task, such as planning, diagnosis, design, etc. As far back as Aristotle there have been theories that conceptualizations consist of concepts and associations that relate similar concepts. According to empiricists (Hume et al), associations come about when concepts co-occur in the experiences of a cognitive agent. For example, the concepts of ‘Student’ and ‘Person’ co-occur every time you encounter a student, so a Student/Person association is meaningful, and likely. Most proposals for conceptual models adopt such an associationist stance, including Semantic Networks, Object-Oriented models and Description Logics. The origins of conceptual modeling can be traced back to the 60s. Ross Quillian [11] proposed in his PhD thesis the notion of Semantic Networks, a form of directed, labelled graph, as models of human (semantic) memory. Nodes of his semantic network proposal represented concepts (more precisely, word senses.) For words with multiple meanings, such as “plant", there would be several nodes, one for each sense, e.g., “plant" as in “industrial plant", “plant" as in “evergreen plant”, “plant" as in “plant my garden every year", etc. Nodes were related through links representing semantic relationships, such as isA (“A bird is a(n) animal", “a shark is a fish”), has (“A bird has feathers"), and eat (“Sharks eat humans"). Moreover, each concept could have associated attributes, representing properties, such as “Penguins can’t fly". There are several noteworthy ideas in Quillian’s proposal. Firstly, his conceptual models consisted of concepts and associations. Moreover, generic concepts were organized into an isA (or, generalization) hierarchy, supported by attribute inheritance. In addition, his proposal came with a radical computational model where finding meanings for a noun phrase, such as ‘horse food’, was accomplished by finding paths that connect the two nodes ‘horse’ and ‘food’, for example, eats

IsA

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IsA

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horse −−−−→ meat −−→ food There was much research on semantic network-based conceptual modeling languages in the early ’70. In AI, there were many proposals, some came with an interpreter that could draw inferences from the labels associated with relationships. Others had attached assertions or procedures with every node, capturing the semantics of the concept being represented ([12], [13]). In Databases, there were proposals for semantic data models, such as the Entity-Relationship Model2 [14] and Taxis [15]. Among them, the KL-ONE knowledge representation language, proposed in the thesis of Ron Brachman, stands out for its treatment of concepts, and the reasoning support provided by the language. In KL-ONE, concepts are represented by descriptions consisting of concepts and roles. Moreover, KL-ONE supported subsumption reasoning with descriptions, where description1 was subsumed by description2 if all its instances were also instances of description2 . For example, “a man on (a hill with a telescope)” is subsumed by “a man on a hill”. KL-ONE led to a family of languages known as Description Logics that constitute the state-of-the-art of automated reasoning support in Conceptual Modeling. There is also a WWW standard for Description Logics, known as the Web Ontology Language (OWL), which was designed as a key technology in making the Semantic Web a reality. Roughly at the same time as Quillian, Ole-Johan Dahl proposed SIMULA 67, a programming language for simulation programs [16]. This language was defined as an extension of Algol 60. The main extension consisted of the notion of a class that had instances, each with associated code so such instances were active, instead of passive data structures. The idea behind SIMULA 67 was that when you want to simulate some part of the world, for example barber shops, you define classes for the kinds of objects you are simulating, such as barber shops, barbers, customers and haircuts. SIMULA was followed by Smalltalk, developed at Xerox PARC, which formed a foundation for object-oriented programming and object-oriented modeling starting in the early 80s. The Unified Modeling Language (aka UML) constitutes a major achievement of this line of research, as it combined several proposals into one, rather loosely defined, language for modeling software designs. UML has been extended into SysML to support modeling systems, as opposed to just software. Douglas Ross proposed in the mid-’70s the Structured Analysis and Design Technique (SADT) as a “language for communicating ideas" [Ross77]. The technique was used by Softech, a Boston-based software company, to specify requirements for software systems. According to SADT, the world consists of activities and data. Each activity consumes some data, represented through input arrows from left to right, produces some data, represented through output arrows from left to right, and also has some data that control the execution of the activity but are neither consume nor produce. For instance, the Buy Supplies activity of Figure 1 has input arrow ’Farm Supplies’, output arrows ‘Fertilizer’ and ‘Seeds’ and control arrows ‘Seed and Vegetable Prices’ and ‘Plan Budget’. Each activity may be defined through a diagram such as that shown in Figure 1 in terms of sub-activities. Thus ’Growing Vegetables’ is defined in terms of the subactivities ’Buy Supplies’, ‘Cultivate’, ‘Pick Produce’ and ’Extract Seeds’. Ross’ contributions include a modeling language that can capture both static and dynamic aspects 2 Despite

its name, the Entity Relationship Model is a modeling language

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of an application. Ross is credited with convincing software engineers, researchers and practitioners alike, that it pays to have diagrammatic descriptions of how a software system is to fit its intended operational environment. This contribution helped launch Requirements Engineering as an accepted and important early phase in software development.

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Figure 1. SADT diagram for the ‘Grow Vegetables’ activity (from [17]).

Given that the task-at-hand for Conceptual Modeling is to build models of conceptualizations, the main constituent of any proposal has been a conceptual modelling language. Such languages include the ER Model, SADT, and Simula 67. Since these early days, there have been hundreds of proposals for such languages in the literature, including popular standards used in industrial practice, such as UML, SysML and BPMN. Any conceptual modelling language consists of (a) a set of primitive classes that represent concepts and associations; (b) a set of abstractions mechanisms, such as generalization, and aggregation, through which models expressed in the language are structured; (c) a logical language for making statements in the language; (d) a set of questions that can be answered through reasoning with respect to a model. For example, the ER Model has primitive classes Entity, Relationship and Attribute; the ER Model does not support any abstraction mechanisms, but the Extended ER Model does support generalization. Finally the language of the ER Model is a visual language that supports the definition of a collection of entity and relationship classes and their associated attributes and does not support any reasoning, so it is a rather rudimentary Logic. In all cases, the modeling languages proposed until Nicola’s work paid scant attention to the primitive concepts they offered for modeling, treating them as mere sorts.

3. Conceptual Modeling and the Ontological Level As previously mentioned, two of the most basic modeling primitives in domain modeling are Entity Types as well as Relationship Types. Nicola’s work made fundamental contri-

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butions in providing real-world semantics for both types of constructs and methodological support for modeling them. The key aspect here was to break with the ontological agnosticism (or neutrality) of traditional conceptual modeling and knowledge representation languages. The importance of philosophical ontology for domain modeling (including Conceptual Modeling and Knowledge Representation) permeated Nicola’s work for nearly the past 30 years. As early as in [18], he explicitly defends the importance of breaking with ontological neutrality: "formal semantics of current knowledge representation languages usually account for a set of models which is much larger than the models we are interested in, i.e., real world models. As a consequence, the possibility to state something which is reasonable for the system but not reasonable in the real world is very high. What we need, instead, is a semantics which is not neutral with respect to some basic ontological assumptions". Despite recognizing the fundamental role played by formal ontology in this context, Nicola never defended the view that the role of Ontology should be providing a single reference model that every modeler should commit to (i.e., universally accepted ontologies3 ). Instead, in his view, the role of Ontology should be to provide modelers with tools such that they could make explicit the content of their (possibly shared) assumptions, their own worldviews, or as he would formally define in [20], their Ontological Commitment. The formalization of this notion of Ontological Commitment is one of the key contributions of Nicola to the conceptual and terminological clarification of the notions of ontology (as the term is employed in Computer Science), conceptualization, knowledge base, logical theory, as well as their relations [21,22]. It also strongly contributed to the definition of ontology-based quality criteria for conceptual modeling languages [19]. Additionally, as discussed in section 4, it strongly influenced a new approach for conceptual model validation via visual simulation. In a nutshell, according to his definition, a conceptualization C can be defined as a set of intended world structures, where each world structure is a set of individuals of the domain and a projection of existing concepts in a given world. Given a logical language L with a vocabulary V, an Ontological Commitment K is then defined as an intensional interpretation (in contrast with the traditional classical interpretation in model-theoretic semantics) mapping elements of V to a conceptualization C. In this case, L is said to commit to K, while C is the conceptualization underlying K. Now, given the commitment of L to K, the set of intended models includes exactly those logical models of L that correspond to intended structures in C. Finally, an ontology is a logical theory that through a suitable set of axioms over V is capable to approximate as much as possible the set of logical models of L to the set of intended ones according to K and its underlying conceptualization C. Informally speaking, when creating a specification, the modeler has a conceptualization in mind (a certain worldview). The ontological commitment is the commitment of the modeler to interpret that specification according to this worldview. However, without the support of a suitable set of formal constraints (of a suitable ontology) what will inevitably happen in practice is that the specification will allow for interpretations that are (logically) valid but non-intended. Figure 2 below (from [21]) illustrates the relations between an ontology, a language, an Ontological Commitment and the intended models of that language. 3 For

a discussion on the difference and relations between Ontology and ontologies, one could refer to [19].

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Figure 2. Relations between language (vocabulary), conceptualization, ontological commitment and ontology (from [19] after [21]).

In other words, in Nicola’s view, the primary role of formal ontology for domain modeling is not to force consensus among different communities of modelers, but rather to provide these communities with theoretical and engineering tools for achieving what in [10] is termed (i) "intra-worldview consistency" and (ii) "inter world-view interoperability". A modeling approach striving for (i) should support its users in justifying their modeling choices and providing sound design rationale for choosing how the elements in the universe of discourse should be modeled in terms of language elements. Regarding (ii), it should support conceptual modelers and domain experts to be explicit regarding their ontological commitments, which in turn enables them to expose subtle distinctions between models to be integrated. Underlying this view there is the assumption that we don’t have to always agree on our worldviews, the problem arises when we falsely believe we agree! This so-called False Agreement Problem is introduced and discussed in [21]. Following this view, in order to support goals (i) and (ii), a conceptual modeling language should offer modeling primitives which are able to capture the nuances and subtleties involving the very essence of the elements constituting a domain. Such a language, cannot be neutral w.r.t. to ontological choices, or to put in Nicola’s terms, it should belong to The Ontological Level [23]. In our view, this notion of ontological level amounts to one of his most important contributions. In this seminal paper, he discusses that Logical-Level languages (e.g., FOL) are “flat” in the sense that they put all predicative terms (e.g., Apple and Red) in the same footing; in constrast, Epistemological-Level languages (e.g., KL-ONE and, hence, Semantic Network descendents, but also UML, ER, OWL) provide ways for elaborating structures which differentiate these terms. For instance, in UML, we have two alternative structuring choices: (SC1) we can define a Class of Apples with an attribute color = red; or (SC2) we can define a Class of Red with an attribute type = apple. What an Epistemological-Level language does not give us is a precise criterion for explaining why structure (a) is better than (b). As Nicola points out in that paper, structuring decisions, such as this one, should not result from heuristic considerations but instead should be motivated and explained in the terms of ontological distinctions. For instance, in this case, the choice of Apple as the sort (a) can be justified by the meta-properties that are ascribed to it. The ontological difference between the two predicates is that Apple corresponds to a Natural Kind whereas Red corresponds to an Attribution or a Mixin [8]. Whilst the former applies necessarily to its instances (an apple cannot cease to be an apple without ceasing to exist), the latter only applies contingently. Moreover, whilst the former supplies a principle of identity for its instances, i.e., a principle through which we judge if two apples are the same, the latter cannot supply

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one. However, it is not the case that an entity could exist without obeying a principle of identity [8], an idea which is defended both in philosophical ontology (e.g., Quine’s dicto "no entity without identity" [24]), and in conceptual modeling (e.g.,Chen’s design rational for ER [14]). Consequently, the structuring choice expressed in (SC2) cannot be justified. In summary, the ontological level is a level where alternative structuring (epistemological) choices over the same logical expression can be assessed and precisely justified on ontological grounds. The idea of using formal ontology and, in particular, ontological meta-properties for motivating distinctions among types of Entity types (or, as he typically prefers to say, types of unary properties or unary relations) dates back to the beginning of the 90’s. For example, as early as [25] and [26], he proposes the use of ontological meta-properties such as the Husserlian notion of foundation and ontological dependence as well as (ontological and temporal) rigidity to give an ontological semantics distinguishing modeling notions and primitives such as natural Concepts, Roles and Qualities. In addition to providing an ontological semantics for these modeling primitives, these meta-properties provide for methodological guidelines that one can use for precisely making and justifying her ontological choices: "we argue that formal ontology may help to distinguish among the relevant kinds of relations we can define in a domain, in order to guide the correct choice of available knowledge representation primitives" [25]. Again, the role of these methodological primitives is to make clear people’s assumptions about a domain. So, he claims: "for instance, a relation like Red may be considered as temporally rigid or not. What is important is that, as soon as the user declares a particular property for a relation, its ontological behavior becomes clear and governed by specific axioms". This strategy was later refined in [27,28] and finally converged into an ontology of unary properties (universals) and a methodology based on that, which was called OntoClean [1,29,2]. OntoClean was perhaps the first methodology in Ontology Engineering to use a precisely defined set of ontological meta-properties and this ontology of properties to systematically analyze, rectify (i.e., "clean") and (re)design taxonomic structures. Complementary to the ontology of universals underlying OntoClean, Nicola leads the group at the Laboratory of Applied Ontology (LOA), in Trento, Italy that proposed an ontology of particulars termed the Descriptive Ontology for Linguistic and Cognitive Engineering (DOLCE). The linguistic and cognitive bias reflected in the name of this ontology represents another fundamental tenet of Nicola’s view of the role of Ontology in domain modeling, namely, that an ontology suitable for supporting "intra-worldview consistency" and "inter world-view interoperability" must be one that takes language and human cognition seriously. In particular, he defends that a system of ontological categories aimed at supporting domain modeling should result from a Descriptive Metaphysics effort. As discussed in [30]: "Descriptive metaphysics aims to lay bare the most general features of the conceptual scheme that are in fact employed in human activities, which is roughly that of common sense. The goal is to make explicit the ontological distinctions underlying natural language and human cognition. As a consequence, the categories refer to cognitive artifacts more or less depending on human perception, cultural imprints and social conventions". This descriptive bias in DOLCE is reflected in one of the most original constructs in the ontology, which is the notion of Quality adopted therein. As a so-called "Four-Category Ontology" [31], DOLCE includes a category for property instances termed qualities (or abstract particulars, property instances, tropes,

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aspects). Qualities are "specific aspects of things we use to compare them". They inhere in their bearers, where inherence is a special kind of asymmetric and anti-transitive existential dependence relation. Qualities are directly comparable, while objects and events can be compared only in respect to a certain quality kind (e.g., to compare physical objects, one resorts to the comparison of their shapes, sizes, weights, and so on). Qualities are distinct from their values (a.k.a. qualia), which are abstract entities representing what exactly resembling qualities have in common, and are organized in spaces called quality spaces; each quality kind has its own quality space. For instance, weight is a quality kind, whose qualia form a linear quality space. Quality spaces may have a complex structure with multiple dimensions, each corresponding to a simple quality that inheres in a complex quality. Typical examples of complex qualities are colors, sound and taste. The notion of qualities in DOLCE was inspired by the classical notion of tropes. However, in a classical trope-based theory, tropes are super-determinate entities that cannot change, except for being replaced by another trope (a phenomenon called tropereplacement [32]). In DOLCE, instead, qualities can maintain their identity while qualitatively changing. This move allows DOLCE to account for linguistic phenomena such as: (a) the color of the apple is changing from red to brown; (b) the temperature of the patient is rising. In (a), we have one single aspect that changes qualitatively while maintaining its identity, namely, the color. In other words, it is not "red" (which happens to be the color of the apple at t1) that is changing but a dependent aspect of the apple, namely, its color. Red and Brown are simply regions in a quality space. Analogously, in (b), it is not 38 ◦ C that is rising (being a number, an abstract entity, 38 ◦ C cannot rise!) but an aspect of the patient, namely, its temperature. The original DOLCE treatment of qualities leave a number of fundamental points open. Firstly, the way a quality changes is by "pointing to" a different region in the same quality space. However, what accounts for such a change is left undefined. In other words, what should be the truthmakers of "apple1 is Red at t1" and "apple1 is brown at t2"? Secondly, in the original treatment, all qualities are essential qualitites, i.e., there is no room there for qualities that an entity loses or acquire in its lifetime. Thirdly, DOLCE leaves it completely undefined whether qualities are endurants (entity-like) or perdurants (event-like). Fourthly, all qualities in DOLCE are instrinsic qualities and, hence, there is no treatment there of relational qualities, which, besides being existentially dependent on their bearer, are also existentially dependent on something else. An example may be John’s love for Mary, which inheres in John but is existentially dependent on Mary4 . These issues have been addressed by new work on aspects (including qualities) and their connection to events. As discussed in depth in [33,34,35], aspects such as qualities, modes, relationships are full-fledged endurants and, as such: 1. They can qualitatively change while maintaining their numerical identity. Moreover, change happens via a mechanism that is akin to the notion of variable and rigid embodiments proposed by [36]. In other words, the same color quality (e.g., the color of apple-1) can be constituted by different color tropes (in the classical sense) in different points in time; the same marriage between John and Mary can be constituted by different sums of commitments and claims in different points 4 Technically speaking, relational qualities inhere in one entity while being specifically dependent on another entity that is mereologically disjoint from their bearer. This is termed external dependence in [8].

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in time; the same Dengue Fever inhering in Paul can be composed of different qualities (e.g., its severity) in different points in time; 2. They are the natural bearers of modal properties. So, while the marriage between John and Mary is necessarily a marriage, it is only contingently a marriage with full separation of assets; while Paul’s Dengue Fever is necessarily a disease it is only contingently a hemorrhagic fever; while the color of apple-1 is necessarily a color, it is only contingently a red color; 3. As the natural bearers of modal properties, endurants of all these types could have been different from what they are, i.e., there are cross-world identities defined for entities of these categories. For example, we could (counter-factually) pose a different world in which Paul’s Dengue fever remained asymptomatic or a a different world in which John and Mary’s marriage lasted much longer and was never subject to the change from full separation of assets to partial separation of assets; 4. As subjects of change, there are changes that endurants of all these categories can undergo while remaining the same (i.e., while maintaining their identity). This criterion, as for all endurants, is given by the unique ultimate sortal type that a particular individual instantiates. For example, a DOG can change a number of features (its size, weight, age, fur color, etc.) without any impact on its identity provided that it does not change any of the essential properties (e.g., psychological continuity, maintenance of the body’s autopoiesis) prescribed by the kind DOG. In an analogous manner, the marriage between John and Mary can change in a number of manners (e.g., change its marital regime, it can become recognized in a different jurisdiction) but there are ways in which it cannot change without ceasing to exist (as the same marriage) and these ways are defined a priori by the kind Marriage. This new theory allows for providing a uniform treatment of endurants dealing with qualitative change in a way that endurants in general (hence, also qualities and relationships) can acquire and lose their own qualities, and which includes both intrinsic and relational qualities (relationships). It also accounts for the ontological status of qualities (as endurants). Moreover, it precisely defines the connection between aspects and events. On one hand, events are manifestations of aspects (qualities, modes, dispositions). For example, the movement of a needle towards a magnet is the manifestation of a number of aspects, such as the disposition of the magnet to attract metallic material, the weight of the needle, their distance, the friction of the surface, etc. Also, in the sense, the marriage between John and Mary qua-process is the sum of manifestations of (qualities of) their marriage qua-endurant, i.e., their mutual commitments, claims, feelings, etc. On the other hand, these endurants give a focus to an event, enriching it with criteria for individuation and unity. For example, how do we establish which events are part of the John and Mary’s marriage qua-process? The answer is: it is those events that are manifestations of the (qualities of the) marriage qua-endurant. Finally, this investigation on the natural of relationships enabled the proposal of a fuller theory of relations that: (a) advanced a typology of relations revising and making finer-grained distinctions within the former broad categories of formal and material relations [37]; (b) clarified the con-

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nection between these different types of relations and their different types of truthmakers [33,38]5 .

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4. Ontology-Driven Conceptual Modeling In conceptual modeling, the idea that “data are fragments of a theory of the real-world and data processing is about manipulating models of such a theory” was there since Mealy’s seminal paper entitled ‘Another Look on Data’ [39]. In fact, Mealy’s paper includes the first mention of the term ‘ontology’ in the Computer and Information Science literature. A number of fundamental conceptual modeling issues of an ontological nature were also discussed in Bill Kent’s classic book ‘Data and Reality’ [40]. This book brought attention to issues like identity, unity and classification, and started exposing the subtleties of fundamental conceptual modeling constructs such as relationships. However, neither Mealy’s paper nor Kent’s book tried to actually develop comprehensive ontological foundations for conceptual modeling. Perhaps the first corpus of work to attempt that goal was reported in the series of publications initiated by Yair Wand, Ron Weber and colleagues [41,42,43] in the late 80’s. Instead of developing a new ontology themselves, Wand and Weber proposed an adaptation of the ontological theory put forth by the Argentinean physicist and philosopher of science Mario Bunge. The result of this effort came to be known as the BWW (Bunge-Wand-Weber) ontology. The authors then employed this theory to evaluate a number of conceptual modeling languages including NIAM [44], ER [45], UML [46] and OWL [47]. Despite the pioneering nature of these efforts, and the guidelines proposed for building ontologically sound conceptual models, the conceptual modeling languages used were still ontologically neutral languages. In the beginning of 2000, there was no conceptual modeling language fully-designed on the basis of a formal ontological theory. By that we mean a language that: (i) contains as modeling primitives the ontological distinctions put forth by a foundational ontology; (ii) restricts possible interpretations to intended ones. In summary, paraphrasing Nicola’s dictum [18], a language whose abstract syntax and semantics were not neutral w.r.t. ontological assumptions. Moreover, in conformance with Nicola’s second aforementioned claim, the system of ontological categories a conceptual modeling language should commit to should be one that takes human language and cognition seriously, i.e., a descriptive ontology (as opposed to a revisionary ontology such as Bunge’s and, hence, BWW - see discussion in [30]). In the early 2000’s, Guizzardi and Wagner initiated a research program aimed at exactly such an objective, i.e., proposing an ontological-level conceptual modeling language satisfying (i) and (ii) above [48,49]. However, in order to that, they needed a reference ontology that could provide proper foundations for conceptual modeling’s most fundamental constructs. As an extension and evolution of a combination of DOLCE, GFO and the ontology of property types underlying OntoClean, the authors then proposed the Unified Foundational Ontology (UFO) [9]6 . In [51], also together with Nicola, they introduced a part of this future language (an extension of UML) based on one of the first 5 More technically, between different types of relational propositions and different types of ontological entities that can make true these relational propositions 6 According to the survey presented at [50], UFO become one of the most influential foundational ontologies in Conceptual Modeling.

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of these micro-theories comprising UFO, namely, a theory dealing with Entity Types and the taxonomic structures involving them. That specific proposal can be seen as an evolution of Nicola’s early proposals of an ontology of unary property types and ultimately as an evolution OntoClean. Inspired in Nicola’s early ideas, the proposal systematically employed a number of formal meta-properties to create a theory and typology of entity types. These entity types were then used to propose finer-grained modeling primitives extending the basic notion of class in UML (see fig.3). Moreover, by employing the axioms of this theory, the proposed UML extension (a UML profile) includes constraints restricting the valid relations that could be established between these entity types.

Figure 3. A Typology of Entity Types.

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This ontologically well-founded version of UML came to be later known as OntoUML [9]. In figure 4, we can see an example of an OntoUML model employing these ontological distinctions. As one can observe, the language makes explicit distinctions such as being (necessarily) of a Kind (e.g., Person), being (contingently) in a certain Phase (e.g., Living Person) and playing (contingely) a certain role (e.g., Private Customer) in a relational context (e.g., a Service Agreement). Moreover, it explicitly models types that instantiated by instances of multiple kinds (e.g., the non-sortal type Customer that can have as instances both people and organizations).

Figure 4. An Example of an OntoUML Model (from [52])

Firstly, this theory allowed for bringing some conceptual clarification to the notions involving Entity Types in conceptual modeling. Notions such as Type, Kind, Class, Role, Phase and Mixin were frequently discussed for many years in the literature of Conceptual and Object-Oriented Modeling. However, up to that point, there was little consensus about their definition.

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Secondly, these ontological meta-properties allowed for more than just defining a formal ontological semantics for these notions. They also provided precise methodological guidelines for choosing how to model things in the universe of discourse. For example, suppose that in a given conceptualization of the domain, the type Student was conceive as: (a) a substantial type, i.e., its instances were existentially independent entities like you and me; (b) a sortal, i.e., all its instances are of the same Kind (e.g., Persons); (c) anti-rigid, i.e., no instance of student is necessarily an instance of student; (d) relationally dependent, i.e., instances of Person become (or cease to be) due to a change in a relational property (their enrollment)7 . So, as a consequence, we would have that, in that particular conceptualization, the type Student should be modeled as a Role. Thirdly, as demonstrated in [53,54], the axiomatization of each of these types in the theory actually defines a particular micro-theory (e.g., a micro-theory defining what Roles are and how they behave w.r.t. to other ontological categories) and these microtheories, in turn, constrain the way the primitives representing these types can appear in conceptual models. In fact, in a modeling language following this theory, constructs representing roles, phase, mixins can only appear in certain configurations forming patterns of a true ontological nature. As a result, the resulting modeling language can actually serve as an Ontology Pattern Language, whose modeling primitives are not low-level primitives (such as class, relation, attribute) but high-level building blocks (Ontology Design Patterns). The advantages of having this include knowledge reuse, agility in the construction of models, a smoother learning curve for novices, and greater uniformity for models. Finally, as demonstrated in [55], these ontological distinctions can also offer unique support for complexity management of large conceptual models by providing natural criteria for model modularization. The new theory of relations and relationships (including unary relationships, i.e., qualities) proposed in [33,34] also allows for some methodological support for recognizing to what ontological kind a domain relation belongs, by systematically searching and exposing the nature of the truthmakers of these relations. Once more, by following a set of ontological meta-properties (e.g., descriptive/non-descriptive, internal/external, essential/non-essential), this theory allows for the clarification and organization of the space of relation types in ontology and allowed for the development of a methodology for the modeling of relations that is evolving towards what Nicola called (half-joking) "OntoClean for Relations". Furthermore, as demonstrated in [38], once more, by using the categories of relations proposed by this theory, a number of modeling patterns for the modeling of relations was proposed. This new theory of relationships is, in fact, part of a new theory of dependent endurants (aspects). As previously mentioned, the theory proposes that a hallmark of all endurants is their ability to qualitatively change while maintaining their identity, i.e., endurants are the natural bearers of modal properties, they have essence and accidents and, hence, they could have been different from what they are. Moreover, identity for all endurants are determined by the unique ultimate sortal type (i.e., the kind) they instantiate. When connecting this theory with the previously mentioned theory of entity types, it becomes clear that all the previously discussed distinctions among entity types are actually 7 One should not mix up the notions of existential dependence and relational dependence. The former applies to individuals and the latter to types. For example, although the type Student is relationally dependent, the instances of Students (e.g., John and Mary) exist independently of other existents [8].

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distinctions among endurant types. In other words, distinctions such as Kinds, Phases, Roles, Mixins (and versions of all the design patterns connected to them) can now be applied to types whose instances are endurants of all types and not only independent endurants (substantials)! For example, the particular marriage between John and Mary is of the Marriage KIND but it can be in a "Full-Separation of Assets" PHASE and it can play the ROLE of a "Marriage that is Legally Recognized in Brazil". A new theory connecting these two former theories (the theory of entity types and the theory of aspects) gave rise in [52] to a new version of the Ontology-Driven Conceptual Modeling language OntoUML. As one can observe in figure 5, in this new combined theory, we have orthogonal classifications, namely: regarding the previously mentioned meta-properties distinguishing entity types (e.g., kind, phase, role, mixin); regarding the ontological nature of the instances of the endurant type in question (e.g., object type, quality type, relationship type). In figure 6, we have an example of a model represented in this new version of OntoUML (dubbed OntoUML 2.0). As one can observe, in this version of the language, we can employ the previously discussed ontological type distinctions also to characterize aspect types. For instance, while a relationship is (necessarily) of particular kind (e.g., Civil Partnership), it can be (contingely) in a certain phase (e.g., Longer-Term Relationship) and it can contingently play a role (e.g., Stable Civil Partnership) in the scope of a relational context (e.g., a legal recognition relation connecting it to a legal jurisdiction - not shown in the figure). As previously discussed, this new theory of aspects has a strong connection to an ontological account of events proposed in collaboration with Nicola. In [35], the authors use this theory to address a fundamental problem in the modeling of events in structural conceptual models (roughly data models, information models). Historically, events have rarely been considered as first-class citizens in structural models. Recently, a number of authors have made a strong case advocating the explicit reification of events in these models [56,57]. However, as demonstrated in [35], if we want: (a) to represent on-going events in these models; (b) while maintaining a classic formal semantics for object identifiers (OIDs); and (c) conforming to the classic view of events in philosophy, then we have as a consequence that our conceptual models can only represent past events, which are necessarily immutable in all sense, i.e., which cannot possibly be different in any respect! In order to address the issue of future events and the illusion of change in event properties, the authors propose a Design Pattern based on this ontological theory. This pattern is an ontologically well-founded engineering tool for dealing with a problem that was hitherto neglected or only naively addressed in the literature of conceptual modeling. Finally, in [58], Nicola builds on this notion of event (and its connection to aspects) to propose a non-classical view of events and a novel way of capturing mutable and future events in conceptual modeling. OntoUML has its syntax (defined both as a metamodel [8] and as a Graph Grammar [54]) and (formal and real-world) semantics formally defined in terms of this ontological theory. This allowed for the development of a number of model-based computational supporting tools for pattern-based model construction [53], formal verification, verbalization and code generation [59]. In particular, it allowed for the development of a novel strategy of conceptual model validation via visual simulation [60]. The approach directly implements Nicola’s notion of Ontological Commitment, which takes an ontology to be a theory that constrains the set of elements in a syntactical specification to approximate, as much as possible, the set of (logical) models of that specification to the set of intended

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Figure 5. A Typology of Entity Types for OntoUML 2.0 (from [52]).

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Figure 6. An Example of an OntoUML 2.0 Model [52]).

ones [21]. Following this idea, in the computational support for this approach, we have the automatic generation of visual instances (exemplars) of a given conceptual model (specification) such that the modeler can be confronted with what her model is actually saying on her behalf. In other words, the strategy is to systematically contrast the set of formally-valid instances of a given conceptual model (i.e., its logical models, which are automatically generated by the visual simulator) with the set of intended instances of that model (i.e., instances that represent state of affairs admissible by the underlying conceptualization), which exists only in the modeler’s mind. Once the modeler detects a deviation between valid and intended instances (either due to overconstraining or underconstraining of the model), she rectifies the model, for instance, by the inclusion of formal domain-specific constraints. This approach, in turn, allowed for a new area of research in conceptual modeling, namely, the study of Ontological Anti-Patterns in Conceptual Models. In three different empirical studies, [61,62,63] managed to show that this approach is also able to detect recurrent structures that tend to cause the deviations between the sets of valid and intended logical models. Once these anti-patterns are catalogued, they were able to devise systematic computational solutions that are able to eliminate these anti-patterns.

5. Final Considerations In this paper, we highlighted three fundamental tenets of Nicola’s thought regarding the role of Formal Ontology for Conceptual Modeling and Knowledge Representation. These are: (1) Languages that are supposed to represent conceptualizations of reality

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cannot be ontologically neutral. Instead, they should make an explicitly commitment to a formal ontological theory; (2) the role of Ontology in Conceptual Modeling is not providing reference domain models capturing single-views of the world that all stakeholders commit to. In other words, it is not about prescribing a single view of reality to all agents and their applications. In contrast, it is about giving stakeholders philosophically and cognitively well-founded theoretical tools such that they make consistent choices in their worldviews and such that these choices can be made transparent to other stakeholders. To put it simply: ontology is not here to make us all agree but to help us understand if, when and precisely in which points we agree and disagree; (3) Conceptual Modeling is about representing aspects of the real-world for the purposes of supporting human users in tasks such as domain understanding and learning, meaning negotiation and problem solving. For this reason, a conceptual modeling language should commit to a descriptive ontological theory (as opposed to a revisionary one) that takes human language and cognition seriously. We also showed here how Nicola’s philosophy of Conceptual Modeling and, in particular, these three tenets, have strongly influenced the design of OntoUML research program for Ontology-Driven Conceptual Modeling. Over the years, OntoUML has been successfully employed in academic, industrial and governmental settings to create conceptual models in a number of different domains, including Geology, Biodiversity Management, Organ Donation, Petroleum Reservoir Modeling, Disaster Management, Context Modeling, Datawarehousing, Enterprise Architecture, Data Provenance, Measurement, Logistics, Complex Media Management, Telecommunications, Heart Electrophysiology, among many others [9,64]. Moreover, it has influenced the design of some aspects of influential conceptual modeling languages (e.g., ORM [65]) and has been considered as a possible candidate for contributing to the OMG SIMF (Semantic Information Model Federation) standardization request for proposal. Finally, empirical evidence shows that OntoUML significantly contributes to improving the quality of conceptual models without requiring an additional effort to produce them [66]. We believe that these benefits brought to Conceptual Modeling theory and practice by OntoUML are strongly a product of the direct influence of Nicola’s philosophy in its design. Nicola’s work has profoundly influenced conceptual modeling languages by offering an ontological level of analysis for their primitive concepts. We anticipate that in the future, no conceptual modeling language will be considered complete until it has revealed its ontological commitments. And for this advance, it is Nicola and his collaborators who deserve full credit.

Acknowledgements We would like to thank Nicola for the many years of pleasant, inspiring and fruitful collaboration. We have a great respect for his ideas as well as his uncompromising attitude towards science. The first author is also grateful to the members of the NEMO and CORE research groups for their collaboration in many of the results reported herein.

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Towards a Logical Foundation of Reification in Modelling Languages Alessandro ARTALE and Enrico FRANCONI KRDB Research Centre, Free University of Bozen-Bolzano, Italy {artale,franconi}@inf.unibz.it Abstract. We consider the notion of reification as adopted in standard conceptual modelling languages and provide a logical formalisation using description logics. To this purpose, we use the description logic DLR`, an extension of the n-ary propositionally closed description logic DLR to deal with attribute-labelled tuples (generalising the positional notation), projections of relations, and objectification/reification of relations. This paper conducts a general investigation on the expressive power required on description logics to capture the different constructs used in conceptual models with a particular emphasis on relation reification.

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1. Introduction Reification is a well established technique in conceptual modelling [1,2,3] and is adopted in standard modelling languages – see, e.g., the notion of association class in UML, the objectification construct in ORM, and the notion of weak entity in ER. The general purpose is to let new entities to emerge from relations, a mechanism which is useful when one needs to represent additional properties of these new emerging entities. Reification has been dealt with also by philosophers as witnessed by various works on formal ontology which mainly concentrate on the process leading to the emergence of new entities during the design phase of an ontology. In particular, such a research topic has been in the recent past deeply investigated in its ontological foundation by Nicola Guarino and his colleagues [4,5,6,7,8,9]. The purpose of this paper is to provide the logical tool to unambiguously represent different usages of reifications, which can serve as the basis to formalise the various aspects and understandings of reification in more philosophically oriented literature. Therefore, we do not take any side in the debate about the meaning and the usage of reification or its ontological characteristics. Indeed, this suggests a future work on how to use the proposed logic-based technology in this paper in order to formalise the deep ontological analysis in the latest works by Guarino and Guizzardi [4,5,6]. This work considers the use of formal methods to represent the notion of reification in conceptual data models and to present the main logical implications that can be drawn in a conceptual model when reification is used. We are interested in the use of logic-based languages, and description logics (DLs) in partic-

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ular, both to establish a set-theoretic semantics and to reason over data models. We are thus in the tradition of works interested in investigating algorithms and their associated complexities for reasoning over information systems and their conceptual data models. Along these lines of research, we briefly mention here the main topics where DLs have been successfully applied and to which this paper is closely related: reasoning over UML/ER [10,11,12,13,14,15,16,17,18,19] and ORM conceptual models [20,21], capturing dynamic and temporal data [22,23,24,25], reasoning on conceptual models under OCL constraints [26,27], applications of reasoning techniques to object-oriented databases [28,29,30], dealing with partof relations in data models [31,32,33,34], capturing and reasoning over database constraints [35,36,37], querying databases via the schema and the vocabulary of a conceptual schema, the so called ontology-based data access (OBDA) scenario [38,39,40,41]. This paper conducts a general investigation on the expressive power required in the framework of description logics in order to capture the different constructs used to model and design an information system while including reification. With this aim, we present the description logic DLR` extending the n-ary DL DLR [42] towards capturing n-ary relations and their constraints. We will motivate the introduced extensions by showing corresponding expressivity needs from the conceptual modelling side. For example, while the DLR family of description logics is used to formalise and perform reasoning in the ORM conceptual modelling language for database design (adopted by Microsoft in Visual Studio) [43,44], we will show how subtle features connected to the way relationships are modelled are still missing in general in DL languages and, in particular, in DLR. We remind that a DLR knowledge base, as defined in [42], can express axioms with piq n-ary relations – as opposed to just binary roles as in classical DLs and OWL – modelled as n-ary predicates with components denoted by their position, i.e., by integers between 1 and n, with n the arity of the relation; piiq propositional combinations of concepts and n-ary relations with the same arity; piiiq concepts as unary projections of n-ary relations—generalising the existential operator over binary roles in classical DLs and OWL, and pivq relations with their typed components. As an example of DLR, in a knowledge base where Pilot and RacingCar are concepts and DrivesCar, DrivesMotorbike, DrivesVehicle are binary relations, the following statements: Pilot Ď Dr1sσ2:RacingCar DrivesCar DrivesCar \ DrivesMotorbike Ď DrivesVehicle

(1) (2)

where σ2:RacingCar DrivesCar types the second argument of the binary relation DrivesCar to be RacingCar, assert that a pilot drives a racing car (1) and that driving a car or a motorbike implies driving a vehicle (2). In this paper we discuss the language DLR` [20], that extends DLR towards capturing constraints over relational databases together with the most common constructs in data modelling languages. In particular we will provide evidences on how DLR` is able to faithfully capture the notion of reification, i.e., the possibility to generate globally unique tuple identifiers for instances of a relation

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so that the relation itself can be seen under two different perspectives: both as a relation and as a concept. In DLR` , reification is called objectification. DLR` is inspired by relational algebra. The main characterising feature of DLR` , with respect to classical description logics such as DLR, are the so called labelled tuples. While components of n-ary relations in classical first-order logic (and in classical description logics) are identified by their position, in DLR` we take a named relational database approach like in relational algebra, i.e., each of the n components of an n-ary relation is identified by a distinct attribute; the instances of an n-ary relation are n-tuples where each of the n components is identified by an attribute label and not by its position in the tuple (see, e.g., [45]). For example, the relation Employee may have the signature with four attributes: τ pEmployeeq “ tfirstname, lastname, dept, deptAddru, and an instance of Employee could be the labelled tuple:

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xfirstname : John, lastname : Doe, dept : Purchase, deptAddr : Londony. Attributes can be locally renamed, just like in relational algebra, in order to allow for compatibility among relations, but also to possibly revert to positional attributes (by renaming the attributes with position numbers). New relations can be formed by projecting a given relation on some of its attributes, generalising the ability of DLR which allows only for concept-forming unary projections. Last but not least, as we mentioned, DLR` has a native reification operator that materialises the reification of a given relation. A reified relation is a concept whose instances are the globally unique tuple identifiers of all the labelled tuples in the relation. E.g., we can reify the binary relation DrivesCar with signature τ pDrivesCarq “ tdriver, vehicleu, to introduce in the knowledge base the concept of CarDrivingEvent defined as follows: å CarDrivingEvent ” DrivesCar Å where is the reification operator. As another example of reification not involving events, we could consider the case when a relation with a primary key (in the sense of relational databases) is reified into a class: å EmployeeClass ” πrfirstname, lastnamesEmployee where the two attributes firstname, lastname form the primary key of the relation Employee and the operator π is the projection over the specified attributes of the relation Employee. The DLR` language we present in this paper generalises the DLR` language presented in [20] by allowing arbitrary projections, arbitrary local attribute renamings, and reification ABox statements. The paper is organised as follows. Section 2 presents the syntax and semantics of DLR` . Section 3 shows the adequacy of DLR` to capture and reason un-

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Å C Ñ CN | C | C1 [ C2 | Děq rUi sR | R R Ñ RN | R1 zR2 | R1 [ R2 | R1 \ R2 | σUi :C R | π ijq rU1 , . . . , Uk sR | ρrU1 ,...,Uq {U11 ,...,Uq1 s R ϕ Ñ C1 Ď C2 | R1 Ď R2 | CN poq | RN pU1 : o1 , . . . , Un : on q | o “ xU1 : o1 , . . . , Un : on y | o1 “ o2 | o1 ‰ o2 Figure 1. The syntax of DLR` .

τ pR1 zR2 q “ τ pR1 [ R2 q “ τ pR1 \ R2 q “ τ pσUi :C Rq “ ijq τ pπ rU1 , . . . , Uk sRq “ τ pρrU1 ,...,Uq {U11 ,...,Uq1 s Rq “

τ pR1 q τ pR1 q τ pR1 q τ pRq tU1 , . . . , Uk u τ pRqztU1 , . . . , Uq u Y tU11 , . . . , Uq1 u

undefined

if if if if if

τ pR1 q “ τ pR2 q τ pR1 q “ τ pR2 q Ui P τ pRq tU1 , . . . , Uk u Ă τ pRq tU1 , . . . , Uq u Ď τ pRq

otherwise

Figure 2. The signature of DLR` relations.

der the presence of reification presenting different scenarios. While DLR` turns out to be undecidable, Section 4 shows how a simple syntactic condition on the appearance of projections sharing common attributes in a knowledge base makes the language decidable. The result of this restriction is a new language called DLR˘ which has a reasoning problem whose complexity does not increase w.r.t. the computational complexity of the basic DLR language. We also present in Section 5 the implementation of an API for the reasoning services in DLR˘ .

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2. The Description Logic DLR` We start by introducing the syntax of DLR` . A DLR` signature is a tuple L “ pC, R, O, U , τ q where C, R, O and U are finite, mutually disjoint sets of concept names, relation names, individual names, and attributes, respectively, and τ is a relation signature function, associating a set of attributes to each relation name τ pRN q “ tU1 , . . . , Un u Ď U , with n ě 2. Furthermore, we assume that attributes names are not shared among relation names; formally, τ pRN1 q X τ pRN2 q “ H, for any RN1 , RN2 P R such that RN1 ‰ RN2 . We will see in Section 3 how we can overcome this restriction by using the renaming operator. The syntax of concepts C, relations R and formulas ϕ is given in Figure 1, where CN P C, RN P R, U P U , o P O, q is a positive integer and 2 ď k ă aritypRq. The arity of a relation R is the number of the attributes in its signature; i.e., aritypRq “ |τ pRq|, with the relation signature function τ extended to complex relations as in Figure 2. ` As mentioned Åin the introduction, the DLR constructors added to DLR are: objectification ( R); relation projection with the possibility to count the projected tuples (π ijq rU1 , . . . , Uk sR), and attribute renaming (ρrU1 ,...,Uq {U11 ,...,Uq1 s R). In DLR` , only arity-preserving renaming operators are allowed, i.e., no two at-

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pCqI pC1 [ C2 qI pDěq rUi sRqI Å p RqI pR1 zR2 qI pR1 [ R2 qI pR1 \ R2 qI pσUi :C RqI ijq pπ rU1 , . . . , Uk sRqI

“ JI zC I “ C1I X C2I ˇ ˇ “ td P Δ | ˇtt P RI | trUi s “ duˇ ě qu “ td P Δ | d “ ıptq ^ t P RI u “ R1I zR2I

“ R1I X R2I “ tt P R1I Y R2I | τ pR1 q “ τ pR2 qu “ tt P RI | trUi s P C I u “ txU1 : d1 , . . . , Uk : dk y P TΔ ptU1 , . . . , Uk uq | ˇ ˇ 1 ď ˇtt P RI | trU1 s “ d1 , . . . , trUk s “ dk uˇ ij qu

pρrU1 ,...,Uq {U 1 ,...,U 1 s RqI “ tt P TΔ pX q | X “ τ pρrU1 ,...,Uq {U 1 ,...,U 1 s Rq and 1

q

1

q

t “ xU11 : d1 , . . . , Uq1 : dq , Uq`1 : dq`1 , . . . , Uk : dk y and xU1 : d1 , . . . , Uq : dq , Uq`1 : dq`1 , . . . , Uk : dk y P RI u

Figure 3. The semantics of DLR` expressions.

tributes from the relation signature can be renamed into a single attribute: formally, ρrU1 ,...,Uq {U11 ,...,Uq1 s R is arity-preserving whenever |τ pρrU1 ,...,Uq {U11 ,...,Uq1 s Rq| “ |τ pRq|. We use the standard abbreviations: K “ C [ C, J “ K, C1 \ C2 “ pC1 [ C2 q, DrUi sR “ Dě1 rUi sR,

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Dďq rUi sR “ pDěq`1 rUi sRq, πrU1 , . . . , Uk sR “ π ě1 rU1 , . . . , Uk sR. A DLR` knowledge base (KB) is a set of formulas ϕ, where we distinguish a TBox and and ABox. A DLR` TBox T is a finite set of concept inclusion axioms of the form C1 Ď C2 and relation inclusion axioms of the form R1 Ď R2 . We use the symbol X1 ” X2 as a shortcut for the two axioms X1 Ď X2 and X2 Ď X1 . A DLR` ABox A is a finite set of concept instance axioms of the form CN poq, relation instance axioms of the form RN pU1 : o1 , . . . , Un : on q, tuple objectification instances of the form o “ xU1 : o1 , . . . , Un : on y, and same/distinct individual axioms of the form o1 “ o2 and o1 ‰ o2 , with oi P O. Restricting ABox axioms to concept and relation names only does not affect the expressivity of DLR` due to the availability of unrestricted TBox axioms. A DLR` knowledge base (KB) will be denoted as KB “ pT, Aq. The semantics of DLR` uses the notion of labelled tuples over a countable potentially infinite domain Δ. Given a set of labels X Ď U an X -labelled tuple over Δ (or tuple for short) is a total function t : X Ñ Δ. For U P X , we write trU s to refer to the domain element d P Δ labelled by U . Given d1 , . . . , dn P Δ, the expression xU1 : d1 , . . . , Un : dn y stands for the tuple t defined on the set of labels tU1 , . . . , Un u such that trUi s “ di , for 1 ď i ď n. The projection of the tuple t over the attributes U1 , . . . , Uk is the function t restricted to be undefined for the labels not in U1 , . . . , Uk , and it is denoted by trU1 , . . . , Uk s. The relation signature function τ is extended to labelled tuples to obtain the set of labels on which a tuple is defined. TΔ pX q denotes the set of all X -labelled tuples over Δ, for X Ď U , and we overload this notation by denoting with TΔ pU q the set of all possible tuples with labels within the whole set of attributes U.

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A DLR` interpretation is a tuple I “ pΔ, ¨I , ıq consisting of a nonempty countable potentially infinite domain Δ specific to I, an interpretation function ¨I , and an objectification function ı. The objectification function is an injective function associating a unique domain element to each tuple, ı : TΔ pU q Ñ Δ, called in the following tuple identifier. Note that, since the range of the objectification function is Δ, tuple identifiers can, in turn, instantiate classes or components of labelled tuples. The interpretation function ¨I assigns a domain element to each individual, oI P Δ, a set of domain elements to each concept name, CN I Ď Δ, and a set of τ pRN q-labelled tuples over Δ to each relation name RN , RN I Ď TΔ pτ pRN qq. Also note that the semantics does not enforce the unique name assumption (UNA) for the individuals (requiring that aI ‰ bI if a ‰ b), but we can syntactically impose it using the distinct individuals axioms in the ABox. The interpretation function ¨I is unambiguously extended over concept and relation expressions as specified in Figure 3. As for the semantics of a DLR` KB, the interpretation I satisfies the concept inclusion axiom C1 Ď C2 if C1I Ď C2I , and the relation inclusion axiom R1 Ď R2 if R1I Ď R2I . It satisfies the concept instance axiom CN poq if oI P CN I, the relation instance axiom RN pU1 : o1 , . . . , Un : on q if xU1 : oI1 , . . . , Un : oIn y P RN I , the axiom o “ xU1 : o1 , . . . , Un : on y if oI “ ιpxU1 : oI1 , . . . , Un : oIn yq, and the axioms o1 “ o2 and o1 ‰ o2 if oI1 “ oI2 , and oI1 ‰ oI2 , respectively. I is a model of the knowledge base pT, Aq if it satisfies all the axioms in the TBox T and in the ABox A. KB satisfiability refers to the problem of deciding the existence of a model of a given knowledge base; concept satisfiability (resp. relation satisfiability) is the problem of deciding whether there is a model of the knowledge base with a non-empty interpretation of a given concept (resp. relation). A knowledge base entails (or logically implies) an axiom if all models of the knowledge base are also models of the axiom. All the decision problems in DLR` can be all reduced to KB satisfiability, as stated in the following:

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Proposition 1 In DLR` , concept and relation satisfiability and entailment are reducible to KB satisfiability. Just few remarks on the introduced semantics. The construct π ijq rU1 , . . . , Uk sR is interpreted as the projection of the relation R over the attributes rU1 , . . . , Uk s, just like the projection operator in relational algebra. The specified cardinality quantity q constrains the number of times a given (projected) tuple participates in the original relation. As we will show in the example below, such cardinalities over projections will allow us to capture functional dependencies in DLR` relations. As for the renaming construct, ρrU1 ,...,Uq {U11 ,...,Uq1 s R introduces a new relation whose instances are tuples of the original relation with their attributes renamed as specified in the renaming operator. The construct Děq rUi sR restricts the projection to be unary and it denotes a concept, and not a unary relation which does not exist in DLR` . 3. Expressivity of DLR` DLR` is an expressive description logic conceived as an extension of the nary DL DLR mainly with the purpose of capturing relevant constraints in the Ontology Makes Sense : Essays in Honor of Nicola Guarino, IOS Press, Incorporated, 2019. ProQuest Ebook Central,

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context of relational databases. In [20] it was showed how DLR` is able to capture DB constraints such as inclusion dependencies (namely inclusion axioms among arbitrary projections of relations), equijoins, functional dependency axioms, key and foreign key axioms, external uniqueness axioms, identification axioms, and path functional dependencies. For example, DLR` can express the fact that the attributes firstname, lastname play the role of a multi-attribute key for the relation Employee: πrfirstname, lastnamesEmployee Ď π ď1 rfirstname, lastnamesEmployee, and that the attribute deptAddr functionally depends on the attribute dept within the relation Employee:

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DrdeptsEmployee Ď Dď1 rdepts pπrdept, deptAddrsEmployeeq . Note that to express the above constraints we use the distinguishing feature in DLR` of expressing relation projections, allowing to form new relations by projecting a given relation on some of its attributes, together with cardinality constraints on such projections. In the following we explore more in details the DLR` ability to capture the notion of reification. We recall here that in DLR` relations names have pairwise disjoint relation signatures, namely they are pairwise non-union compatible: two have the same signature. Thus, not only relations are union compatible Å if they Å RN1I X RN2I “ H but also RN1I X RN2I “ H, for any RN1 , RN2 P R such that RN1 ‰ RN2 . Since relations are set of attribute-labelled tuples, attribute labels have a crucial role when we objectify a relation. Indeed, tuples with different signatures are objectified as different tuple identifiers, even in the case when they have the same sequence of values. We call the values of a labelled tuple xU1 : o1 , . . . , Un : on y the elements of the set to1 , . . . , on u. For example, take the relations with the following signature: τ pDrivesCarq “ tD.name, D.surname, drivencaru, τ pOwnsCarq “ tO.name, O.surname, ownedcaru, and the following knowledge base KB: DrivesCarpD.name :john, D.surname :Smith, drivencar :Ferrari q OwnsCarpO.name :john, O.surname :Smith, ownedcar :Ferrari q o1 “ xD.name :john, D.surname :Smith, drivencar :Ferrari y o2 “ xO.name :john, O.surname :Smith, ownedcar :Ferrari y å CarDrivingEvent ” DrivesCar å CarOwningEvent ” OwnsCar

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which introduces the reified objects o1 and o2 for the corresponding labelled tuples; in this example, these objects are intended to identify the car driving or owning events associated to each DrivesCar or OwnsCar labelled tuple in the relations. Since the two tuples have different labels, DLR` treats their objectifications as different tuple identifiers, i.e., KB |ù o1 ‰ o2 , even if they have the very same values. Moreover, we observe that KB |ù CarDrivingEventpo1 q and KB |ù CarOwningEventpo2 q. Since in DLR` relations names have pairwise disjoint relation signatures, the example above holds for any pair of relation names. For the same reason, the relations and their corresponding reified relations are disjoint: KB |ù DrivesCar [ OwnsCar Ď K å å KB |ù DrivesCar [ OwnsCar Ď K

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KB |ù CarDrivingEvent [ CarOwningEvent Ď K as it would be any similar statement involving (reifications of) arbitrary distinct relation names. In order to compare relations with respect to the values of their attributes, regardless from the attribute names themselves, DLR` provides a so called renaming operator (similar to the renaming operator in relational algebra) to rename attributes labels so that their values can be compared with values of the same attributes in different relations. In general, as we have noted above, a relation inclusion axiom, R1 Ď R2 , involving non union compatible relations would always imply R1 to be empty, and an [- and \-set expression involving non union compatible relations would always beÅ empty. Similarly, concept Å Å inclusions between R1 Ď relation objectifications, R2 , would result in R1 to be interpreted as the empty concept if the involved relations are not union compatible. The renaming operator allows to establish union compatibility among relations. In this way we overcome the assumption that relations are pairwise disjoint admitting the possibility to express sub-relations, i.e., relation inclusion axioms, and to build complex relations as a Boolean combination of other relations. For example, we can add to KB an axiom stating that whoever drives a car should also own it: ρrD.name,D.surname,drivencar{O.name,O.surname,ownedcars DrivesCar Ď OwnsCar

(3)

where ρrD.name,D.surname,drivencar{O.name,O.surname,ownedcars DrivesCar is a relation where each tuple of DrivesCar has the attribute labels renamed as the labels of the relation OwnsCar: the obtained relation is now union compatible with the relation OwnsCar. Thus, while DrivesCar and OwnsCar and their reifications (namely, the corresponding events) are disjoint as previously mentioned, the renamed version of DrivesCar is not anymore necessarily disjoint with OwnsCar, i.e.: KB * ρrD.name,D.surname,drivencar{O.name,O.surname,ownedcars DrivesCar [ OwnsCar Ď K Furthermore, if the definition of the event OwnedCarDrivingEvent is added to KB with the following axiom:

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OwnedCarDrivingEvent ” å ρrD.name,D.surname,drivencar{O.name,O.surname,ownedcars DrivesCar then the following logical implication would hold as a consequence of (3): KB |ù OwnedCarDrivingEvent Ď CarOwningEvent With this example we understand that a data model with labelled tuple semantics, as opposed to a data model with (positional) regular tuple semantics, is needed in order to properly represent reified relations. The renaming operator could also be useful to simulate the positional perspective on relations using the DLR` named attribute perspective. In accordance with the positional view on relations, each relation name would have associated globally a total order among the attributes in its signature, and it would be systematically replaced in the knowledge base with a renamed version, where each attribute of the relation is renamed with a consecutive integer number corresponding to the order of the attribute: τ pRNq “ tU1 , ¨ ¨ ¨ , Un u

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RN

replaced with

ρrU1 ,¨¨¨ ,Un {1,¨¨¨ ,ns RN.

Concerning the relationship between DLR` and conceptual modelling languages, the rich set of constructors in DLR` allows us to extend the known mappings in description logics of popular conceptual database models, and to provide the foundations for their reasoning tasks. The EER mapping as introduced in [11] can be extended to deal with multi-attribute keys for entities (see [20]) and named roles in relations; the ORM mapping as introduced in [43,44] can be extended to deal with arbitrary subrelations and exclusive relation constructs (by using inclusions and disjointness, respectively, among projections of relations), objectification (with an appropriate use of attribute renaming), named roles in relations, and fact type readings (by using renaming axioms); the UML mapping as introduced in [13] can be fixed to deal properly with association classes (by using the DLR` notion of objectification) and named roles in associations. 4. The DLR˘ Decidable Fragment of DLR` Since a DLR` knowledge base can express inclusions and functional dependencies, the entailment problem is undecidable [46]. Thus, in this section we present DLR˘, a decidable syntactic fragment of DLR` limiting the scope of the renaming operator and the coexistence of relation projections in a knowledge base. Definition 1 (Projection Signature) Consider the renaming operator ρ as an equivalence relation (reflexive, transitive, and symmetric) over the attributes U , pρ, U q. We denote as τρ the relation signature function where each attribute label, U , is replaced by the unique canonical representative denoted as rU sρ . Given a DLR` knowledge base KB “ pT, Aq, we define the projection signature of KB

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as the set T containing the following sets: the signatures τρ pRN q of all relations RN P R, the singleton sets associated with each attribute label rU sρ P U, and the relation signatures τρ resulting from projection constructs in some axiom from T . In the following we use the notation U to mean rU sρ . The projection signature graph of KB is the directed acyclic graph corresponding to the Hasse diagram of T ordered by the proper superset relation Ą, whose sinks are the attribute singletons tU u. We call this graph pĄ, T q. Given a set of attributes τ “ tU1 , . . . , Uk u Ď U , the projection signature graph dominated by τ , denoted as Tτ , is the sub-graph of pĄ, T q with τ as root and containing all the nodes reachable from τ . Given two sets of attributes τ1 , τ2 Ď U , pathT pτ1 , τ2 q denotes the set of directed paths in pĄ, T q between τ1 and τ2 . pathT pτ1 , τ2 q “ H when a path does not exist. The notation childT pτ1 , τ2 q means that τ2 is a child (i.e., a direct descendant) of τ1 in pĄ, T q. We now introduce DLR˘ as follows. Definition 2 (DLR˘ ) A DLR˘ knowledge base is a DLR` knowledge base that satisfies the following syntactic conditions:

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1. the projection signature graph pĄ, T q is a multitree: i.e., for every node τ P T , the graph Tτ is a tree; and 2. for every projection construct π ijq rU1 , . . . , Uk sR (concept expression of the form Děq rU1 sR) appearing in T , if q ą 1 then the length of the path pathT pτ pRq, tU1 , . . . , Uk uq (pathT pτ pRq, tU1 uq) is 1. The first condition in DLR˘ restricts DLR` in the way that multiple projections of relations may appear in a knowledge base: intuitively, there cannot be different projections sharing a common attribute. Moreover, observe that in DLR˘ pathT is necessarily functional, due to the multitree restriction. By relaxing the first condition the language becomes undecidable, as we mentioned at the beginning of this Section. The second condition is necessary to map DLR˘ into the decidable DL ALCQI (see the mapping in [20] for more details); however, we do not know whether this condition could be relaxed while preserving decidability. Example 1 Consider the relation names R1 , R2 with τ pR1 q “ tW1 , W2 , W3 , W4 u, τ pR2 q “ tV1 , V2 , V3 , V4 , V5 u, and a TBox Texa : πrW1 , W2 sR1 Ď π ď1 rW1 , W2 sR1 πrV3 , V4 , V5 sR2 Ď πrV3 , V4 , V5 spρrW1 ,W2 ,W3 {V3 ,V4 ,V5 s R1 q.

(4) (5)

Figure 4 shows that the projection signature graph of the knowledge base pTexa , Hq is indeed a multitree. Note that in the figure we have collapsed equivalent attributes in a unique equivalence class, according to the renaming ρ. Furthermore, since all its projection constructs have q “ 1, this knowledge base belongs to DLR˘ . Note that DLR is included in DLR˘ , since the projection signature graph of any DLR knowledge base is always a degenerate multitree with maximum depth equal to 1. While DLR˘ cannot represent all database constraints as DLR` (see [20] for more details), it is still able to capture and reason in presence of

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tW1 , W2 , W3 , W4 u " tW4 u

tV1 , V2 , V3 , V4 , V5 u W 1 , W2 , W3 V3 , V4 , V5 "

"

W1 V3

*

W 1 , W2 V3 , V4 "

W2 V4

*

* tV1 u "

W3 V5

tV2 u

*

*

Figure 4. The projection signature graph of Example 1.

objectification (both at the TBox and ABox level). Concerning the ability of DLR˘ to capture conceptual data models, only the mapping of ORM schemas is affected by the DLR˘ restrictions: DLR˘ is able to correctly express an ORM schema if the projections involved in the schema satisfy the DLR˘ multitree restriction. We finally mention that a DLR˘ KB can be translated into an equi-satisfiable KB in OWL (in [20] we provide a translation into ALCQI). Thus, reasoning in DLR˘ is an ExpTime-complete problem.

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5. Implementation of a DLR˘ API We have implemented the framework discussed in this paper. DLRtoOWL is a Java library fully implementing DLR˘ reasoning services. The library is based on the tool ANTLR4 to parse serialised input, and on OWLAPI4 for the OWL2 encoding, and it includes the OWL reasoner JFact. DLRtoOWL provides a Java DLR API package to allow developers to create, manipulate, serialise, and reason with DLR˘ knowledge bases in their Java-based application, extending in a compatible way the standard OWL API with the DLR˘ tell and ask services. During the development of this new library we strongly focused on performance. Since the OWL encoding is only possible if we have already built the ALCQI projection signature multitree, in principle the program should perform two parsing rounds: one to create the multitree and the other one to generate the OWL mapping. We faced this issue using dynamic programming: during the first (and only) parsing round we store in a data structure each axiom that we want to translate in OWL and, after building the multitree, by the dynamic programming technique we build on-the-fly a Java class which generates the required axioms. We have used the DLR˘ API within a plugin for general ontology reasoning for conceptual design tools based on languages such as EER, UML (with OCL), and ORM (with derivation rules) [47]. This plugin supports the detection of inconsistencies, redundancies, complete derivations of the strictest implicit constructs and unexpected behaviours. Reasoning helps the modeller to detect

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relevant formal properties of the ontology that may be undetected during the modelling phase, which give rise to design quality degradation and/or increased development times and costs. The system is still at an early stage of completion, but it has been proved to be highly effective and efficient: indeed, it computes derivations in real time in the background while the ontology is being designed.

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6. Conclusions We considered the very expressive DLR` description logic, which extends DLR towards database and data modelling oriented constraints. DLR` is expressive enough to cover directly and more thoroughly the EER, UML, and ORM conceptual data models, among others. In particular, we provided an extensive analysis of the expressive power of DLR` in order to capture reification of both relations and tuples. The main characterising feature of DLR` is the so-called labelled tuples, so that DLR` can faithfully represent the reification of n-ary relations whose components are identified by an attribute label and not by a position. Although reasoning in DLR` is undecidable, we showed a decidable sublanguage, DLR˘ , where a simple syntactic constraint on KBs restores decidability. To enhance the use and adoption of DLR˘ , we have developed an API that fully implements reasoning for this language, and maps input knowledge bases into OWL. Using a standard OWL reasoner, we are able to provide a variety of DLR˘ reasoning services and thus a reasoning capability towards conceptual models captured by DLR˘ KBs. For what concerns the connections of this work with the work by Guarino and his colleagues on relationships and their reifications [4,5,6], this paper does not contribute to the ontological dispute on what kinds of relations need to be reified or on what is the nature of the relations that are amenable to be reified. Indeed, using the terminology of [4], in this paper we provide examples of reification of event-like relations like the DrivesCar relation, and reification of fact-like relations like the Employee relation. The main purpose of our investigation is to provide a logical framework able to capture the various notions of reification, i.e., the possibility to generate tuple identifiers for instances of a relation so that the relation itself can be seen under two different perspectives: both as a relation (set of labelled tuples of instances) and as a concept (set of instances). The peculiarity of our approach lies in the notion of labeled tuples and their importance in defining reification. Furthermore, via label renaming we show how the a relation can be alternatively viewed as a set of tuples with different labels but same values: this provides the freedom to produce different reifications of a relation. As a future work we are interested in applying the presented logical framework to capture the different ontological notions of reification as presented in more philosophical-oriented literature. References [1]

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Science, pages 37–52. Springer, 2017. P. R. Fillottrani, C. M. Keet, and D. Toman. Polynomial encoding of ORM conceptual models in CFDI. In D. Calvanese and B. Konev, editors, Proc. of the 28th Int. Workshop on Description Logics (DL’15), volume 1350. Ceur, 2015. A. Artale, E. Franconi, and F. Mandreoli. Description logics for modelling dynamic information. In J. Chomicki, R. van der Meyden, and G. Saake, editors, Logics for Emerging Applications of Databases, pages 239–275. Springer, 2003. A. Artale, C. Parent, and S. Spaccapietra. Evolving objects in temporal information systems. Annals of Mathematics and Artificial Intelligence, 50(1–2):5–38, 2007. A. Artale and E. Franconi. Foundations of temporal conceptual data models. In A. Borgida, V. Chaudhri, P. Giorgini, and E. Yu, editors, Conceptual Modeling: Foundations and Applications, volume 5600 of Lecture Notes in Computer Science, pages 10–35. Springer, 2009. A. Artale, R. Kontchakov, V. Ryzhikov, and M. Zakharyaschev. Complexity of reasoning over temporal data models. In J. Parsons, M. Saeki, P. Shoval, C. Woo, and Y. Wand, editors, Proc. of the 29th Int. Conf. on Conceptual Modeling (ER’10), volume 6412 of Lecture Notes in Computer Science, pages 277–292. Springer, 2010. A. Artale, D. Calvanese, A. Queralt, and E. Teniente. OCL-Lite: Finite reasoning on UML/OCL conceptual schemas. Data & Knowledge Engineering, 73:1–22, 2012. A. Queralt and E. Teniente. Reasoning on UML class diagrams with OCL constraints. In D. Embley, A. Oliv’e, and S. Ram, editors, Proc. of the 25th Int. Conf. on Conceptual Modeling (ER 2006), volume 4215 of Lecture Notes in Computer Science, pages 497–512. Springer, 2006. A. Artale, F. Cesarini, and G. Soda. Describing database objects in a concept language environment. IEEE Transactions on Knowledge and Data Engineering, 8(2):345–351, 1996. S. Bergamaschi and C. Sartori. On taxonomic reasoning in conceptual design. ACM Transactions on Database Systems, 17(3):385–422, 1992. D. Calvanese, G. De Giacomo, and M. Lenzerini. Structured objects: Modeling and reasoning. In L. V. T.W. Ling, A.O. Mendelzon, editor, Proc. of the 4th Int. Conf. on Deductive and Object-Oriented Databases (DOOD 1995), volume 1013 of Lecture Notes in Computer Science, pages 229–246. Springer, 1995. A. Artale, E. Franconi, N. Guarino, and L. Pazzi. Part-whole relations in object-centered systems: An overview. Data & Knowledge Engineering, 20(3):347–383, 1996. P. Seyed, A. L. Rector, U. Sattler, B. Parsia, and R. Stevens. Representation of part-whole relationships in SNOMED CT. In R. Cornet and R. Stevens, editors, Proc. of the 3rd Int. Conference on Biomedical Ontology (ICBO 2012), volume 897. Ceur, 2012. C. M. Keet, F. C. Fern´ andez-Reyes, and A. Morales-Gonz´ alez. Representing mereotopological relations in OWL ontologies with ontoparts. In E. Simperl, P. Cimiano, A. Polleres, O. Corcho, and V. Presutti, editors, Proc. of the 9th Extended Semantic Web Conference (ESWC’12), volume 7295 of Lecture Notes in Computer Science, pages 240–254. Springer, 2012. C. M. Keet and A. Artale. Representing and reasoning over a taxonomy of part-whole relations. Applied Ontology, 3(1-2):91–110, 2008. A. Borgida. Description logics in data management. IEEE Transactions on Knowledge and Data Engineering, 7(5):671–682, 1995. F. Bry and R. Manthey. Checking consistency of database constraints: a logical basis. In W. W. Chu, G. Gardarin, S. Ohsuga, and Y. Kambayashi, editors, Proc. of the Twelth Int. Conf. on Very Large Data Bases (VLDB’86), pages 13–20. Morgan Kaufmann, 1986. A. Borgida, D. Toman, and G. E. Weddell. On referring expressions in query answering over first order knowledge bases. In C. Baral, J. Delgrande, and F. Wolter, editors, Proc. of the Int. Conference on Principles of Knowledge Representation and Reasoning (KR’16), pages 319–328. AAAI Press, 2016. A. Poggi, D. Lembo, D. Calvanese, G. De Giacomo, M. Lenzerini, and R. Rosati. Linking data to ontologies. Journal on Data Semantics, X:133–173, 2008. D. Calvanese, G. De Giacomo, D. Lembo, M. Lenzerini, and R. Rosati. Tractable reason-

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Alessandro Artale, Diego Calvanese, Marco Montali a and Wil van der Aalst b a KRDB Research Centre, Free University of Bozen-Bolzano, Italy {artale,calvanese,montali}@inf.unibz.it b Process and Data Science (PADS), RWTH Aachen University, Germany [email protected] Abstract. Existing process modelling notations ranging from Petri nets to BPMN have difficulties capturing the essential features of the domain under study. Process models often focus on the control flow, lacking an explicit, conceptually well-founded integration with real data models, such as ER diagrams or UML class diagrams. In addition, they essentially rely on the simplifying assumption that each process model focuses on a single, explicitly defined notion of case, representing the type of objects that are separately manipulated when the process is instantiated into actual executions. To overcome this key limitation, Object-Centric Behavioural Constraints (OCBC) models were recently proposed as a new notation where data and control-flow are described in a single diagram, and where their interconnection is exploited to elegantly capture real-life processes operating over a complex network of objects. In this paper, we illustrate the essential and distinctive features of the OCBC approach, and contrast OCBC with contemporary, case-centric notations. We then relate the approach to recent developments in the conceptual understanding of processes, events, and their constituents, introducing a series of challenges and points of reflections for the community.

1. Introduction Despite the plethora of notations available to model business processes, process modellers struggle to capture real-life processes using mainstream notations such as Business Process Model and Notation (BPMN), Event-driven Process Chains (EPC), and UML activity diagrams. All such notations require the simplifying assumption that each process model focuses on a single, explicitly defined notion of case, representing the type of objects that are separately manipulated when the process is instantiated into actual executions. The discrepancy between this assumption and reality becomes evident when using process mining techniques to reconstruct the real processes based on the available data [1]. Process mining starts from the available data and, unless one is using a Business Process Management (BPM) of Workflow Management (WFM) system for process executions, explicit case information is typically missing. Real enterprise systems from vendors such as SAP (S/4HANA), Microsoft (Dynamics 365), Oracle (E-Business Suite), and

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Salesforce (CRM) are database-centric. Process activities can be viewed as updates on the underlying data, and the notion of process instance (i.e., case) does not exist. Process-centric diagrams using BPMN, EPCs, or UML describe the life-cycle of individual cases. When formal languages like Petri nets, automata, and process algebras are used to describe business processes, they also tend to model cases in isolation. Moreover, the data perspective is secondary or missing completely. Object-Centric Behavioural Constraint (OCBC) models [2] have been recently proposed to address the following interrelated problems: • Modelling the interaction between multiple process instances, specifically when there is a one-to-many or many-to-many relationship between them. For example, an order may relate to multiple order lines and one delivery may refer to multiple order lines belonging to different orders. How to model activities related to orders, order lines, and deliveries in a single diagram? • Modelling both the data and the control-flow perspective in a unified and integrated manner. Existing approaches focus on one of the two or resort to the use of multiple diagrams. For example, the relation between class diagrams and activity diagrams in UML is indirect and not visualized. Note that languages like BPMN allow modellers to attach simple data objects to processes, but the more powerful constructs present in Entity Relationship (ER) models and UML class models cannot be captured in such process models. In particular, complex constraints over data attached to processes (e.g., cardinality constraints) must influence the behaviour of the process itself (think to the activities that must generate those data objects). In contemporary languages, neither complex constraints over data nor a way to capture how data can influence processes are reflected at all. Also other mainstream business process modelling notations can only describe the lifecycle of one type of process instance at a time, but not the co-evolution of multiple, interacting instances (such as the management of different orders, where the evolution of one order impacts on the possible evolutions of the related orders). Object-Centric Behavioural Constraint (OCBC) models have been proposed as a modelling language that combines ideas from declarative, constraint-based languages like DECLARE [3], and from structural conceptual modelling languages (such as ER, UML, or ORM) [2]. OCBC allows to describe the temporal interaction between activities in a given process and is able to attach (structured) data to processes in a unified framework. In this way, we can capture in a uniform way processes, data, and their interplay. OCBC models are related to artifact- and data-centric approaches [4, 5, 6]. These approaches also aim to integrate data and processes. However, this is not done in a single diagram representing different types of process instances and their interactions (which are governed by the data). In addition, these approaches usually assume complete knowledge over the data, and require to fully spell out data updates when specifying the activities [7, 8]. The few proposals dealing with artifact-centric models whose structural aspects are interpreted under incomplete information [9] do not come with a fully integrated, declarative semantics, but follow instead the Levesque functional approach [10] to separate the evolution of the system from the inspection of structural knowledge in each state. The

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semantics of an OCBC model, instead, can be fully characterised by resorting to first-order temporal logic, where the temporal dimension capturing the dynamics of the process interacts with the structural dimension of objects and their mutual relationships [11]. In this paper, we illustrate the essential and distinctive features of the OCBC approach, using a simple, yet very sophisticated example, and contrast OCBC with contemporary, case-centric notations. We then relate the approach to recent developments in the conceptual understanding of processes, events, and their constituents, introducing a series of challenges and points of reflections for the community that could be effectively attacked by relying on recent works by Nicola and colleagues.

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2. Case-Centric Notations and Many-to-Many Processes As pointed out in the introduction, contemporary process modelling notations such as BPMN, EPC, and UML activity diagrams typically require a one-to-one correspondence between a process 1 and a corresponding notion of case. This notion of case represents the main object type targeted (and manipulated) by the process. For this reason, in the remainder of the paper we use the umbrella term casecentric to refer to such notations. Examples of cases are orders in order-to-cash e-commerce scenarios, or prospective students in the context of admission processes to university study programs. The intuition behind this correspondence is that each instance of the process will target (and evolve) a single object of the corresponding case class. Since contemporary notations mainly focus on the process control-flow, that is, on the activities/tasks to be executed and on their acceptable execution orderings, being case-centric also implies that each task execution in a given process instance will target, again, a single case object. A limited form of one-to-many relationship between cases and tasks is supported through the usage of loops and multi-instance constructs in the process. Such constructs usually implicitly indicate the presence of object classes acting as subcases, where many subcases may refer to the same case. An example here consists of the various order lines composing an order. The usage of loops or multi-instance constructs in the process is only possible if the evolution of all subcases can be synchronously bound to that of the corresponding case and of the other “sibling" subcases referring to the same case object. This is not obvious, nor feasible in general. All in all, case-centric notations fall short when managing complex one-tomany relationships, and many-to-many relationships relating different objects that are co-evolved by the same process. Such situations are widespread in real organisations. For example, e-commerce companies like Amazon© flexibly handle order-to-delivery processes by relating multiple customer orders with multiple packages, so that a package sent to a customer may contain a mix of order lines belonging to different orders placed by that customer. This makes it impossible to fix a single notion of case when capturing the process as a whole, since it intrinsically relates objects of different types (such as orders and packages) in a 1 Recall

that, in the BPM literature, process is a synonym for process schema.

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Person

1..∗ Application

Candidate 1  made by

∗

1

Job Offer ∗

responds to

1 Job Profile

refers to

Figure 1. UML class diagram capturing the main object and relationship types of the job hiring domain.

many-to-many fashion. Depending on the subjective view and scope of interest within the process, different case objects may be selected to understand how the process works. For example, a courier may see the order-to-delivery process as centred around the notion of package. A customer, instead, may prefer a view centred on each single order in isolation, ranging from the order placement and payment to its delivery (which is materially realised by delivering all packages containing order lines for that order). Similarly, in a job hiring process there is a many-to-many relationship between candidates seeking a job, and job offers placed to fill available positions. This requires to decouple the flow of activities under the responsibility of the company placing the job offer, from that followed by each applying candidate. In the following, we take inspiration from [12] and discuss in more details a fragment of a typical job hiring process, pointing out the challenges it pose to case-centric notations. 2.1. A Job Hiring Process

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We consider the fragment of a job hiring process enacted by an organisation whenever there is the need of filling an internal position. For simplicity, we consider only two types of actors involved in the process: • The organisation itself, responsible for the publishing and management of job offers, as well as for the selection of winning applications. • Candidates interested in the offered positions, who participate to the selection process by registering their personal data and by submitting their applications. The complexity of the process resides in the fact that it relates many candidates to many job offers, using the key notion of application as relator. In the following, we assume that the main object and relationship types of the job hiring domain are those illustrated in the UML class diagram of Figure 1. We illustrate various constraints to describe tasks in the job hiring process together with their mutual temporal relations. For the sake of readability, we use the following fonts and colors: • boxed, violet sans-serif font to indicate object types; • violet, underlined sans-serif font to indicate relationship types; Ontology Makes Sense : Essays in Honor of Nicola Guarino, IOS Press, Incorporated, 2019. ProQuest Ebook Central,

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• blue, bold typewriter font within a rounded rectangle to indicate tasks; • blue, italics font to highlight temporal aspects, such as the amount of times a task can be repeated, or whether some task is expected to occur before or after another task; • green, dash-underlined italics sans-serif font to point out relationships between tasks and object types. • blue, dash dot-underlined italics font to denote a co-reference indicating which instances of tasks are related via the objects they manipulate. The relevant constraints for our job hiring example are (see also Figure 7): C.1 The register data task is about a Person . C.2 A Job Offer is created by executing the post offer task. C.3 A Job Offer is closed by determining the winner . C.4 A Job Offer is stopped by canceling the hiring . C.5 An Application is created by executing the submit task. C.6 An Application is promoted by marking it as eligible . C.7 An Application can be submitted only if, beforehand , the data the Candidate who made that C.8 A

winner

one

can be

Application has been registered .

determined

Application , responding to

about

for a that

Job Offer

only if at least

Job Offer , has been previously

marked as eligible .

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C.9 For each Application

responding to a Job Offer , if the Application

is marked as eligible then a winner must be finally for that

determined

Job Offer , and this last task is executed only once for that

Job Offer . C.10 When a winner is determined for a Job Offer , Applications responding to that

Job Offer cannot be marked as eligible anymore.

C.11 A Job Offer

closed by a determine winner task cannot be stopped by

executing the cancel hiring task (and vice-versa).

2.2. Capturing the Job Hiring Example with Case-Centric Notations The most fundamental issue when trying to capture the job hiring example of Section 2.1 using case-centric notation is to identify what is the case. This, in turn, determines what is the orchestration point for the process, that is, which participant coordinates process instances corresponding to different case objects.

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Candidate

Candidate

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Application

check if eligible

post offer

…

Job Offer

(a) A job hiring process receiving at most one application

Hiring Company

Hiring Company

Application

handle candidate post offer

check if eligible

…

Job Offer

(b) A job hiring process receiving multiple applications in a sequential way; a new application is only handled when the previous applications has been checked for eligibility

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Figure 2. Common beginner mistakes when capturing a job hiring process (diagrams inspired from [12])

This problem is apparent when looking at BPMN, which specifies that each process should correspond to a single locus of control, i.e., confined within a single pool.2 In our example, we have two participants: candidates (in turn responsible for managing Applications), and the job hiring organisation (in turn responsible for the management of JobOffers). However, we cannot use neither of the two to act as unique locus of control for the process: on the one hand, candidates may simultaneously create and manage different applications for different job offers; on the other hand, the organisation may simultaneously spawn and manage different job offers, each one resulting in multiple applications being evaluated. A typical modelling mistake done by novices is to select the job hiring organisation as unique locus of control, and squeeze all tasks therein. This leads to very cumbersome courses of execution as shown in Figure 2. As clearly pointed out in textbooks (see, e.g., Chapter 8 of [12]), the only way to handle in BPMN a many-to-many process such as the job hiring process considered here, is to distribute the process across multiple, separate pools – in our case study, the candidate and the hiring company. Each of such pools focuses on a different case class – in our case study, the hiring company focuses on job offers, whereas the candidate focuses on his/her own applications. However, such multiple pools cannot execute their internal flows in separation, but must instead be properly interconnected using suitable synchronisation mechanisms, so as to ensure that the evolution of certain process instance within a pool is properly aligned with the evolution of process instances within another pool. For example, in our case study a job offer can be canceled only if no candidate has created an application for it, which also implicitly indicates that once a job hiring has been canceled, none of its applications can be marked as eligible for it. This requires to relate job offers with applications, which can only be done by introducing complex event or data-based synchronisation mechanisms [12] that are not at all mentioned in the description of the process provided in Section 2.1. 2 Recall

that a BPMN pool represents a participant [13].

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3. The OCBC Model We now present the syntax and graphical appearance of OCBC models, and informally comment about their formal semantics. We use the job hiring example of Section 2.1 to illustrate the main concepts and to show the sophistication of this approach. The original proposal of the OCBC model [14, 11] is the way activities and data are related. In particular, an OCBC model captures, at once: • data dependencies, represented using standard data models containing classes , relationships and constraints between them; • activities , accounting for units of work within a process; • mutual relationships between activities and classes , linking the execution of activities in a given process with the data objects they manipulate; • temporal constraints between activities; • co-reference constraints that enforce the application of temporal dependencies, and in particular scope their application to those activities instances that indirectly co-refer thanks to the objects and relationships they point to. We start by recalling data models and temporal constraints, which are then used as the basic building blocks of the OCBC approach. 3.1. The Data Model – ClaM

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We assume that data used by the activities is structured according to the ClaM data model (which stands for CLAss data Model ). While we do not advocate here for a new data model, for simplicity, we assume ClaM to be a simplified version of UML, with object classes that can be organized along ISA hierarchies (with possibly disjoint sub-classes and covering constraints), binary relationships between object classes and cardinalities expressing participation constraints of object classes in relationships. More formally we have: Definition 1 (ClaM Syntax). A conceptual schema Σ in the Class Model, ClaM, is a tuple Σ = (UC , UR , τ, #dom , #ran , ISA, ISAR , disj, cov), where: • UC is the universe of object classes. We denote object classes as O1 , O2 , . . .; • UR is the universe of binary relationships among object classes. We denote relationships as R1 , R2 , . . .; • τ : UR → UC × UC is a total function associating a signature to each binary relationship. If τ (R) = (O1 , O2 ) then O1 is the range and O2 the domain of the relationship;  N × (N ∪ {∞}) is a partial function defining cardinality • #dom : UR × UC → constraints of the domain of a relationship. #dom (R, O) is defined only if there is O1 s.t. τ (R) = (O, O1 ); • #ran : UR × UC → N × (N ∪ {∞}) is a partial function defining cardinality constraints of the range of a relationship. #ran (R, O) is defined only if there is O1 s.t. τ (R) = (O1 , O);

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response

A

unary-response

B precedence

A

A

non-response

B

A

unary-precedence

B

A

B

non-precedence

A

responded-existence

A

B

B non-coexistence

B

A

B

Figure 3. Types of temporal constraints between activities

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• ISA ⊆ UC × UC is a binary relation defining the super-class and sub-class hierarchy on object classes. If ISA(C1 , C2 ) then C1 is said to be a sub-class of C2 while C2 is said to be a super-class of C1 ; • ISAR ⊆ UR × UR , similar to ISA, allows to specify sub-relationships in the model; • disj ⊆ 2UC × UC is a binary relation defining the set of disjoint sub-classes in an ISA hierarchy on object classes; • cov ⊆ 2UC × UC is a binary relation defining the set of sub-classes covering the super-class in an ISA hierarchy on object classes.  As for the formal set-theoretic semantics of ClaM and its translation to DLs we refer to [15, 16, 17]. There, cardinality constraints are interpreted as the number of times each instance of the involved class participates in the given relationship, ISA is interpreted as sub-setting, while disj and cov are interpreted in the obvious way using disjointness/union between the denotation of the involved classes. More specifically, since we are using data models in a dynamic setting where object and relationships evolve over time, we interpret them along the temporal semantics presented in [18, 19, 20] for temporal data models. Essentially, the constraints captured therein must be satisfied in each snapshot (i.e., time point) of the system. Example 1. Figure 1 can be represented as a ClaM conceptual schema as: UC = {Person, Candidate, Application, Job Offer, Job Profile}; UR = {made by, responds to, refers to}; τ (made by) = (Application, Candidate); . . . ISA = {(Candidate, Person)}; #dom (made by, Application) = (1, ∞); . . . #ran (made by, Candidate) = (1, 1); . . .

Note that cardinalities are shown in the diagram of Figure 1 using the UML reading. 

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response(A, B) unary-response(A, B) precedence(A, B) unary-precedence(A, B) responded-existence(A, B) non-response(A, B) non-precedence(A, B) non-coexistence(A, B)

265

If A is executed, then B must be executed afterwards. If A is executed, then B must be executed exactly once afterwards. If A is executed, then B must have been executed before. If A is executed, then B must have been executed exactly once before. If A is execute, then B must also be executed (either before or afterwards). If A is executed, then B will not be executed afterwards. If A is executed, then B was never executed before. A and B cannot be both executed.

Figure 4. Intuitive meaning of temporal constraints

3.2. Temporal Constraints over Activities Taking inspiration from the DECLARE patterns [3], we present here the temporal constraints between (pairs of) activities that can be expressed in OCBC. Figure 3 graphically renders such constraints, while their textual representation is defined next.

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Definition 2 (Temporal constraints). Let • UA be the universe of activities, denoted with capital letters A1 , A2 , . . .; • UTC be the universe of temporal constraints, i.e., UTC = {response, unary-response, precedence, unary-precedence, responded-existence, non-response, non-precedence, non-coexistence}, as shown in Figure 3, where each tc ∈ UTC is a binary relation over activities, i.e., tc ⊆ UA × UA . The set of temporal constraints in a given OCBC model is denoted as ΣTC and is conceived as a set of elements of the form tc(A1 , A2 ), where tc ∈ UTC and A1 , A2 ∈ UA .  In the literature, such constraints are typically formalised using linear temporal logic over finite traces [21, 22]. We report their intuitive meaning in Figure 4. We observe that the non-precedence constraint is syntactic sugar, as it can be emulated using non-response: non-precedence(A, B) ≡ non-response(B, A). Thus, in the following we will not consider it anymore. When defining later on the OCBC model we will consider the set Σ+ TC of positive constraints containing response, unary-response, precedence, unary-precedence, and responded-existence, and the set Σ− TC of negative constraints containing non-response and non-coexistence. 3.3. OCBC Models and their Components We are now ready to define the OCBC model, and comment on its constitutive components, starting from data models and temporal constraints as respectively defined in Sections 3.1 and 3.2. Ontology Makes Sense : Essays in Honor of Nicola Guarino, IOS Press, Incorporated, 2019. ProQuest Ebook Central,

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Definition 3 (OCBC syntax). An OCBC model, M, is a tuple: (ClaM, UA , URAC , τRAC , #act , #obj , cref, neg-cref), where: • ClaM is a data model as in Definition 1; • UA is the universe of activities; • URAC is the universe of activity-object relationships being a set of binary relationships; • τRAC : URAC → UA × UC is a total function associating a signature to each activity-object relationship. If τRAC (R) = (A, O) then A ∈ UA and O ∈ UC ; • #act : URAC × UA →  N × (N ∪ {∞}) is a partial function defining cardinality constraints on the participation of activities in activity-object relationships. #act (R, A) is defined only if there is O s.t. τRAC (R) = (A, O); • #obj : URAC × UC →  {1} is a partial function that, when defined, denotes the activity that generated a given object in O. #obj (R, O) is defined only if there is O s.t. τRAC (R) = (A, O); • cref is the partial function of co-reference constraints s.t. cref : Σ+  UC ∪ UR ; TC × URAC × URAC → • neg-cref is the partial function of negative co-reference constraints s.t. neg-cref : Σ−  UC ∪ UR . TC × URAC × URAC → 

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In the following we detail the semantics of an OCBC model by concentrating on the two main aspects, i.e., activity-object relationships and co-reference constraints. Activity-object relationships capture how activities relate to classes. Let R ∈ URAC so that τRAC (R) = (A, O). The intuitive meaning of R is that each instance of activity A operates over a objects of type O (typically, a single one). In this light, inverses of activity-object relationships are assumed to be functional. On top of this, we single out activity-object relationships capturing the fact that objects of the related class are generated when instances of the related activity are executed. We call these special relationships as generating activity-object relationships while we denote the task as object generating task. If R is o a generating activityobject relationship, then it is associated to a cardinality constraint of the form #obj (R, O) = 1. The semantics of this cardinality constraint is as follows: whenever an object o is of type O at a given time t, then there must have been a previous time t at which an activity instance a of type A was executed on o (i.e., such that R(a, o) held at time t ). Cardinality constraints for participation of activities in activity-object relationships (#act ) are instead captured as classical cardinalities in data models (see [15, 18, 20]) with the intended meaning that a task can manipulate many objects. In the following, we show how activity-object relationships can be used to capture some of the constraints of our job hiring case study, and comment on interesting properties of the resulting OCBC model. Example 2. Figure 5 shows how constraints C.1–C.6 from the job hiring case study from Section 2.1 can be captured in OCBC. We maintain the shape, color and font Ontology Makes Sense : Essays in Honor of Nicola Guarino, IOS Press, Incorporated, 2019. ProQuest Ebook Central,

267

A. Artale et al. / Enriching Data Models with Behavioral Constraints register data

submit

mark as eligible

determine winner

1

is about 1 Person

closes promotes

creates 1

 made by

cancel hiring

1 creates

1

1..∗ Application

Candidate 1

post offer

∗

1

1

1

stops 1

Job Offer ∗

responds to

1 Job Profile

refers to

Figure 5. Activity-object relationships in the job hiring scenario of Section 2.1

coding schemes used in Section 2.1, so as to facilitate establishing a connection between the textual description of constraints, and their corresponding OCBC representation. The activities submit and post offer are object generating activities,

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and the relationships connecting submit to Application and post offer to Job Offer are generating activity-object relationships. In particular, while a person can exist in the domain even if no data have been registered for him/her, an application can exist in the domain only if it was created by an instance of the submit task (similarly for a job offer). Notably, even though the OCBC model in Figure 5 does not contain any explicit temporal constraint, the presence of activity-object relationships that generate objects, and their interplay with the constraints present in the data model, already imply the existence of implicit constraints over the allowed activity executions. First and foremost, activities pointing to a class that is also pointed by a generating activity-object relationship, can only be executed on an object if that very same object was previously created. This means that an application can be marked as eligible only if it was previously created through the execution of a submit activity instance. Similarly, a job offer can be stopped by a cancel hiring activity instance, or closed by a determine winner activity instance, only if it has been previously created by executing a post offer activity instance. These temporal dependencies could also propagate further, depending on how the pointed classes are related to each other. We discuss in particular two examples from Figure 5. When a job offer is created by posting it, given the cardinality constraints, it must also refer to exactly one job profile. Thus, such profile must belong to the class Job Profile at the same time when the relationship holds. Even more interesting is the creation of an application, which requires, on the one hand, the candidate owning that application and, on the other hand, a job offer. Thus, due to the interplay between the two generating activity-object relationships for Application and Job Offer , mediated by the responds to relationship linking each application to exactly one job offer (but not viceversa), a complex precedence constraint is implicitly introduced stating that: whenever an Application is submitted

responding to some Job Offer , that

Job Offer must have been

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Example 2 already gives an intuition about the sophistication, but also the subtleties, arising when adopting the OCBC approach. This is an intrinsic characteristic of declarative process modelling notations, as extensively discussed in [21, 23]. Co-reference constraints constitute the most powerful construct in OCBC. They have the ability of scoping the temporal constraints defined in Section 3.2, in such a way that they do not apply to any instances of the corresponding activities, but only to those activity instances that co-refer to each other via the objects they refer to. The co-reference may insist on a class, thus requiring such manipulated objects to be the same object, or on a relationship, thus requiring such manipulated objects to be related to each other via that relationship. This is of utmost importance. Take for example constraint C.7 from Section 2.1. That constraint is not satisfied if submitting an application is preceded by an arbitrary instance of the register data task. The constraint requires that there exists a preceding instance of the register data task that is about the very same candidate who is related to that

Application via the made by relationship.

Similarly, according to C.11, the execution of an instance of the cancel hiring task on some Job Offer does not prevent the possibility of determining the

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winner for other offers.

According to Definition 3, there are two kinds of co-reference constraints: positive and negative, and they can range either over object classes (as illustrated in Fig. 6a and 6c) or over relationships (as illustrated in Fig. 6b and 6d). The semantics of co-reference temporal constraints, considering response and not-response as prototypical example, is informally given in Figure 6. A similar meaning can be assigned to precedence and not-precedence (by substituting aftewards with before), and to responded-existence and not-coexistence (by removing afterwards and considering the entire timeline). To better clarify the usage of such constraints, and also their interesting (and subtle) features, we make again use of our case study in the job hiring domain. Example 3. The OCBC model illustrated in Figure 7 captures all constraints described in Section 2.1. Interestingly, each constraint mentioned in Section 2.1 is mirrored into a corresponding activity-object relationship or co-referenced temporal constraint in the diagram. The co-reference constraints involving object classes specify constraints on how objects connected to different activities can/cannot be shared. For example, the Job Offer instance stopped by a cancel hiring activity cannot be the same one closed by a determine winner activity due to the non-coexistence constraint. This means that when one of the two activities is executed on a job offer, the other cannot be executed on the same offer, but may be still executable for other offers. This constraint can be expressed using the following OCBC syntax:   neg-cref non-response(determine winner, cancel hiring), closes , stops = Job Offer

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A1

A2

R1

R2 O

269

Every time an instance a1 of A1 is executed on some object o of type O (i.e., with R1 (a1 , o, t1 )), then an instance a2 of A2 must be executed afterwards on the same object o (i.e., with R2 (a2 , o, t2 ) and t1 < t2 )

(a) Co-reference of response over an object class

A1

A2

R1

R2

O1

O2 R

Every time an instance a1 of A1 is executed on some object o1 of type O1 (i.e., with R1 (a1 , o1 , t1 )), then an instance a2 of A2 must be executed afterwards on some object o2 of type O2 (i.e., with R2 (a2 , o2 , t2 ) and t1 < t2 ) that relates to o1 via R at the moment of execution of a2 (i.e., having R(o1 , o2 , t2 )).

(b) Co-reference of response over a relationship

A1

A2

R1

R2 O

Every time an instance a1 of A1 is executed on some object o of type O (i.e., with R1 (a1 , o, t1 )), then no instance a2 of A2 that relates to the same object o can be executed afterwards (i.e., with R2 (a2 , o, t2 ) and t1 < t2 )

(c) Co-reference of non-response over an object class A1

A2

R1

R2

O1

O2

Every time an instance a1 of A1 is executed on some object o1 of type O (i.e., with R1 (a1 , o1 , t1 )), then no instance a2 of A2 that relates to o1 via R can be executed afterwards (i.e., there is no a2 , o2 with R2 (a2 , o2 , t2 ), R(o1 , o2 ) and t1 < t2 )

R

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(d) Co-reference of non-response over a relationship Figure 6. Co-reference response constraints over (a) object classes and (b) relationships, with their negated versions (c-d)

The co-reference constraints involving relationships specify constraints on how activities can/cannot occur on given objects connected to each other through the data model. As an example, the co-reference precedence temporal constraint relating submit to register data enables the possibility of submitting only applications made by candidates who already registered their data. The corresponding OCBC syntax is:   cref(precedence submit, register data), creates , is about = made by. Obviously, although not directly linked to Candidate , the is about activityobject relationship is inherited by that class given the ISA linking it to Person . It is interesting to notice that this constraint does by no means affect when and how many times the register data task can be executed for a given Person .

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register data

submit

mark as eligible

determine winner

1

is about 1 Person

closes promotes

creates 1

 made by

cancel hiring

1 creates

1

1..∗ Application

Candidate 1

post offer

∗

1

1

1

stops 1

Job Offer ∗

responds to

1 Job Profile

refers to

Figure 7. OCBC model for the job hiring scenario of Section 2.1, where each one of C.1–C.11 therein corresponds to either an activity-object relationship or a co-reference temporal constraint in the OCBC model. The lightweight non-response constraint is redundant: it is implied by the other constraints in the diagram.

Indeed, the model implicitly captures the fact that the same Person may update his/her personal data multiple times. Of particular interest is the unary-response constraint that relates mark as eligible to determine winner (which captures C.9 from Section 2.1), in particular when multiple applications submitted to the same job offer (say, job offer jo ) are marked as eligible. In this case, the constraint requires that every instance of the mark as eligible task promoting an Application that responds to jo , is eventually followed by a single instance of the determine winner task

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that closes offer jo . Such a single instance of determine winner for offer jo will be actually the same for all such eligible applications. In fact, having two distinct instances of determine winner for offer jo would violate the fact that the constraint is a unary response. This has a twofold implication: • The (unique) instance of determine winner for jo must occur after all the occurrences of mark as eligible for applications that respond to jo . • Once the (unique) instance of determine winner for jo is executed, it is no more possible to mark as eligible any application responding to jo . For otherwise, they would require a later occurrence of determine winner for jo , which would clash with the uniqueness requirement. This shows that the non-response constraint relating determine winner to mark as eligible via the responds to relationship is actually redundant: it is implied by the unary-response constraint relating mark as eligible to determine winner via the same responds to relationship. Notice that further applications may be still submitted for a closed job offer, but they will not be marked as eligible. • For similar reasons, the following is also implied: once an eligible Application responds to a Job Offer , then that

Job Offer cannot anymore be

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A. Artale et al. / Enriching Data Models with Behavioral Constraints

stopped . Indeed, an eligible

Application

271

requires that the (unique)

Job Offer is eventually closed (and thus cannot anymore be stopped due to the non-coexistence constraint between determine winner and cancel hiring ).



4. Conclusion and Discussions We have presented the OCBC model, which enriches structural conceptual models with behavioural constraints. By means of a small, but relevant case study, we have shown how OCBC captures the interconnection between the process and the data perspective, in a way that allows one to elegantly capture complex many-to-many processes simultaneously operating over different objects. We have discussed that such processes are recurrent in practice, but they can hardly be represented using conventional, case-centric process modelling notations. We believe that the OCBC approach can constitute the basis for novel research at the intersection of business process management, conceptual modelling, automated reasoning, and formal ontology. A line of research focussed on the discovery of OCBC models from event logs of process executions has been already started [24, 25] . We discuss next some of the main challenges that are still open, and were we believe the synergy with recent works by Nicola and colleagues is essential to effectively attack them.

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4.1. Formal semantics and relationship with other process modelling approaches As already recalled in the introduction, the formal semantics of OCBC can be defined in pure logical terms by resorting to first-order temporal logic, FOL(