Semantic Matchmaking with Nonmonotonic Description Logics 1614993351, 9781614993353

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SEMANTIC MATCHMAKING WITH NONMONOTONIC DESCRIPTION LOGICS

Studies on the Semantic Web Semantic Web has grown into a mature field of research. Its methods find innovative applications on and off the World Wide Web. Its underlying technologies have significant impact on adjacent fields of research and on industrial applications. This book series reports on the state of the art in foundations, methods, and applications of Semantic Web and its underlying technologies. It is a central forum for the communication of recent developments and comprises research monographs, textbooks and edited volumes on all topics related to the Semantic Web. www.semantic-web-studies.net Editor-in-Chief: Pascal Hitzler Editorial Board: Fausto Giunchiglia, Carole Goble, Asunción Gómez-Pérez, Frank van Harmelen, Riichiro Mizoguchi, Mark Musen, Daniel Schwabe, Steffen Staab, Rudi Studer

Volume 001 Titles in preparation Vol. 002. Johanna Völker, Learning Expressive Ontologies Vol. 003. Raúl Garcia Castro, Benchmarking Semantic Web Technology

ISSN 1868-1158

Stephan Grimm Albtalstr. 21 76307 Karlsbad Germany E-Mail: [email protected] Zur Erlangung des akademischen Grades eines Doktors der Wirtschaftswissenschaften (Dr. rer. pol.) von der Fakultät für Wirtschaftswissenschaften der Universität Karlsruhe (TH) genehmigte DISSERTATION von MSc. CS. Stephan Grimm Tag der mündlichen Prüfung: 11. Juni 2008 Referent: Prof. Dr. Rudi Studer 1. Korreferent: Prof. Dr. Detlef Seese 2. Korreferent: Prof. Dr. Andreas Geyer-Schulz Karlsruhe 2008

Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; Detailed bibliographic data is available on the Internet at http://dnb.ddb.de. © 2009, Akademische Verlagsgesellschaft AKA GmbH, Heidelberg Akademische Verlagsgesellschaft AKA GmbH Postfach 103305 69023 Heidelberg Deutschland Tel. +49 (0) 6221 21881 FAX +49 (0) 6221 167355 E-Mail: [email protected]

Verlagsauslieferung HEROLD Auslieferung & Service GmbH Raiffeisenallee 10 82041 Oberhaching Deutschland Tel. +49 (0) 89 6138710 FAX +49 (0) 89 61387120 E-Mail: [email protected]

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without prior permission from the publisher. Reproduced from PDF supplied by the author Printed in the Netherlands ISSN 1868-1158 ISBN 978-3-89838-620-3 (AKA) ISBN 978-1-60750-009-4 (IOS Press)

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Acknowledgements This thesis is the result of my work as a research assistant in the environment of the research group of Prof. Dr. Rudi Studer, which is formed by the knowledge management department at FZI (Forschungszentrum Informatik) and the institute AIFB (Angewandte Informatik und Formale Beschreibungsverfahren) at the university of Karlsruhe. While this group with all its members provided me with a fruitful environment for my research work as a whole, various people gave me particular support on my way to the successful completion of this thesis. First of all I would like to thank Prof. Dr. Rudi Studer. As my doctoral advisor he constantly monitored the progress of my research work and provided me with valuable feedback for intermediate work like scientific publications and presentations, and finally for this thesis. Due to the style of leading his research group I had an optimal working environment with fruitful discussions and cooperations as well as a good mix of obligations in project work and sufficient freedom for pursuing my research goals. Furthermore, I want to express my gratitude to PD Dr. Pascal Hitzler. He accompanied large parts of my research work as a supervisor in technical questions. He taught me most of what I learned about working scientifically, writing and reviewing papers, arguing in dialog with a research community and planning of research goals. Moreover, he gave me strong support in mastering the formal apparatus of nonmonotonic description logics with their model-theoretic semantics. We had many fruitful in-depth discussions that helped me to gain insights in this area. I also want to thank Dr. Andreas Abecker. As the head of my associated research depart ment at FZI and manager of resources, he provided me with great freedom in pursuing my research goals next to the obligations of work in projects. He was always open for advising me in managing work in research projects with local industrial partners as well as at an international level. Last but not least, I want to thank Dr. Boris Motik. As a research assistant colleague he supported me in studying the logic side of knowledge representation and ontologies especially in the beginning of my time at FZI. He was a source for advice and stimulating discussions in joint publication activities, which helped me finding and narrowing down my thesis topic.

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Abstract Semantic technology offers a promising tool to address the problem of today’s information overload by interpreting the meaning of content and data for their automated processing within computer systems. In the Semantic Web, ontologies provide the vocabulary needed for such a meaningful and machine-understandable interpretation of data, and they are the basis for semantic annotation of web resources. As artifacts of knowledge representation, ontologies allow to reason about semantically described resources, and one way of reasoning about semantic descriptions is their matchmaking in terms of resource compatibility. A particular application of matchmaking in the Semantic Web is the discovery of Web Services annotated by descriptions of service functionality, where inference mechanisms are used to judge whether a service offer is compatible with a service request. The reasoning machinery provided by current Semantic Web language standards like OWL, however, lacks various forms of common-sense behaviour due to the monotonicity of the underlying description logic formalism, while nonmonotonic extensions to description logics allow for such common-sense reasoning. In this thesis, we investigate several nonmonotonic extensions to description logics (DLs), namely autoepistemic DLs, circumscriptive DLs and terminological default rules, all of which extend standard DL inference mechanisms by forms of closed-world and default reasoning associated to common-sense features. We establish a matchmaking framework for semantic resource descriptions formulated in the DL formalism that uses various DL inferences to judge about resource compatibility. We put special emphasis on mapping the technical formalities of model-theoretic semantics of DLs to more intuitive notions that abstract from the details of logic for the framework’s easier adoption in applications. Moreover, we incorporate the common-sense features realised by nonmonotonic DLs into the matchmaking mechanism to improve matching behaviour in situations where semantic resource descriptions are incomplete. Based on this framework, we apply the technique of matchmaking to the problem of service discovery in the Semantic Web with services annotated by OWL descriptions for mulated in terms of domain ontologies. We evaluate the thus obtained service discovery mechanism by testing its applicability and usefulness in a concrete application scenario taken from a project case study in the logistics domain. The particular contributions of this thesis span the fields of nonmonotonic reasoning with description logics in Artificial Intelligence, matchmaking of ontology-based descriptions and Semantic Web Service discovery. We introduce a novel tableaux calculus for reasoning in circumscriptive DLs, and we demonstrate how the various nonmonotonic extensions to description logics can be used to realise common-sense features and local closed-world reasoning in a Semantic Web setting in general. We characterise the use of various DL inferences for solving the matchmaking problem and show how different realisations of local closed-world reasoning help to overcome problems that arise due to the open-world semantics of OWL and classical DLs. We also provide initial methodological guidance to the modelling of semantic resource descriptions in the context of matchmaking. Furthermore, we position our semantic matchmaking technique as an adequate tool for supporting Semantic Web Service discovery and demonstrate its applicability in a concrete use case scenario.

viii In essence, we extend classical description logics by nonmonotonic reasoning capabilities, incorporate the resulting features of common-sense inference into semantic matchmaking mechanisms and apply this technique to the problem of Semantic Web Service discovery.

Contents 1 Introduction 1.1 Motivation . . . . . . . . . . . 1.2 Research Objectives . . . . . . 1.3 Contributions . . . . . . . . . . 1.3.1 Research Fields . . . . . 1.3.2 Particular Contributions 1.3.3 Publications . . . . . . . 1.4 Reader’s Guide . . . . . . . . .

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Foundations

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2 Knowledge Representation and Reasoning 11 2.1 Principles of Knowledge Representation . . . . . . . . . . . . . . . . . . . . . 11 2.1.1 Forms of Representing Knowledge . . . . . . . . . . . . . . . . . . . . 12 2.1.2 Reasoning about Knowledge . . . . . . . . . . . . . . . . . . . . . . . . 14 2.2 Logical Knowledge Representation Formalisms . . . . . . . . . . . . . . . . . 16 2.2.1 Classical ModelTheoretic Semantics . . . . . . . . . . . . . . . . . . . 16 2.2.2 Description Logics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.2.3 Nonmonotonic Logics . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.2.4 Logic Programming . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.3 Knowledge Representation Paradigms . . . . . . . . . . . . . . . . . . . . . . 21 2.3.1 OpenWorld versus ClosedWorld View . . . . . . . . . . . . . . . . . 21 2.3.2 Conceptual Modelling versus Rules . . . . . . . . . . . . . . . . . . . . 23 2.3.3 ClearCut Predication versus Metamodelling . . . . . . . . . . . . . . 24 3 Ontologies and the Semantic Web 3.1 Ontologies in Information Systems . . . . . . . . . 3.1.1 Notion of an Ontology . . . . . . . . . . . . 3.1.2 Appearance of Ontologies . . . . . . . . . . 3.1.3 Utilisation of Ontologies . . . . . . . . . . . 3.2 Semantic Annotation in the Web . . . . . . . . . . 3.2.1 The Semantic Web Vision . . . . . . . . . . 3.2.2 Ontology Languages for the Semantic Web

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CONTENTS

4 OWL and Description Logics 4.1 The Web Ontology Language OWL . . . . . . . 4.1.1 Syntax and Semantics . . . . . . . . . . 4.1.2 Web Aspects and RDF(S) Compatibility 4.1.3 Software Support . . . . . . . . . . . . . 4.2 Description Logics . . . . . . . . . . . . . . . . 4.2.1 Formal Syntax and Semantics . . . . . . 4.2.2 Reasoning Problems . . . . . . . . . . . 4.2.3 Concrete Domains . . . . . . . . . . . . 4.3 Reasoning with OWL Ontologies . . . . . . . . 4.3.1 Validation . . . . . . . . . . . . . . . . . 4.3.2 Deduction . . . . . . . . . . . . . . . . .

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Nonmonotonic Reasoning in the Semantic Web

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5 Nonmonotonic Description Logics 5.1 Autoepistemic Description Logics . . . . . . . . . . . . . 5.1.1 Formal Semantics for Autoepistemic DLs . . . . 5.1.2 Reasoning with Epistemic Operators . . . . . . . 5.2 Circumscriptive Description Logics . . . . . . . . . . . . 5.2.1 Formal Semantics for Circumscriptive DLs . . . . 5.2.2 Reasoning with Circumscribed Knowledge Bases 5.3 Terminological Defaults . . . . . . . . . . . . . . . . . . 5.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . .

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6 A Reasoning Algorithm for Circumscriptive Description Logics 6.1 Principle Idea of a Tableaux Extension . . . . . . . . . . . . . . . . 6.1.1 Extending DL Tableaux Calculi by Preference Clashes . . . 6.1.2 Restrictions on the Formalism . . . . . . . . . . . . . . . . . 6.2 Deciding Circumscriptive ALCO . . . . . . . . . . . . . . . . . . . 6.2.1 Constraint Systems and their Solvability . . . . . . . . . . . 6.2.2 Tableaux Expansion Rules . . . . . . . . . . . . . . . . . . . 6.2.3 Notions of Clash and Detection of Inconsistencies . . . . . . 6.2.4 Sound and Complete Reasoning in Circumscriptive ALCO . 6.3 Implementation and Optimisation Issues . . . . . . . . . . . . . . . 6.3.1 Prototypical Implementation . . . . . . . . . . . . . . . . . 6.3.2 Possible Performance Optimisations . . . . . . . . . . . . .

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7 Reasoning in Rule-Based WSML 7.1 Rule-Based Inferencing and WSML . . . . . . 7.1.1 The Web Service Modeling Language . 7.1.2 Reasoning in Rule-Based WSML . . . 7.2 Reduction of WSML to Datalog . . . . . . . .

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CONTENTS

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7.2.1 Ontology Transformations . . . . . . . . . . . . . . 7.2.2 WSML Semantics through Meta-Level Axioms . . 7.2.3 WSML Reasoning by Datalog Queries . . . . . . . 7.2.4 Realising Datatype Reasoning . . . . . . . . . . . . Debugging Support . . . . . . . . . . . . . . . . . . . . . . 7.3.1 Identifying Constraint Violations . . . . . . . . . . 7.3.2 Debugging by Meta-Level Reasoning . . . . . . . . System Architecture and Implementation . . . . . . . . . 7.4.1 Architecture and Internal Layering . . . . . . . . . 7.4.2 Interface and Integration with Existing Technology

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Matchmaking of Semantically Annotated Resources

8 Semantic Matchmaking with Description Logics 8.1 Notion of Matchmaking . . . . . . . . . . . . . . . . . . . . . 8.1.1 Intuition . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1.2 Technical Characterisation . . . . . . . . . . . . . . . 8.1.3 Applications . . . . . . . . . . . . . . . . . . . . . . . 8.2 Ontology-Based Modelling of Resources in Description Logics 8.2.1 Resource Classes as Description Logic Concepts . . . . 8.2.2 Variance and Incompleteness in Resource Descriptions 8.2.3 Intuitive Reading of DL-Based Descriptions . . . . . . 8.2.4 Example Scenario of an Electronic Marketplace . . . . 8.3 Matching by Description Logic Reasoning . . . . . . . . . . . 8.3.1 Standard DL Inferencing for Matchmaking . . . . . . 8.3.2 Various Matching Inferences . . . . . . . . . . . . . . . 8.3.3 Discussion of Matching Inferences . . . . . . . . . . . 8.4 Deficiencies of Matchmaking with Classical DLs . . . . . . . . 8.4.1 Intersection Matching under Open-World Semantics . 8.4.2 Cases of Undesired Matching Behaviour . . . . . . . .

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9 Matchmaking with Local Closed-World Reasoning 9.1 Nonmonotonic Reasoning and the Local Closed World View in Matchmaking 9.1.1 Notion of Local Closure and Improvement of Matching Behaviour . . 9.1.2 Forms of Local Closure . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2 LCW-Based Matchmaking with Autoepistemic DLs . . . . . . . . . . . . . . . 9.2.1 Local Closure with the K-operator . . . . . . . . . . . . . . . . . . . . 9.2.2 Autoepistemic Closure by Example . . . . . . . . . . . . . . . . . . . . 9.3 LCWBased Matchmaking with Circumscriptive DLs . . . . . . . . . . . . . . 9.3.1 Local Closure with Circumscription Patterns . . . . . . . . . . . . . . 9.3.2 Circumscriptive Closure by Example . . . . . . . . . . . . . . . . . . . 9.4 LCW-Based Matchmaking with Terminological Defaults . . . . . . . . . . . . 9.4.1 Local Closure with Default Rules . . . . . . . . . . . . . . . . . . . . .

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10 Methodological Modelling Issues 10.1 Towards a Methodology for Building Resource Descriptions . . . . . . . 10.1.1 Motivation of Methodological Guidance . . . . . . . . . . . . . . 10.1.2 Building Blocks of a Modelling Methodology . . . . . . . . . . . 10.2 Modelling Patterns for Resource Descriptions with Classical DLs . . . . 10.2.1 Towards Abstract Modelling Constructs . . . . . . . . . . . . . . 10.2.2 Explicit Modelling Patterns . . . . . . . . . . . . . . . . . . . . . 10.3 Modelling Guidelines for Resource Descriptions with Nonmonotonic DLs 10.3.1 Regarding the Instance Situation . . . . . . . . . . . . . . . . . . 10.3.2 Joint Application of Separate Closure . . . . . . . . . . . . . . .

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9.4.2 Default Closure by Example . . Discussion of the Different Approaches 9.5.1 Comparison . . . . . . . . . . . 9.5.2 Conclusion . . . . . . . . . . .

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Application of Matchmaking to Semantic Web Service Discovery 193

11 Semantic Web Service Discovery 11.1 Semantic Web Services . . . . . . . . . . . . . . . . . . . . 11.1.1 Classical Web Services . . . . . . . . . . . . . . . . 11.1.2 Semantic Annotation for Web Services . . . . . . . 11.1.3 Various SWS Description Approaches . . . . . . . 11.2 Discovery of Services in the Semantic Web . . . . . . . . . 11.2.1 General Notion of Discovery . . . . . . . . . . . . . 11.2.2 Service Discovery Lifecycle . . . . . . . . . . . . . 11.2.3 Architectural Issues . . . . . . . . . . . . . . . . . 11.3 DL-Based Matchmaking for SWS Discovery . . . . . . . . 11.3.1 DL-Based Description of Service Functionality . . 11.3.2 DL Inferencing for Matching Service Descriptions . 11.3.3 Alternative Approaches to Matchmaking of Service

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12 Discovery in a Logistics Case Study 12.1 A Logistics Use Case based on Semantic Web Services 12.1.1 Scenario Description . . . . . . . . . . . . . . . 12.1.2 Technological Setting . . . . . . . . . . . . . . 12.1.3 Ontologies for the Logistics Scenario . . . . . . 12.2 Discovery within the Logistics Use Case Scenario . . . 12.2.1 Discovery Architecture and Technology . . . . 12.2.2 Discovery by Classical Matchmaking . . . . . . 12.2.3 Improved Discovery by Local Closure . . . . .

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CONTENTS

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Finale

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13 Related Work 237 13.1 Nonmonotonic Reasoning in the Semantic Web . . . . . . . . . . . . . . . . . 237 13.2 Matchmaking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 13.3 Semantic Web Service Discovery . . . . . . . . . . . . . . . . . . . . . . . . . 240 14 Conclusion 14.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . 14.1.1 Matchmaking Strategies with DL-Inferencing 14.1.2 Incorporation of Common-Sense Reasoning . 14.1.3 Methodological Modelling Guidelines . . . . . 14.2 Outlook . . . . . . . . . . . . . . . . . . . . . . . . .

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CONTENTS

Chapter 1

Introduction 1.1

Motivation

The World Wide Web has become an ubiquitous media for communication and constitutes a great achievement in connecting both end users and businesses or any other form of organisations. Nevertheless, the power of the current web is limited by the ability of human users to navigate the disparate sources for the information they require, and recently, the idea of the Semantic Web was envisioned, which aims towards automation by making the web machineunderstandable. Semantics is often associated with the interpretation of data, and the vision of the Semantic Web is to annotate web resources with meta data that can be interpreted by computers in an automated way. Ideally, humans are to be replaced by computational agents that surf through the web on their behalf, reasoning about the semantic meta data that describe the meaning of web content they come across, e.g. what a web page is about or what functionality is offered by a service. In this vision, intelligent matchmaking of semantically annotated resources is a crucial and frequent task that agents need to perform to be an adequate surrogate for the human and to achieve the desired automation. Various different kinds of resources are semantically annotated, and agents need to match and compare these semantic descriptions for their internal decision making in order to judge whether a particular resource is relevant for the fulfilment of their current mission. Specific applications of matchmaking comprise e.g. the matching of product supply and demand at electronic marketplaces or the comparison of skill profiles and job offers at electronic employment agencies. The vocabulary for semantic annotation is provided by ontologies, which constitute com putational knowledge models for a specific domain of interest. Hence, semantic resource descriptions are formulated in domain-specific terms, and an agent can draw from the background knowledge in such ontologies when reasoning about semantic annotations. Considering domain specific background knowledge accounts for intelligent and human-like matchmaking. However, while ontological engineering is in general considered a difficult task, ontology based annotation requires a careful and well thought use of ontology formalisms and languages for modelling semantic descriptions, and the intelligent behaviour for matchmaking is therefore not easily achieved.

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Chapter 1: Introduction

The machine-interpretable content of ontologies is typically processed by means of automated reasoning, which is another aspect in achieving intelligent behaviour of computational agents. The reasoning tasks and techniques defined for current ontology languages in the Semantic Web provide the basis for processing semantic annotations for the realisation of matchmaking. However, certain forms of common sense reasoning that account for making conjectures and default assumptions in open environments with incompletely specified infor mation, like the Semantic Web, are not available in the predominant ontology language standards, but could also be useful for matchmaking. Nonmonotonic reasoning is a well-known branch of symbolic Artificial Intelligence that can realise such common-sense behaviour, and it is therefore desirable to extend current Semantic Web languages with nonmonotonic features. A particular application of the technique of matchmaking is the discovery of services in the Semantic Web. Semantic Web Services instantiate the idea of semantic annotation for the case of Web Service technology, where the resources are Web Services, typically annotated by a description of their functionality. The finding of appropriate services with relevant capabilities is automated by applying matchmaking to semantic service descriptions, enabling an agent to judge about the relevance of a particular service for a given request. In this thesis, we will report on our work on matchmaking of semantically annotated resources with nonmonotonic description logics. Matchmaking refers to the comparison of semantic annotations in terms of relevance in the above sense. The generic notion of a resource indicates that we will consider matchmaking as a general technique independent from any particular kind of resources, although we will be concerned with Semantic Web Service discovery as a use case for a particular application of matchmaking. The notion of semantics is understood in the sense of interpretation of data, with annotations being based on ontologies and techniques of symbolic knowledge representation. Description logics are the formalism underlying the currently prominent ontology languages in the web, and their nonmonotonic extensions are proposals to augment these languages by features of commonsense reasoning.

1.2

Research Objectives

We develop the main research questions addressed in our work based on the notion of semantic matchmaking sketched above in the context of the Semantic Web. We identify concrete research objectives starting from developing a problem statement that reflects the current situation in research on semantic matchmaking. Our overall objective is to obtain an intuitively usable mechanism for intelligent matchmaking of semantically annotated resources by employing logic-based knowledge representation and forms of common sense reasoning. As ontologies are knowledge representation artefacts, ontology based information is typically processed by techniques of automated reasoning, which also applies for the comparison of semantic descriptions in matchmaking. However, reasoning can be applied in various forms, and it is still an open issue in which part of the matchmaking process logical inferencing is to be applied in which form to achieve a beneficial matchmaking behaviour. In particular, the interplay between reasoning techniques and the constitution of semantic descriptions is not

1.2 Research Objectives

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thoroughly investigated, as most approaches to matchmaking rather focus on the embedding of reasoning as a black box functionality into an overall comparison process. Especially approaches based on the currently prominent Semantic Web Ontology Language OWL, with its roots in description logics (DLs), have not exhaustively considered the peculiarities of description logic reasoning performed on OWL descriptions at the technical level of model-theoretic semantics, which is necessary for developing a thorough understanding of the interplay between description and matchmaking techniques. To this end, our first research objective is to conduct such a thorough investigation towards an optimal use of current ontology standards and inferencing mechanisms for the realisation of semantic matchmaking, clearly relating description and matching techniques. Objective 1 (matchmaking strategy). Investigate the interrelation between semantic descriptions and reasoning techniques to obtain intuitive matchmaking strategies based on logical inferencing. This investigation led to the awareness of problems with certain forms of matchmaking due to the open-world semantics of OWL, i.e. the way in which situations of incomplete and underspecified information are handled in the knowledge representation paradigm associated with the Semantic Web. While some of these problems can be tackled by a strict and guided modelling in classical DLs that adheres to certain patterns, a more flexible solution suggests to come from non-classical knowledge representation formalisms that provide features of nonmonotonic reasoning. These nonmonotonic logical formalisms are commonly associated with the notion of common-sense reasoning and allow for incorporating conjectures and default assumptions into the represented knowledge besides the classical statements that express universal truth. Since these features enable a controlled regulation of the open-world semantics, our second research objective is to make common-sense reasoning available in current Semantic Web languages and to utilise them for an improved matchmaking. Objective 2 (common-sense reasoning). Adopt forms of common sense reasoning for ontology languages in the Semantic Web context and incorporate them into the matchmaking strategy. Both matchmaking with classical and with specialised common-sense reasoning mechanisms raises the need for a methodology that advises modelers of semantic descriptions in using ontological modelling techniques, such that the resulting descriptions suit the chosen matchmaking strategy. While ontological engineering is in itself already considered a difficult task that requires skill and experience, the design of semantic descriptions in the context of matchmaking does even more so call for methodological advise. Since this aspect is largely neglected in research on logic-based matchmaking, our third objective is to devise methodological guidelines that help knowledge engineers designing semantic annotations in accordance with the matchmaking strategy. Objective 3 (methodological guidelines). Develop methodological guidelines for the modelling of ontology-based resource descriptions to achieve a proper matchmaking behaviour. We will give an overview on the contributions by which we have addressed these objectives in the subsequent section, and we will relate them to particular chapters of the thesis afterwards.

4

Chapter 1: Introduction

1.3

Contributions

Our work is related to several fields of research, which we sketch first, before we then list our particular contributions within these fields.

1.3.1

Research Fields

Our work intersects different (partly overlapping) fields of research and technology, which we characterise in the following. • Logic – logic is a field of mathematics concerned with the study of truth of statements and of inference. From here, we borrow the logical formalisms, in particular description logics, that underly current ontology language standards and their model theoretic semantics for investigating the relationship between semantic descriptions and reasoning techniques employed for matchmaking. • Knowledge Representation and Reasoning – Research on symbolic knowledge representation is concerned with the use of (primarily) logical formalisms for the machineinterpretable representation of knowledge for computational purposes. It is inherently coupled with reasoning as a technique to process this knowledge and to derive implicit information. From here, we exploit techniques for reasoning, in particular for nonmonotonic formalisms, to achieve intelligent matchmaking behaviour. We also borrow from knowledge representation paradigms, in particular from a local closed-world view for the flexible handling of situations of incomplete information. • Ontologies – Research on ontologies is concerned with conceptual modelling of domains of interest and an appropriate forming of ontological vocabularies using techniques of knowledge representation. We investigate ontological engineering guidelines and patterns concerning the “how-to” of modelling semantic annotations. • Semantic Web – Research centred around the Semantic Web is concerned with the use of ontologies for semantic annotation of web content and web resources. In here, we exploit semantic annotation techniques and web standards for ontology languages. Moreover, we use the Semantic Web setting as a basis for our use cases. • Web Services – Web Services constitute a communication technology for realising distributed information systems by web standards, while their combination with Semantic Web technology aims towards automation in service-oriented systems, e.g. for an improved information integration. Herein, we apply the techniques for semantic annota tion and matchmaking based on ontologies and reasoning to the automated discovery of services in the Semantic Web. We present contributions in several areas that combine these fields of research. The area of nonmonotonic reasoning applies logic as a branch of mathematics to reason about the truth of statements in a nonmonotonic way for the simulation of common-sense behaviour. We are particularly concerned with such reasoning techniques on formalisms that are relevant in the context of the Semantic Web, such as description logics. The area of semantic matchmaking

1.3 Contributions

5

addresses the comparison of ontological descriptions that encode meaning in terms of symbolic knowledge representation. We are particularly concerned with logic-based matchmaking by means of description logic inferencing. The area of Semantic Web Service discovery combines the Semantic Web idea of ontology based annotation with Web Service technology for an automated finding of services based on semantic descriptions of their functionality.

1.3.2

Particular Contributions

The contributions of our work span the different fields of research laid out previously, and aim towards the realisation of a framework for intuitive matchmaking of semantically annotated resources that shows an intelligent behaviour due to the employment of logic-based commonsense reasoning, taking into account background knowledge of domain ontologies. By this, we bridge between theory oriented work on logical formalisms and nonmonotonic reasoning, conceptual work on matchmaking strategies for ontological descriptions based on such forms of reasoning, and application-oriented work on employing matchmaking for service discovery in the Semantic Web. We list our particular contributions in the areas of nonmonotonic reasoning, semantic matchmaking and Semantic Web Service discovery in the following. Nonmonotonic Reasoning in the Semantic Web — We have devised a novel tableaux decision procedure for the nonmonotonic formalism of circumscriptive description logics, which is obtained from tableaux methods for conventional DLs augmented by our notion of a preference clash. We have proved soundness and completeness of this preferen tial tableaux calculus and realised a prototypical proof-of-concept implementation of a reasoner for circumscriptive ALCO. We have demonstrated how nonmonotonic description logics can be used to realise forms of common-sense reasoning and local-closed world behaviour, by means of illustrative examples. In particular, we have employed autoepistemic DLs and circumscriptive DLs for this demonstration. For the case of autoepistemic DLs, we have further more defined the reasoning task of epistemic concept satisfiability, for the handling of which we have adopted a calculus for answering epistemic queries from [36] in a prototypical implementation of a reasoner for the logic ALCK. We have also devised a reasoning framework for rule-based variants of the Web Service Modeling Language WSML that works on top of existing Datalog engines. Our implementation of this framework constitutes the first available reasoner for the WSML language. Semantic Matchmaking — We have characterised the use of various DL inferences as solutions to matchmaking based on a thorough analysis of their properties at the modeltheoretic level, having given them an intuitive reading that explains their effect on OWL descriptions in an abstract way. During this analysis, we have identified problems of matchmaking with classical DLs that are due to the open-world semantics of the OWL language and its handling of situations of incomplete information.

6

Chapter 1: Introduction

Based on a formal argumentation and on illustrative examples, we have shown that the formerly identified problems can be overcome by incorporating forms of common-sense reasoning into the matchmaking process. Namely, we have employed nonmonotonic extensions to description logics for realising a local closed-world view on semantic descriptions. In particular, we have shown how the use of autoepistemic DLs, circumscriptive DLs and terminological defaults can achieve a more flexible handling of situations of incomplete knowledge. We have furthermore developed methodological guidelines to advise the designers of semantic descriptions in the use of ontology languages, ensuring the compliance of descriptions to matchmaking strategies. While we have proposed modelling patterns for the case of classical description logics as an alternative or complementary solution for treating open-world semantics, we have also given such methodological advise for the use of their nonmonotonic extensions. Semantic Web Service Discovery — We have shown how the formerly developed techniques for semantic matchmaking can be utilised for the problem of Semantic Web Service discovery. Here, we have positioned matchmaking of OWL service descriptions as a useful technique for an early stage in the overall process of finding relevant services. We have furthermore demonstrated the adequacy of the thus obtained discovery mechanism by its application to a use case scenario in the logistics domain that is based on Web Service technology and taken from a project case study with industrial partner involvement.

1.3.3

Publications

Most of the work presented in this thesis has been published previously in proceedings of international conferences and workshops and in international journals. Parts of the foundations of knowledge representation and ontologies were published in [142, Chapter 3]. First results on the preferential tableaux calculus were published in [53]. A more elaborate article is under submission in the knowledge representation community and is made available in the technical report [52]. The application of epistemic operators to local closed world reasoning for their use in the Semantic Web was published in [56]. The use of circumscriptive DLs for defeasible inferencing with OWL ontologies was presented in [53, 54]. The reasoning framework for rule-based variants of the WSML language was published in [55]. The discussion and analysis of the use of DL inferences for matchmaking was published in [57, 130, 58, 54]. There, the problematic matching behaviour due to open-world semantics was identified and intuitive readings for matching inferences were given. Methodological guidelines and modelling patterns for the design of semantic descriptions with classical DLs were presented in [57, 51].

1.4 Reader’s Guide

7

The solution of problematic matchmaking in open-world settings through local closedworld reasoning was published in [58] for the case of autoepistemic DLs and in [54] additionally for the case of circumscriptive DLs. The publications [57, 58, 51] also account for the application of matchmaking techniques to the problem of service discovery in the Semantic Web, as they consider matchmaking in this context. The concrete application of matchmaking to the discovery of logistics services was published in [120, 51] and in [142, Chapter 8].

1.4

Reader’s Guide

The organisation of the thesis reflects the problem statement from Section 1.2 in a reverse order. After laying the foundations for knowledge representation and ontologies in Part I at an intuitive level but with increasing formality towards the end, the techniques for realising common-sense reasoning through nonmonotonic formalisms are treated first and on formal grounds in Part II. Then, matchmaking mechanisms are realised based on these formalisms in Part III, with an emphasis on intuition but using formal argumentation. Finally, matchmaking mechanisms are employed for Semantic Web Service discovery in Part IV from an application point of view, which was an initial motivation for the investigation of matchmak ing. Part I Foundations In the first part, we lay the foundations for our work on semantic matchmaking, presenting preliminaries in the fields of logic-based knowledge representation, ontologies and the Semantic Web. In Chapter 2, we will present the principles of knowledge representation, logical formalisms and the basic ideas behind reasoning about knowledge. In Chapter 3, we will introduce the notion of ontologies and their role in the Semantic Web vision. In Chapter 4, we will provide an overview on the ontology language OWL and formally introduce description logics. Part II Nonmonotonic Reasoning in the Semantic Web In the second part, we are concerned with nonmonotonic forms of reasoning, primarily as extensions to the description logic paradigm, but also in a rule-based formalism. In Chapter 5, we will introduce the formalisms of autoepistemic DLs, circumscriptive DLs and terminological defaults, and demonstrate their use for common-sense reasoning in the Semantic Web, addressing Objective 2. In Chapter 6, we will present our preferential tableaux calculus for reasoning with circumscriptive DLs, by which we additionally support Objective 2. In Chapter 7, we will present our reasoning framework for rule-based WSML, by which we give complementary support for Objective 2, addressing an alternative nonmonotonic formalism. Part III – Matchmaking of Semantically Annotated Resources — In the third part, we are concerned with semantic matchmaking of resource descriptions as the main theme of the thesis, by application of the techniques for nonmonotonic reasoning presented before. We treat matchmaking with classical as well as nonmonotonic description logics and

8

Chapter 1: Introduction

also cover methodological modelling issues. In Chapter 8, we will introduce our notion of matchmaking and provide an intuition for the model-theoretic aspects of matching ontologybased descriptions by means of DL-based inferencing. Here, we will identify problematic cases of matchmaking that are due to the open-world semantics, addressing Objective 1 directly. In Chapter 9, we will demonstrate how the different nonmonotonic extensions to description logics can effectively improve the matchmaking behaviour in these cases, providing for a flexible handling of incomplete information. By incorporating common-sense reasoning into the matchmaking process, we directly address Objective 2. In Chapter 10, we will elaborate on methodological guidelines and modelling patterns for the construction of proper semantic descriptions, addressing Objective 3. Part IV – Application of Matchmaking to Semantic Web Service Discovery — In this part we present the application of our matchmaking techniques to the problem of service discovery in the Semantic Web, using a project case study from the logistics domain for illustration. In Chapter 11, we will introduce the idea of Semantic Web Services and their discovery, and we will show how DL-based matchmaking can be applied to semantic service descriptions. By this, we support Objective 1, showing feasibility of the use of matchmaking techniques for service discovery. In Chapter 12, we will present a logistics case study based on Semantic Web Service technology and demonstrate how DL-based matchmaking solves a particular discovery scenario within this use case. By this, we additionally support all the objectives 1,2 and 3, demonstrating the usefulness of common-sense reasoning in matchmaking for discovery of logistics services by concrete examples. Part V – Finale — In the final part we conclude the thesis by referring to related work, summarising our contributions and pointing out open issues. In Chapter 13, we will relate our work to previous work in the areas of nonmonotonic reasoning in the Semantic Web, semantic matchmaking techniques and Semantic Web Service discovery. In Chapter 14, we will make concluding remarks comprising a summary of our work and an outlook on future research topics.

Part I

Foundations

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Chapter 2

Knowledge Representation and Reasoning As a field of Artificial Intelligence, knowledge representation is an attempt to simulate human intelligence by storing knowledge in symbolic form within a computer system, while reasoning is concerned with deriving conclusion from such knowledge by appropriate symbol manipulation. In this chapter, we give a brief introduction to the basics of knowledge representation and reasoning with an emphasis on the intuition behind model theoretic semantics and the local closed world paradigm. In Section 2.1, we will introduce to the principles and basic ideas behind knowledge representation and reasoning. In Section 2.2, we will describe the most common logical formalisms used for knowledge representation, which we will also need for our investigations of common-sense reasoning and semantic matchmaking in subsequent chapters. In Section 2.3, we will describe the prevalent knowledge representation paradigms that play an important role in the Semantic Web. In particular, we will distinguish an open-world from a closed world view and introduce the notion of a local closed-world view, which we will later on employ for an improved matchmaking.

2.1

Principles of Knowledge Representation

Knowledge representation and reasoning aims at designing computer systems that reason about a machine-interpretable representation of the world, similar to human reasoning. Knowledge-based systems have a computational model of some domain of interest in which symbols serve as surrogates for real world domain artefacts, such as physical objects, events, relationships, etc. [137]. The domain of interest can cover any part of the real world or any hypothetical system about which one desires to represent knowledge for computational purposes. A knowledge-based system maintains a knowledge base, which stores the symbols of the computational model in form of statements about the domain, and it performs reasoning by manipulating these symbols. Applications can base their decisions on answers to domainrelevant questions posed to a knowledge base.

2.1 Principles of Knowledge Representation

15

knowledge a system has about the domain of interest. The ability to process explicit knowledge computationally allows a knowledge-based system to reason over the domain by deriving implicit knowledge that follows from what has been told explicitly. This leads to the notion of logical consequence or entailment. A knowledge base KB is said to entail a statement α if α “follows” from the knowledge stored in KB , which is written as KB |= α. A knowledge base entails all the statements that have been added via the tell-operation plus those that are their logical consequences. As an example, consider the following knowledge base with sentences in first-order logic. KB = { Person(MisterX), participates(MisterX, FL4711), Flight(FL4711), books(UbiqBiz, FL4711), ∀x, y, z : (Flight(y) ∧ participates(x, y) ∧ books(z, y) → employedAt(x, z)), ∀x, y : (employedAt(x, y) → Company(y) ∧ Employee(x)), ∀x : (Person(x) → ¬Company(x)) } The knowledge base KB explicitly states that “MisterX is a person who participates in the flight FL4711 booked by UbiqBiz”, that “participants of flights are employed at the company that booked the flight”, that “the employment relation holds between companies and employees” and that “persons are different from companies”. If we ask the question “Is MisterX employed at UbiqBiz?” by saying ask(KB , employedAt(MisterX, UbiqBiz)) the answer will be yes. The knowledge base KB entails the fact that “MisterX is employed at UbiqBiz”, i.e. KB |= employedAt(MisterX, UbiqBiz), although it was not “told” so explicitly. It follows from its general and specific knowledge about the domain. A further consequence is that “UbiqBiz is a company”, i.e. KB |= Company(UbiqBiz), which is reflected by a positive answer to the question ask(KB , Company(UbiqBiz)). This follows from the former consequence together with the fact that “employment holds between companies and employees”. Another important notion related to entailment is that of consistency or satisfiability. Intuitively, a knowledge base is consistent or satisfiable if it does not contain contradictory facts. If we would add the fact that “UbiqBiz is a person” to the above knowledge base KB by saying tell(KB , Person(UbiqBiz)), it would become unsatisfiable because persons are said to be different from companies. We explicitly said that UbiqBiz is a person while at the same time it can be derived that it is a company. In general, an unsatisfiable knowledge base is not very useful, since in logical formalisms it would entail any arbitrary statement. The ask-operation would always return a positive result independent from its parameters, which is clearly not desirable for a knowledgebased system. The inference procedures implemented in computational reasoners aim at realising the entailment relation between logical statements [129]. They derive implicit statements from

16

Chapter 2: Knowledge Representation and Reasoning

a given knowledge base or check whether a particular statement is entailed by a knowledge base. An inference procedure that only derives entailed statements is called sound . Soundness is a desirable feature of an inference procedure, since an unsound inference procedure would potentially draw wrong conclusions. If an inference procedure is able to derive every statement that is entailed by a knowledge base then it is called complete. Completeness is also a desirable property, since a complex chain of conclusions might break down if only a single statement in it is missing. Hence, for reasoning in knowledge-based systems we desire sound and complete inference procedures.

2.2

Logical Knowledge Representation Formalisms

Logical formalisms are the theoretical underpinning of symbolic knowledge representation as laid out above. Various logical formalisms have evolved in Artificial Intelligence research, ranging from general purpose logics over mechanisms for handling inconsistencies and uncer tainty to specific formalisms for reasoning over space and time. In the context of our work on matchmaking with nonmonotonic reasoning in a Semantic Web setting, some logical formalisms and principles are particulary important, namely description logics, nonmonotonic logics and logic programming. In this section, we will therefore review these formalisms with a focus on issues of modeltheoretic semantics and knowledge representation features at an intuitive level. We will first sketch the intuition behind the mechanism of classical model-theory for first-order predicate logic, before we will present the basic ideas behind description logics, nonmonotonic formalisms and logic programming.

2.2.1

Classical Model-Theoretic Semantics

First-order (predicate) logic is the prevalent and single most important knowledge representation formalism. Its importance stems from the fact that basically all current symbolic knowledge representation formalisms can be understood in their relation to first order logic. Its roots can be traced back to the ancient Greek philosopher Aristotle, and the modern first order predicate calculus was created in the 19th century, when the foundations for modern mathematics were laid. First-order logic captures some of the essence of human reasoning by providing a notion of logical consequence that is realised in terms of a model-theoretic semantics. A knowledge base KB is viewed as a set of first-order formulas that constitute a logical theory T . In a model-theoretic way, the semantics of a logical theory T is defined in terms of interpretations. Formally, an interpretation I is a mapping from the elements in the formulas in T into a set ΔI , called the interpretation domain. Constant symbols, for example, directly map to objects in the interpretation domain, while predicate symbols are interpreted as subsets of or relations over ΔI , which are called their extensions. Intuitively, an interpretation specifies a particular arrangement of objects in the interpretation domain in terms of membership in predicate extensions. For example, in one interpretation a constant symbol like MisterX can

2.2 Logical Knowledge Representation Formalisms

17

be in the extension of the predicate Employee, in another interpretation it can be in the extension of the concept Flight, and in yet another one it can be in the extensions of both. If the arrangement of objects in an interpretation I is in accordance with the formulas in T then I is called a model of T . For example, if we state that MisterX is an employee and that employees are disjoint from flights in a theory T = {Employee(MisterX), ∀x : Employee(x) → ¬Flight(x)}, then interpretations in which MisterX is in the extension of the predicate Flight cannot be models of T as they do not satisfy its formulas. Even after filtering out those interpretations that do not satisfy the formulas in a logical theory T , it has in general a multitude of models in which things are interpreted differently. For example, if we did not say whether MisterX is employed at UbiqBiz or not, there are models in which he is and such in which he is not. In this case, we say that we have incomplete knowledge about the employment of MisterX, which is captured by the situation of multiple models. Contrarily, if we explicitly list all employees together with their respective companies and also state that there are no other employment relations, we say that we have complete knowledge about employment, which is reflected by T having having only models in which the employees of companies are exactly those from our explicit list. This classical model-theoretic style of semantics is sometimes also referred to as “Tarskian” semantics. Reasoning about a theory T is now defined based on its models. The reasoning task of validation, concerned with the theory’s consistency, is to check whether T has a model. The reasoning task of deduction is concerned with the derivation of logical consequences, which are statements that are true in all models of T . Deduction allows to access knowledge that is not explicitly given but implicitly represented by T . Although first-order predicate logic is a very expressive formalism for which reasoning is even undecidable in general, there are some features of knowledge representation that cannot be conveniently realised with classical semantics. From the study of such expressive features in symbolic Artificial Intelligence, various knowledge representation formalisms with non classical semantics have evolved. Most of these formalisms can be characterised by an alteration of the notion of logical consequence, which is obtained by not requiring a statement to be true in all models of a theory but only in some, in more, or simply in other models or interpretations.

2.2.2

Description Logics

Description Logics (DLs) [6] are a family of class (concept) based knowledge representation formalisms with well-studied representational and computational properties. They are the modern descendants of early knowledge representation systems such as KL-One [20] or CLASSIC [19] and have been developed to give a precise formalisation to semantic networks. As such, they typically form decidable fragments of the first order logic predicate calculus restricted to unary and binary predicates to capture the nodes and arcs in a network graph. The basic elements used to represent knowledge in the description logic formalism are concepts, individuals and roles. Intuitively, concepts denote classes of things, such as Employee or Flight. Individuals denote instances, such as MisterX or FL4711. Roles denote relationships between things, such as participates or employedAt. Moreover, DLs are often augmented by so called concrete domains [95] to also capture datatypes such as integer or string.

20

Chapter 2: Knowledge Representation and Reasoning

knowledge base might result in loss of conclusions, i.e. our knowledge does not necessarily grow monotonically with new observations. Logics with classical semantics are monotonic, as a conclusion is only drawn if there is sufficient evidence, and thus, they are not feasible for handling assumptions and conjectures. More formally, reasoning in a knowledge representation formalism is monotonic if, for two knowledge bases KB and KB  with KB ⊂ KB  and for any axiom α, KB |= α implies KB  |= α, and it is nonmonotonic otherwise. A particular way of realising nonmonotonic formalisms at the semantical level is to prefer some of the models of a knowledge base over others and to only consider the preferred models for reasoning, which results in a preference model semantics. We will study such preference model semantics in the context of nonmonotonic extensions to description logics in Chapter 5.

2.2.4

Logic Programming

Logic programming (LP) was originally conceived as a way to use first order logic as a programming language, e.g. in case of the language Prolog [93]. To ensure computability of the language, statements are syntactically restricted to so-called Horn clauses and only certain kinds of logical consequences are being considered. Syntactically, Horn clauses can be understood as rules. For example, the expression Trip(t)∨¬Flight(t) is a Horn clause, which is semantically equivalent to ∀t : Trip(t) ← Flight(t). This can also be interpreted as the rule (1) from page 13 written in the typical Prolog style notation Trip(?t) : − Flight(?t). However, the semantics of the Horn clause is given by means of first-order logic semantics, whereas logic programming rules are usually understood in a different, non-classical sense. One of the differences stems from the fact that in a logic programming system only certain types of logical consequences are being considered, namely ground instances of predicates.1 Applying the above rule to a fact Flight(FL4711) would allow to conclude Trip(FL4711) both in first-order logic and in logic programming. A conclusion such as Trip(FL4711) ∨ ¬Flight(FL4711), however, would only be possible in first-order logic, and not derivable in a LP system. Moreover, negative information is handled differently within the LP paradigm than it is in classical logic. In the example above we could be interested in whether the statement Trip(FL2306) holds. In classical logics, neither truth nor falsity of this statement is derivable. In logic programming, however, the statement would be considered false, as LP systems typically treat the lack of information as a form of default negation called negation-as-failure. Since no information on FL2306 is available, it is considered to be not a trip. The semantics of LP formalisms is based on minimal models, i.e. those models of a knowledge base that have the least extensions of predicates, while other models are not considered for reasoning. Due to the lack of evidence for FL2306 being a trip no model in which Trip(FL2306) holds is minimal. In the LP paradigm, a knowledge base is understood as a logic program, which is a set of rules H : − B where H is called the head and B is called the body of the rule. Facts are rules with an empty body, i.e. what is stated in their head holds regardless of any conditions. 1

A ground (instance of a) predicate is an atomic formula which does not contain any variable symbols.

2.3 Knowledge Representation Paradigms

21

The various logic programming dialects allow different forms for the heads and the bodies of rules. The most basic LP variants restrict the head to atomic predicates, while they allow for conjunction (∧) and negation-as-failure in the body. Examples for such systems are Prolog [93] and Datalog [147], a language that has its origin in deductive databases. More advanced systems, such as disjunctive Datalog [40] or Answer Set Programming [49], allow for disjunctions of predicates in the head and provide a more sophisticated treatment of negation. Yet another special case of a LP-rule is a constraint, which is a rule that has an empty head with the semantics of deriving the empty clause. From the database background, such a rule is also called an integrity constraint, as a successfully instantiated body causes an inconsistency, indicating an unallowed instance situation that violates data integrity. We refer to [4] for a formal treatment of LP formalisms and for an overview on various styles of minimal model semantics, such as stable model semantics or well founded semantics. We will investigate an inferencing mechanism for a particular LP formalism, namely the language WSML-Flight, in the context of Semantic Web reasoning in Chapter 7.

2.3

Knowledge Representation Paradigms

Besides various logical formalisms, different modelling paradigms have evolved that characterise the representation of knowledge. Some of them, such as the local closed-world paradigm, are particularly important for our work on matchmaking. In this section, we will therefore reflect on some major distinctions made for the use of knowledge representation formalisms, namely on an open world versus closed-world view, on a conceptual versus rule-based modelling paradigm, and on the metamodelling approach.

2.3.1

Open-World versus Closed-World View

An essential choice that has to be made when selecting a formalism for representing knowledge is how situations of incomplete information are handled. One option is to take an openworld view, assuming that at any time new knowledge can be learned that resolves previous ambiguity. Another option is to take a closed world view, assuming to have full knowledge about a particular situation by what has been observed so far. Furthermore, a combined view applies a mix of both strategies to different parts of the domain model under consideration. Open-World View — Knowledge representation based on logics with classical semantics operates under the open-world assumption, which allows for a distinction between negative knowledge and the lack of knowledge. An example of negative knowledge is an entry for absence in the appointment calender of MisterX for a particular day at which he is booked for a flight, having the form of a negated assertion ¬available(MisterX, 26.09.2007). From this, anyone who wants to invite MisterX for an internal meeting at this particular day can safely conclude that he is not available. In an open-world view, this is different from the lack of an assertion about MisterX’s availability, from which a knowledge-based system would not draw any conclusion. The question as to whether MisterX is available would be answered with “unknown”, since neither ¬available(MisterX, 26.09.2007) nor available(MisterX, 26.09.2007) could be derived.

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Chapter 2: Knowledge Representation and Reasoning

Depending on the particular use case, an open-world view can either be beneficial or hindering. While in some situations it is preferable to quickly take the action of finding a substitute person for the meeting, MisterX might just not have synchronised his calender tool yet, such that the indication of his availability being “unknown” can be a valuable information, worth to be distinguished from certain unavailability. The open-world view in classical logics is technically realised by the connection of logical consequence to the underlying mechanism of the model-theoretic semantics. In a situation of incomplete information, unspecified issues can be resolved in different ways, each represented by a different model of the respective knowledge base. If there is no information about MisterX’s availability, there are models in which he is available and such in which he is not. Neither conclusion can be drawn, since conclusions need to hold in all models. The open world view has been argued to be particularly suitable for knowledge-based applications used in the web due to its open and volatile nature. Closed-World View — When making the closed-world assumption, negative knowledge coincides with the lack of knowledge, and what cannot be proven to be true is assumed to be false. Thus, a knowledge-based system that takes a closed-world view assumes to have complete information when reasoning about a particular situation. In consequence, such a system never produces “unknown” as an answer but always takes a decision as to whether a particular statement holds or does not hold. The lack of information about the availability of MisterX at a particular day, for example, is simply interpreted as unavailability, taking the form of ¬available(MisterX, 26.09.2007). Similar to the open-world view, it is sometimes beneficial and pragmatical and sometimes inadequate to take the closed-world view, depending on the actual use case. A closed-world perspective is particularly natural from a database point of view. An employee is assumed to be not booked on a trip unless a booking record can be found in the database. The closed world assumption is intrinsically made in logic programming and deductive database systems, where it is realised by the underlying minimal model semantics that takes only models with minimal predicate extensions into account for reasoning. In absence of the fact available(MisterX, 26.09.2007), only models in which MisterX is not available are minimal, such that his unavailability becomes a logical consequence due to negation-as-failure. Hence, the closed-world view is directly related to nonmonotonic reasoning, as negative consequences due to negation as-failure are retracted in the presence of positive counter evidence. For classical first-order logic, the closed-world assumption has been formulated as the closure of predicates in a logical theory by means of additional axioms in [124]. If the above lack of information about MisterX’s availability occurs in a first-order logic knowledge base then a form of closed-world view can also be achieved by including the axiom ¬available(MisterX, 26.09.2007) in a dynamic way, derived by the absence of the respective positive information. However, a truly dynamic and defeasible closure in the sense of non monotonic reasoning cannot be achieved in this way, since classical logics are monotonic. If MisterX were to state his availability at one of two days by available(MisterX, 26.09.2007) ∨ available(MisterX, 27.09.2007) then the inclusion of both ¬available(MisterX, 26.09.2007) and ¬available(MisterX, 27.09.2007) would be inconsistent with the above statement instead of realising the closed world view.

2.3 Knowledge Representation Paradigms

23

Local Closed-World View — From the above we have seen that neither a pure openworld view nor a pure closed-world view accounts for all situations that can occur in possible use cases. Hence, it seems natural to take a combined view tat allows for both paradigms. In particular, it should be possible to make the treatment of incomplete information dependent on the particular parts of the domain about which knowledge is to be represented. Such a combination of the two paradigms is known as the local closed world assumption, which takes a general open-world view but allows for a restricted, local use of the closed-world assumption. As characterised in [42], the local closed-world view starts from the open-world assumption but takes a closed world view on dedicated parts of the domain model, which can be selected by the knowledge engineer or user of the knowledge-based system. In our example, we could decide to take an open world view on the availability of employees in the highly dynamic calender tool, while we might want to locally apply the closed-world assumption to the rather invariable status of persons’ employment at companies. For this purpose, we would mark the respective predicate employedAt to be interpreted in a closed-world sense, leaving other parts of the domain open. Then, any question as to whether a person is employed at a company would either yield a positive answer for those with known employment records or a negative answer for all others. Even more than the close-world assumption, the local closed-world assumption is strongly related to nonmonotonic reasoning. While defeasible conclusions due to local closure can be retracted, the constructs of various nonmonotonic formalisms can be used to select the parts of the domain model to be locally closed. We will be concerned with the realisation of the local closed world view through nonmonotonic extensions of description logics in Chapter 5, which we will apply in the context of matchmaking in Chapter 9.

2.3.2

Conceptual Modelling versus Rules

The description logic and logic programming formalisms form the two major strands for research on knowledge representation in symbolic Artificial Intelligence, standing for antithetic paradigms. As we have seen in the previous sections, both represent different forms of knowledge representation that give the modelling of domain knowledge a specific flavour. While description logics build on conceptual modelling by means of intensional descriptions of concepts and their interrelation, logic programming provides the basic construct of a rule for the derivation of facts. Both formalisms can be seen as deviations from the first order predicate calculus in two different directions: while description logics limit the arity and use of predicates to fit semantic network graphs under classical semantics yielding decidable fragments of first-order logic, logic programming formalisms restrict the shape of statements that can be derived to ground facts under certain forms of minimal model semantics to yield efficient derivation rule systems. Hence, the features they exhibit as forms of knowledge representation are those of conceptual modelling versus rules. The modelling of knowledge for knowledge-based systems in these two paradigms has different applications. Description logics are rather used in applications that require schemaintensive reasoning and classification of concepts according to their intensional descriptions, whereas logic programming systems are more used for data intensive reasoning tasks and for

24

Chapter 2: Knowledge Representation and Reasoning

the retrieval of instance data from large extensional knowledge bases. Related to this, the two types of formalisms also differ in their computational properties concerning efficiency. While schema-intensive reasoning is rather intricate and DL reasoning problems typically have exponential runtime complexity, the reduction of LP consequences to ground facts makes reasoning with logic programs more tractable. Both these paradigms have different expressivity and allow for complementary features. Hence, it is desirable to combine the formalisms of DL and LP to yield a more powerful tool for knowledge representation. Despite their inherent semantic incompatibility, there have recently been attempts to a seamless integration of description logics and rules at a semantic level on formal grounds, as reported in [104, 105].

2.3.3

Clear-Cut Predication versus Metamodelling

In knowledge representation based on first-order logic, there is an intrinsic distinction between an intensional part of a knowledge base, which captures general statements about classes of objects and their properties, and an extensional part, which captures statements about particular situations of individual objects in the interpretation domain. This distinction is due to the “first-order” nature of the formalism, which induces a clear separation between concrete domain objects and the predicates used to express their properties.2 One particular paradigm for knowledge representation is to impose a clear-cut separation between the intensional and the extensional part of a knowledge base, such that no symbol serves as a property in the intensional part and as an individual object in the extensional part at the same time. Although this separation is intuitive, it is sometimes inadequate for certain domains. For example, if we want to state that MisterX is a human and that humans are a particular species by Human(MisterX) and Species(Human) then we break the separation between intensional and extensional statements, since Human is used both as a concrete object in the domain and as a property for another object MisterX in form of a unary predicate. This alternative paradigm of not imposing a clear-cut separation between intensional and extensional knowledge is also referred to as metamodelling [103]. In terms of semantic networks, metamodelling amounts to using concepts also in place of individuals.

2

In higher-order logics this separation is abrogated and variables can range over predicates.

Chapter 3

Ontologies and the Semantic Web Ontologies, as used in information systems, are conceptual yet computational models of a domain of interest that build on techniques of knowledge representation. They play a key role in the Semantic Web, where they support the meaningful annotation of web content and resources. In this chapter, we give a brief introduction to ontologies and the Semantic Web to lay the ground for the matchmaking of ontology-based descriptions in a web setting. In Section 3.1, we will introduce the notion of an ontology as we will use it later on to provide the background knowledge for semantic matchmaking. In Section 3.2, we will present the vision of the Semantic Web based on the idea of semantic annotation using ontologies, together with an overview on current ontology languages.

3.1

Ontologies in Information Systems

Recently, the notion of ontologies as computational artefacts has appeared in Artificial Intelligence and Computer Science, while “ontology” originally denotes the study of existence in philosophy. In information systems, ontologies are conceptual models of what “exists” in some domain, brought into machine-interpretable form by means of knowledge representation techniques. In this section, we will start from a general definition of the notion of ontology and elaborate on its appearance and usage in computer science.

3.1.1

Notion of an Ontology

Ontology — In its original meaning in philosophy, ontology is a branch of metaphysics and denotes the philosophical investigation of existence. It is concerned with the fundamental questions of “what is being?” and “what kinds of things are there?” [31]. Dating back to Aristotle, the question of “what exists?” lead to studying general categories for all things that exist. Ontological categories provide a means to classify all existing things, and the systematic organisation of such categories allows to analyse the world that is made up by these things in a structured way. In ontology, categories are also referred to as universals, and the concrete things that they serve to classify are referred to as particulars.

26

Chapter 3: Ontologies and the Semantic Web

Philosophers have mostly been concerned with general top-level hierarchies of universals that cover the entire physical world. Examples of universals occurring in such top-level hierarchies are most general and abstract concepts like “substance”, “physical object”, “intangible object”, “endurant” or “perdurant”. Philosophers have argued about the appropriateness of different such abstract categorisations and about the general properties of everything ex isting. Transferred to knowledge representation and computer science, information systems can benefit from the idea of ontological categorisation. When applied to a limited domain of interest in the scope of a concrete application scenario, ontology can be restricted to cover a special subset of the world. Examples of ontological categories in the business trips domain are “Person”, “Company”, “Trip” or “Flight”, whereas examples for particular individuals that are classified by these categories are the person “MisterX”, the company “UbiqBiz” or the particular flight “FL4711”. In general, the choice of ontological categories and particular objects in some domain of interest determines the things about which knowledge can be represented in a computer system [137]. In this sense, ontology provides the labels for nodes and arcs in a semantic network or the names for predicates and constants in rules or logical formulas, that constitute an ontological vocabulary. By defining “what exists” it determines the things that can be predicated about. The terms of the ontological vocabulary are then used to represent knowledge, forming statements about the domain. Ontologies — While “ontology” studies what exists in a domain of interest, “an ontology” as a computational artefact encodes knowledge about this domain in a machineprocessable form to make it available to information systems. In various application contexts, and within different communities, ontologies have been explored from different points of view, and there exist several definitions of what an ontology is. Within the Semantic Web community the dominating definition of an ontology is the following, based on [60]. Definition 3.1 (ontology). An ontology is a formal explicit specification of a shared con ceptualisation of a domain of interest. This definition captures several characteristics of an ontology as a specification of domain knowledge, namely the aspects of formality, explicitness, being shared, conceptuality and domain-specificity, which require some explanation. • formality An Ontology is expressed in a knowledge representation language that provides a formal semantics. This ensures that the specification of domain knowledge in an ontology is machine-processable and is being interpreted in a well-defined way. The techniques of knowledge representation help to realise this aspect. • explicitness An ontology states knowledge explicitly to make it accessible for machines. Notions that are not explicitly included in the ontology are not part of the machine-interpretable

3.1 Ontologies in Information Systems

27

conceptualisation it captures, although humans might take them for granted by common sense.1 • being shared An ontology reflects an agreement on a domain conceptualisation among people in a community. The larger the community, the more difficult it is to come to an agreement on sharing the same conceptualisation. Thus, an ontology is always limited to a particular group of people in a community, and its construction is associated with a social process of reaching consensus. • conceptuality An ontology specifies knowledge in a conceptual way in terms of symbols that represent concepts and their relations. The concepts and relations in an ontology can be intu itively grasped by humans, as they correspond to the elements in our mental model. (In contrast to this, the weights in a neural network or the probability measures in a Bayesean network would not fit such a conceptual and symbolic approach.) Moreover, an ontology describes a conceptualisation in general terms and does not only capture a particular state of affairs. Instead of making statements about a specific situation involving particular individuals, an ontology tries to cover as many situations as possible that can potentially occur [62]. • domain specificity The specifications in an ontology are limited to knowledge about a particular domain of interest. The narrower the scope of the domain for the ontology, the more an ontology engineer can focus on axiomatising the details in this domain rather than covering a broad range of related topics. In this way, the explicit specification of domain knowledge can be modularised and expressed using several different ontologies with separate domains of interest. Technically, the principal constituents of an ontology are concepts, relations and instances. Concepts map to the generic nodes in semantic networks, or to unary predicates in logic, or to concepts as in description logics. They represent the ontological categories that are relevant in the domain of interest. Relations map to arcs in semantic networks, or to binary predicates in logic, or to roles in description logics. They semantically connect concepts, as well as instances, specifying their interrelations. Instances map to individual nodes in semantic networks, or to constants in logic. They represent the named and identifiable concrete objects in the domain of interest, i.e. the particular individuals which are classified by concepts. 1 Notice that this notion of explicitness is different from the distinction between explicit and implicit knowledge, introduced earlier. Implicit knowledge that can be derived by means of automated deduction does not need to be included in an ontology for a computer system to access it. However, knowledge that is neither explicitly stated nor logically follows from what is stated, can by no means be processed within the machine, although it might be obvious to a human. Such knowledge remains implicit in the modeller’s mind and is not represented in the computer.

28

Chapter 3: Ontologies and the Semantic Web

These elements constitute an ontological vocabulary for the respective domain of interest. An ontology can be viewed as a set of statements, expressed in terms of this vocabulary, which are also referred to as axioms. A simple axiom would, for example, state that “Mister X is an employee”, involving an instance and a concept. A more complex axiom could state that “only employees of a particular company can be on trips booked by this company”, imposing a restriction on a relation between two concepts. Conceptual modelling with ontologies seems to be very similar to modelling in objectoriented software development or to designing entity-relationship diagrams for database schemas. However, there is a subtle twofold difference. First, ontology languages usually provide a richer formal semantics than object-oriented or database-related formalisms. They support encoding of complex axiomatic information due to their logic-based notations. Hence, an ontology specifies a semantically rich axiomatisation of domain knowledge rather than a mere data or object model. Second, ontologies are usually developed for a different purpose than object-oriented models or entity-relationship diagrams. While the latter mostly describe components of an information system to be executed on a machine or a schema for data storage, respectively, an ontology captures domain knowledge as such and allows to reason about it. In summary, an ontology used in an information system is a conceptual yet executable model of an application domain. It is made machine-interpretable by means of knowledge representation techniques and can therefore be used by applications to base decisions on reasoning about domain knowledge.

3.1.2

Appearance of Ontologies

When engineered for or processed by information systems, ontologies appear in different forms related to the forms of knowledge representation that we have discussed in the previous chapter. A knowledge engineer views an ontology by means of some graphical or formal visualisation, while for storage or transfer it is encoded in an ontology language with some machine-processable serialisation format. A reasoner, in turn, interprets an ontology as a set of axioms that constitute a logical theory. We illustrate these different forms of appearance in ontology engineering, machine-processing and reasoning by an example. The business trips scenario used in Chapter 2 involves several domains of interest. On the one hand, reasoning about business trips requires knowledge about travelling infrastructure for trains, flights and rental cars, while on the other hand it involves financial knowledge about prices, different currencies and methods of payment when it comes to comparing different offers. Yet another related domain is that of geographic knowledge about locations of sources and destinations for trips, which we use as an example to illustrate appearance of ontologies. A geographic ontology encodes countries and continents with their geographic regions, as well as geographic features like rivers, roads, rail tracks or cities. It relates geographic features to their regions, stating, for example, that a city occupies a certain region, and it defines containment between such regions; the geographic region of a European city is, for example, contained in that of Europe. Besides these general geographic concepts and their relations, such an ontology also determines concrete instances, such as particular cities, countries and continents, and relates them appropriately.

30

Chapter 3: Ontologies and the Semantic Web

on a disk or for transfer over the wire, all of its information is expressed in the ontology language supported by the tool. Hence, the way an ontology appears to a developer of an ontology editor, storage facility or reasoning tool is in form of ontology language constructs in some serialisation format suitable for machine processing. For illustrating a fragment of our example geographic ontology, we use the RDF serialisation format of the OWL ontology language in the following listing. ... < owl:Class rdf:ID = " City " > < rdfs:subClassOf > < owl:Restriction > < owl:onProperty rdf:resource = " # locatedIn " / > < owl:allValuesFrom rdf:resource = " # PlanarRegion " / >

< rdfs:subClassOf rdf:resource = " # Infrastructure " / > < owl:disjointWith rdf:resource = " # Road " / > < owl:disjointWith rdf:resource = " # IndustrialFacility " / >

< owl:ObjectProperty rdf:ID = " locatedIn " > < rdf:type rdf:resource = " & owl ; F unctionalProperty " / > < rdfs:domain rdf:resource = " # GeographicLocation " / > < rdfs:range rdf:resource = " # GeographicRegion " / > < owl:inverseOf rdf:resource = " # isRegionFor " / >

< EuropeanCity rdf:ID = " London " / > ...

The listing shows an excerpt of the geographic ontology as it is processed by software systems for serialisation and parsing and for transfer over a network. It exhibits the specification of OWL classes (concepts), properties (relations) and individuals (instances), all expressed by tags and attributes of a customised XML serialisation. Formal Appearance — As ontology languages like OWL are based on logical formalisms, the formal semantics of the language precisely defines the meaning of an ontology in terms of logic. To a reasoner, therefore, an ontology appears as a set of logical formulas that express the axioms of a logical theory. It can verify whether these axioms are consistent or derive logical consequences. This form of appearance of an ontology is free of syntactical or graphical additions or ambiguities and reflects the pure knowledge representation aspect. We use description logic notation to exemplify some of the axioms in our example geographical ontology in their logical form. The following DL formulas constitute a definition of a European city.

31

3.1 Ontologies in Information Systems

∃ locatedIn.  ∃ contains.  GeographicLocation Continent









GeographicLocation

∀ locatedIn.GeographicRegion GeographicRegion

∀ contains.GeographicRegion = 1 locatedIn GeographicLocation

(Europe) PlanarRegion

GeographicRegion

GeographicLocation ∀ locatedIn.PlanarRegion City ≡ City ∀ locatedIn.∃ contains− .∃ locatedIn− .{Europe} EuropeanCity Continent

In this logical form, an ontology is the set of axioms that constitutes the explicit knowledge represented about its domain of interest. By means of automated deduction, implicit knowl edge of the same form can be derived but is not part of the ontology’s explicit specification.

3.1.3

Utilisation of Ontologies

Often, an ontology is distinguished from a knowledge base in that it is supposed to describe knowledge on a schema level, i.e. in terms of conceptual taxonomies and general statements, whereas the more data intensive knowledge base is thought of containing instance information on particular situations. We take a different perspective and perceive the relation between an ontology and a knowledge base as the connection between an epistemological specification of domain knowledge and a technical means for working with knowledge. From this point of view, an ontology is a piece of knowledge that can be used by a knowledge-based application among other pieces of knowledge, e.g. other ontologies or meta data. To properly cover its domain of interest, it can make use of both schema level and instance level information. Whenever the knowledge-based system needs to consult the ontology, it accesses (parts of) its specification through a knowledge base, most likely together with other pieces of knowledge, to take it into account for reasoning. A business trips booking system, for example, would probably make combined use of a geographical ontology, a financial one, and one for public transportation, when comparing offers for trips, loading all relevant domain knowledge in its knowledge base. In this sense, a knowledge-based application uses an ontology through its knowledge base. Usage of Ontologies — The computational domain model of an ontology can be used for various purposes, and some typical types of applications have evolved that make use of ontologies in different ways. We list some of them as examples of how applications can leverage the formalised conceptual domain models that ontologies provide. • information integration A promising field of application for ontologies is their use for integrating heterogeneous information sources on the schema level. Often, different databases store the same kind of information but adhere to different data models. An ontology can be used to mediate between database schemas, allowing to integrate information from differently organised

32

Chapter 3: Ontologies and the Semantic Web

sources and to interpret data from one source under the schema of another. A geographic ontology, for example, could be used to integrate geographic databases with different schemas, one relating cities directly to their countries as different entities, and another one modelling a single entity for geographic places which have the property of being either a city or a country. In either schema, the local entities and relations can be mapped to the respective notions of e.g. City, Country, GeographicRegion and locatedIn in the ontology, realising unified querying and reasoning over both information sources. • information retrieval Motivated by the success and key role of Google3 in the World Wide Web, semantically enhanced information retrieval on web documents is a widely recognised field of appli cation, and the use of ontologies is one particular approach to improving the retrieval process. The idea behind ontology-based information retrieval is to increase the precision of retrieval results by taking into account the semantic information contained in queries and documents, lifting keywords to ontological concepts and relations. When interpreted according to a geographic ontology, a query like “capital of Germany”, for example, would yield documents that are about Berlin, the capital of Ger many. Some of the false positive matches that keyword based retrieval systems typically produce, such as documents about the German venture capital market, can be filtered out this way. • semantically enhanced content management In many areas of computation the data that is actually computed is annotated with meta data for various purposes. Ontologies provide the domain-specific vocabulary for annotating data with meta data. The formality of ontology languages allows for an automated processing of this meta data and their grounding in knowledge representation facilitates machine-interpretability. The concepts and relations provided by a geographic ontology, for example, could be used to annotate manifold geographic content, such as geographic books and articles in an electronic library to better find and archive them or 3D-models of geographic sites in surveying and mapping, in order to better group and relate them, providing easier access to their content. • knowledge management and community portals In companies or other organised associations, or in communities of practice, individual knowledge can be viewed as a strategic resource that is desirable to be shared and systematically maintained, which is referred to as knowledge management. Ontologies provide a means to unify knowledge management efforts under a shared conceptual domain model, connecting technical systems for navigating, storing, searching and ex changing community knowledge. A geographic ontology could serve as the backbone for a geographic knowledge portal in the internet, through which land surveying offices, urban planning institutions and other interested community members provide access to geography-related resources. 3

http://www.google.com

34

Chapter 3: Ontologies and the Semantic Web

such as medicine or geography, or the knowledge about a particular task, such as diagnosis or configuration. In this sense, they have a much narrower and more specific scope than top-level ontologies. Prominent ontologies exist in natural sciences, such as medicine, genetics, geographic and communal efforts such as environment information, tourism, as well as cultural heritage and museum exhibits. Examples are GALEN5 for the medical domain or GO6 for the domain of bio-informatics. Task ontologies have been devised, e.g. for scheduling and planning tasks, intelligent computer-based tutoring, missile tracking, execution of clinical guidelines, etc. • application ontologies Further narrowing the scope, application ontologies provide the specific vocabulary required to describe a certain task enactment in a particular application context. They typically make use of both domain and task ontologies, and describe e.g. the role that some domain entity plays in a specific task (see e.g. [141]). Altogether, we can say that Figure 3.2 represents an inclusion scheme: the lower ontologies inherit and specialise concepts and relations from the upper ones. The lower ontologies are more specific and have thus a narrower application scope, whereas the upper ones have a broader potential for reuse.

3.2

Semantic Annotation in the Web

One particular application of ontologies is their use for ontology based annotation of web content in the vision of the Semantic Web. To make ontologies available to information systems for this purpose, various ontology languages have been designed and proposed for standardisation. In this section, we will review the basic ideas behind the Semantic Web, and we will give a brief overview on current ontology languages.

3.2.1

The Semantic Web Vision

The World Wide Web has become a powerful tool for communication, research and commerce, however, it is limited to manual navigation of human users who interpret the content of web sites in order to access the information they provide. As stated in [16], the vision of the Semantic Web is to make the Web machine-understandable, allowing computers to integrate information from disparate sources to achieve the goals of end users. To this end, data in the World Wide Web is to be upgraded to a semantic level, such that it can be used by machines not just for display purposes, but for automation, integration and reuse across various applications in an automated way. In the context of the Semantic Web, ontologies play a particularly important key role. While the content of the current web is primarily produced for human consumption, also information produced mainly for machines, such as the records in a database, should be made 5 6

http://www.co-ode.org/galen/ http://www.geneontology.org

3.2 Semantic Annotation in the Web

35

available to processing over the web. The idea of the Semantic Web is to annotate both human-readable and machine-tailored web content by machine-interpretable meta data, such that computers are able to process this content on a semantic level. Ontologies provide the domain vocabulary in terms of which semantic annotation is formulated. Meta statements about web content in such annotations refer to a commonly used domain model by includ ing the concepts, relations and instances of a domain ontology. The formality of ontology languages allows to reason about semantic annotation from different sources, connected to background knowledge in the domain of interest. There are a couple of characteristics of the web which affect the use of ontologies for semantic annotation. One aspect is the natural distributedness of content in the web. The knowledge captured in semantic annotations and ontologies is not locally available at a single node but spread over different sites. This imposes additional constraints on the use of ontologies in the Semantic Web, taking into account distributedness of knowledge. Techniques for unique identification of ontological entities or for a modular and distributed organisation of ontologies and the reasoning process are required. Another related aspect is that content on the web is created in an evolutionary manner and maintained in a decentralised way. There is no central control over semantic annotation and ontologies that evolve in the Semantic Web, and information in one ontology can conflict with information in another one. To either avoid or deal with conflicting pieces of knowledge, modelling methodologies or techniques for reasoning with inconsistencies are required. A particular kind of web resources are Web Services, and their semantic annotation according to the Semantic Web idea leads to the notion of Semantic Web Service. Semantic Web Services are typically annotated with a description of their functionality for the purpose of automating their use, e.g. in the context of information integration, and we will review them in the context of matchmaking and service discovery in Part IV.

3.2.2

Ontology Languages for the Semantic Web

In the light of widespread impact and industrial usability, the standardisation of ontology languages is of great importance to the Semantic Web community. Various different aspects are considered for language standardisation, such as issues of the underlying knowledge representation formalism in terms of expressiveness and computational properties, web-related features like global unique identification and XML serialisation syntax, or usability add-ons like the inclusion of datatypes such as strings or numbers. The influence of different research and user communities with manifold requirements have resulted in a complex landscape of a multitude of languages backed by different past and ongoing standardisation efforts. It is still an open topic stimulating lively discussions in current research which languages are best suited for what purpose, how they can be efficiently implemented, realised in a user friendly way, or technically and semantically made interoperable. In Figure 3.3 we make an attempt to sketch this landscape of languages, giving an overview of the most important ontology languages with respect to current trends in the Semantic Web. Since some languages build on others and on formerly achieved standards, this landscape can be perceived as a hierarchy of languages for the Semantic Web. However, besides a

36

Chapter 3: Ontologies and the Semantic Web

Figure 3.3: An overview of Semantic Web ontology languages hierarchical structure with some languages being clearly layered on top of others, there are also parallel branches and cross-relations between languages and formalisms.7 One of the major distinctions of Semantic Web languages is by the knowledge representation paradigm they follow. On the left-hand side in Figure 3.3, there is the description logic family of languages that build on various DL dialects and their rule-extensions. They adhere to the classical model-theoretic semantics of first-order predicate logic and to the open-world assumption. On the right hand side there is the family of logic programming languages that build on rules with negation-as-failure. They typically follow a semantics of minimal or preferred models and adhere to the closed-world assumption. There are also languages in between these two main strands, which cannot be clearly assigned to either paradigm. These have been designed with a focus set on aspects other than a logically clear semantics, or are attempts to combine features from both worlds, while the pure DL and LP family languages have well understood properties in terms of computability and inferential behaviour. 7 This figure shall convey a rough intuition about the relationships between major languages with respect to their underlying knowledge representation formalisms and paradigms. It therefore abstracts from certain language details and is necessarily imprecise and vague in some aspects.

3.2 Semantic Annotation in the Web

37

Languages that are placed near to the top in Figure 3.3 are more expressive than languages that are placed close to the bottom, meaning that they allow for expressing more complex knowledge and for richer inferencing through more sophisticated logical consequences than less expressive languages do. Accordingly, high expressivity of a language is traded for higher computational complexity of procedures for reasoning. Within recent standardisation efforts, it is considered highly desirable to at least maintain decidability as a design goal for a Semantic Web ontology language, and Figure 3.3 shows a boundary for decidability, above of which languages do not meet this goal. Three different kinds of arrows in Figure 3.3 express different ways in which a language is embedded in another one. A solid arrow denotes complete semantic containedness of a less expressive language in a more expressive one, meaning that anything that can be expressed in the former can also be expressed in the latter by means of a direct mapping of languages constructs. A dashed arrow denotes a weaker form of embedding, where not all the features of the less expressive language do completely fit the more expressive target language, meaning that the former is in principle (approximately) covered by the latter apart from moderate deficiencies in some language constructs and their semantic interpretation. A dash-dotted arrow denotes a syntactic embedding such that the language constructs of the (syntactically) less expressive language can be directly used in the more expressive one, although they may semantically be interpreted in a different way. An early initiative to standardise a language for semantic annotation of web resources by the World Wide Web consortium (W3C) resulted in RDF [83] and RDFS [22], which form now a well established and widely accepted standard for encoding meta data. The RDF(S) language can be used to express class membership of resources and subsumption between classes but its peculiar semantics does neither fit the classical nor the LP-style. If semantically restricted to a first-order setting, RDF(S) can be mapped to a formalism named description logic programs (DLP) [59], which is sometimes used to interoperate between DL and LP by reducing expressiveness to their intersection. On top of RDF(S), W3C standardisation efforts have produced the OWL family [116] of languages for describing ontologies in the Semantic Web, which comes in several flavours with increasing expressiveness. Only the most expressive language variant, namely OWL-Full, has a semantically proper layering on top of RDF(S), allowing for features of metamodelling and reification. The less expressive variants OWL-Lite and OWL-DL map to certain description logic dialects and fit the classical semantics as subsets of first-order logic. Besides the class membership and subsumption relations inherited from RDF(S), OWL offers the con struction of complex classes from simpler ones by means of DL-style concept constructors. Among ongoing standardisation efforts, OWL-DL is currently the most prominent Semantic Web ontology language following the description logic paradigm, and in Chapter 4 it is described in more detail. A current trend in research on knowledge representation formalisms in the context of the Semantic Web is to integrate DL-style ontologies with LP style rules to be interoperable on a semantic level. One attempt to do so is the Semantic Web Rule Language (SWRL[69]8 ) that extends the set of OWL axioms to include Horn like rules interpreted under first order 8

http://www.w3.org/Submission/SWRL/

38

Chapter 3: Ontologies and the Semantic Web

semantics. Interoperability with OWL ontologies is realised by referring to OWL classes and properties within SWRL rules, however, the combination of OWL-DL and SWRL rules results in an undecidable formalism. Another approach to amalgamate OWL ontologies and rules are the so-called DL-safe rules [107], which extend DL knowledge bases in a way similar to SWRL. However, DL-safe rules preserve decidability of the resulting language by imposing an additional safety restriction on SWRL rules, ensuring that rules are only applied to individuals explicitly known to the knowledge base. Languages that follow the logic programming paradigm mainly stem from deductive database systems, which apply rules on the facts stored in a database to derive new facts by means of logical inferencing. A common declarative language used in deductive databases is Datalog [147], which is syntactically similar to Prolog [93]. In the Semantic Web context, F-Logic [80] is a more prominent rule language that combines logical formulas with object oriented and frame-based description features. In its logic programming variant F-Logic (LP), it adopts the semantics of Datalog rules. Finally, the Web Service Modeling Language (WSML) family [32] is the most recent attempt to standardise ontology languages for the web as part of the WSMO9 initiative, with a special focus on annotating Semantic Web Services. Since WSML tries to cover all the major aspects of different knowledge representation formalisms, its various language variants are spread over the scheme of Figure 3.3. They fit semantically in between existing languages by being based on similar formalisms in both the DL and the LP strands. While WSML-DL adheres to DL semantics, WSML-Flight and WSML-Rule are rule languages.

9

http://www.wsmo.org

Chapter 4

OWL and Description Logics The Web Ontology Language OWL is the most prominent effort of standardising an ontology language for the use in the web. In this chapter, we briefly present OWL and description logics as its underlying knowledge representation formalism, including its model-theoretic semantics. In Section 4.1, we will give an introduction to OWL with a focus on web-related aspects. In Section 4.2, we will formally introduce description logics as a basis for our subsequent presentation of nonmonotonic DLs and reasoning with them. In Section 4.3, we will illustrate how description logic inferencing is used for reasoning with OWL ontologies by means of examples.

4.1

The Web Ontology Language OWL

The Web Ontology Language (OWL) [116] has been standardised by the W3C consortium as a language for modelling and semantic annotation of web content and is widely accepted within the Semantic Web community. It is primarily based on the description logic knowledge representation paradigm, while it is also designed for the use in the web as an extension to the Resource Description Framework (RDF)[83]. In this section, we will describe the features of OWL concerning its syntax and semantics, web-related aspects and tool support.

4.1.1

Syntax and Semantics

The OWL standard defines different syntaxes based on RDF(S) [22], XML and proprietary text format. The OWL RDF/XML syntax allows for an encoding of an OWL ontology within the RDF(S) framework in RDF/XML serialisation.1 The OWL XML presentation syntax provides a more compact XML format for OWL ontologies, independent from RDF(S). In contrast to these machine-oriented serialisations, the OWL abstract syntax serves as a human readable text format to present OWL ontologies to knowledge engineers. Yet another popular way to present OWL content to a reader in a more scientific context is to make use of 1

An example of an ontology fragment in OWL RDF/XML syntax has been shown in Chapter 3 on page 30.

40

Chapter 4: OWL and Description Logics

DL formulas. We choose this compact formal DL notation to present fragments of OWL ontologies throughout the thesis. An important issue for the design of OWL was the trade-off between expressivity of the language on the one hand and scalability of reasoning on the other. To this end, OWL comes in three different flavours, namely OWL-Lite, OWL-DL and OWL-Full, reflecting different degrees of expressiveness. The design of OWL-Lite and OWL-DL has been significantly influenced by descriptions logics, and hence these two variants correspond to the description logic dialects SHIF(D) and SHOIN (D), respectively. OWL-Full, on the contrary, departs from description logic semantics in order to provide compatibility with RDF(S). The DLbased OWL variants benefit from well understood computational properties and decidability of description logics, while OWL-Full has shown to be undecidable [103]. When using OWL, we will refer to OWL-DL as the most prominent language variant with extensive support by the Semantic Web community. OWL-DL provides syntactic modelling constructs for the basic elements of an ontology, i.e. concepts, relations and instances. In OWL-DL these are called classes, properties and individuals, respectively, and they correspond to concepts, roles, and individuals in description logics. OWL-DL strictly separates classes from individuals and allows for building complex classes out of simpler ones by means of class constructors, just as description logics do. Also the semantics of OWL-DL is fully based on the description logic formalism, and an OWL-DL ontology is interpreted as a SHOIN (D) knowledge base. We will present the formalities of SHOIN (D) in Section 4.2, and we will exemplify how reasoning is performed with OWL-DL ontologies in Section 4.3.

4.1.2

Web Aspects and RDF(S)-Compatibility

Besides the knowledge representation aspects given through its close connection to description logics, OWL-DL is also designed to be a language for annotation in the Semantic Web. Therefore, it is tightly integrated with existing web standards and also has extra-logical features related to its use in the web and to its compatibility to RDF(S). From RDF(S), OWL-DL inherits some of its syntactic vocabulary, such as rdf:type or rdfs:subClassOf, as well as the property that all elements are interpreted as resources in relation to rdf:Resource. It also inherits the mechanism of global unique identification through Uniform Resource Identifiers (URIs) with their namespace concept. Together with the owl:imports construct, this allows for a modular design of OWL-DL ontologies that are distributed and linked over the web. Moreover, OWL-DL provides several serialisation formats in XML, which enables an easy interchange of ontologies over the network using existing web technologies. It also reuses facilities from XML Schema to support datatypes and data values in the language. Furthermore, OWL-DL incorporates mechanisms to include meta data about ontologies and their elements. For example, there are constructs like rdfs:label for human-readable entity names, or like owl:versionInfo for versioning information.

4.2 Description Logics

4.1.3

41

Software Support

Since OWL is technically built on top of RDF(S), some RDF(S) specific tools can be readily applied, e.g. for parsing and serialisation in the OWL RDF/XML format, while others have also been upgraded to OWL versions. The ontology editor Prot´eg´e [63] also supports OWL and comes with a variety of plugins that allow for visualisation and management of OWL ontologies. In addition to different graphical views of the explicit class and property hierarchies, it facilitates the visual editing of OWL axioms and enables the embedding of reasoning tools for computing inferred subsumption hierarchies. Other visual editors for OWL ontologies that offer similar functionality are SWOOP2 [73] or the commercial tools Altova Semantic Works 3 and TopBraid4 . For the programmatic handling of OWL ontologies, the OWL API5 [13] as well as Jena [97] can be used by software developers to process OWL descriptions within their applications. They provide means for parsing and serialisation of the different OWL syntax formats and for in memory manipulation of OWL ontologies. As OWL is an expressive knowledge representation language, reasoning plays an impor tant role, and there are a number of description logic reasoners available that can be used for querying OWL ontologies with respect to inferred knowledge or for verifying their consistency. The most common description logic reasoners in the Semantic Web context are based on the tableau calculus, and available systems that support the OWL language are Racer6 [65], FaCT7 [68] and Pellet8 [135]. Recently, new DL reasoning algorithms – based on deductive database technology – were devised for the development of the KAON29 [106] system, which is particularly optimised for querying ontologies with large A Boxes.

4.2

Description Logics

The Web Ontology Language OWL is largely based on description logics with their classical formal semantics, and a thorough understanding of some of the principles of classical modeltheory is crucial for the use of OWL in Semantic Web and matchmaking scenarios and for its extension towards nonmonotonicity. In this section, we will therefore present the formal foundations of OWL-DL that we need for our subsequent investigations. We will introduce the formal syntax and semantics of description logics together with their associated reasoning problems. 2

http://www.mindswap.org/2004/SWOOP/ http://origin.altova.com/products semanticworks.html http://www.topbraidcomposer.com/ 5 http://owl.man.ac.uk/api.shtml 6 Meanwhile RacerPro – http://www.racer-systems.com/ 7 Meanwhile FaCT++ – http://owl.man.ac.uk/factplusplus/ 8 http://www.mindswap.org/2003/pellet/ 9 http://kaon2.semanticweb.org/ 3 4

42

4.2.1

Chapter 4: OWL and Description Logics

Formal Syntax and Semantics

To introduce the formal framework of description logics, we consider the logic SHOIN , which underlies the OWL-DL language variant.10 For various nonmonotonic extensions, and for our application of description logics to matchmaking, we will consider various fragments of SHOIN mainly focused on the basic DL ALC. The countably infinite sets NI , NC and Nr of individual names, concept names and role names, respectively, form the basis to construct the syntactic elements of SHOIN according to the following grammar, in which A ∈ NC denotes an atomic concept, C, Ci denote complex concepts, s ∈ Nr denotes an atomic role, r denotes a possibly inverse role, ai ∈ NI denote individuals and n denotes a natural number. C, Ci −→ A | ⊥ |  | ¬C | C1 C2 | C1  C2 | ∃ r.C | ∀ r.C | ≥ n r | ≤ n r | {a1 , . . . , an } r −→ s | s− A SHOIN knowledge base KB is a set of axioms that are formed by concepts, roles and individuals according to the following rules, where αT , αR and αA denote axioms. αT

−→ C1 C2 | C1 ≡ C2

concept inclusion concept equivalence

αR −→ r1 r2 | r1 ≡ r2 | Trans(r)

role inclusion role equivalence role transitivity

| αA −→ C(a) r(a1 , a2 ) | a1 ≈ a2 | a1 ≈ a2

concept assertion role assertion individual equality individual inequality

A concept inclusion is an axiom of the form C1 C2 that states the subsumption of the concept C1 by the concept C2 , while a role inclusion is an axiom of the form r1 r2 that states the subsumption of the role r1 by the role r2 . An equivalence axiom of the form C1 ≡ C2 for concepts or r1 ≡ r2 for roles is a shortcut for two inclusions C1 C2 and C2 C1 or r1 r2 and r2 r1 . A role transitivity statement is an axiom of the form Trans(r) that states transitivity for the role r. A concept assertion is an axiom of the form C(a) that assigns the membership of an individual a to a concept C. A role assertion is an axiom of the form r(a1 , a2 ) that assigns a directed relation between two individuals a1 , a2 by the role r. The axioms in KB are partitioned into a T Box , an R Box and an A Box and take the forms αT , αR and αA , respectively. The T-Box and R-Box describe terminological knowledge in terms of general statements about the domain, whereas the A-Box describes assertional knowledge in terms of particular instance situations. By σ(KB ) we denote the signature of the knowledge base KB , which is the set of all concept, role and individual names that occur in the axioms of KB . 10 OWL-DL actually corresponds to the description logic SHOIN (D), which augments SHOIN by concrete domains for representing datatypes. Since we will not work with concrete domains on a formal basis, we introduce them informally in addition to the formal syntax and semantics of SHOIN .

43

4.2 Description Logics

I AI (C1 C2 )I (C1  C2 )I (¬C)I (∀ r.C)I (∃ r.C)I (≥ n r.)I (≤ n r.)I {a1 , . . . , an }I (r− )I

= = = = = = = = =

= ΔI ⊆ ΔI

, ,

⊥I rI

= ∅ ⊆ Δ I × ΔI

C1I ∩ C2I C1I ∪ C2I ΔI \ C I {a ∈ ΔI | ∀b.(a, b) ∈ rI → b ∈ C I } {a ∈ ΔI | ∃b.(a, b) ∈ rI ∧ b ∈ C I } {a ∈ ΔI | #{b ∈ ΔI | (a, b) ∈ rI ∧ b ∈ C I } ≥ n} {a ∈ ΔI | #{b ∈ ΔI | (a, b) ∈ rI ∧ b ∈ C I } ≤ n} {aI1 , . . . , aIn } {(b, a) | (a, b) ∈ rI }

Table 4.1: Model-theoretic semantics for SHOIN descriptions The semantics of the syntactic elements of SHOIN is defined in terms of an interpretation I = (ΔI , ·I ) with a non-empty set ΔI as the interpretation domain and an interpretation function ·I that maps each individual a ∈ NI to a distinct element aI ∈ ΔI and that interprets (possibly) complex concepts and roles as indicated in Table 4.1. An interpretation I satisfies a concept inclusion C1 C2 if C1I ⊆ C2I and a concept equivalence C1 ≡ C2 if C1I = C2I . Similarly, it satisfies a role inclusion r1 r2 if r1I ⊆ r2I and a role equivalence r1 ≡ r2 if r1I = r2I . A transitivity axiom Trans(r) is satisfied in I if for all a1 , a2 , a3 ∈ ΔI (aI1 , aI2 ) ∈ rI and (aI2 , aI3 ) ∈ rI together imply (aI1 , aI3 ) ∈ rI . Moreover, I satisfies a concept assertion C(a) if aI ∈ C I , a role assertion r(a1 , a2 ) if (aI1 , aI2 ) ∈ rI , an individual equality a1 ≈ a2 if aI1 = aI2 and an individual inequality a1 ≈ a2 if aI1 = aI2 . An interpretation that satisfies all axioms of a knowledge base KB is called a model of KB , and we denote by M(KB ) the set of all models of KB . Reasoning with a description logic knowledge base is defined in terms of this notion of a model. The general semantics of DLs as laid out in Table 4.1 includes (in)equality between individuals, a feature also supported by OWL. However, in applications individuals are often treated as uniquely named such that no two named individuals coincide in the interpretation domain, which is known as the unique name assumption [6]. The unique name assumption can be axiomatised in OWL by including inequality axioms of the form a1 ≈ a2 for any pair a1 , a2 of known individuals. For our investigations of nonmonotonic extensions to DLs and for our examples we will assume unique names for individuals in the subsequent parts II, III and IV. Moreover, we denote by the symbol O a special concept that comprises all individuals known to KB as its instances, i.e. OI = {oI ∈ ΔI | o ∈ σ(KB )}.

4.2.2

Reasoning Problems

The basic reasoning problems for description logics are defined in terms of standard reasoning tasks [6] as follows.

44

Chapter 4: OWL and Description Logics

Definition 4.1 (reasoning tasks). Let KB be a knowledge base, C, Ci be concepts and a be an individual. The following standard reasoning tasks are defined for description logics. • knowledge base satisfiability: KB is satisfiable if it has a model. • concept satisfiability: C is satisfiable with respect to KB if there exists a model I of KB such that C I = ∅. • instance checking: a is an instance of C with respect to KB , denoted by KB |= C(a), if aI ∈ C I holds for all models I of KB . • subsumption: C1 is subsumed by C2 with respect to KB , denoted by KB |= C1 C2 , if C1I ⊆ C2I holds for all models I of KB . Knowledge base satisfiability corresponds to the classical task of testing whether a first order logical theory can be satisfied, and all the other reasoning tasks can be reduced to this test (see e.g. [6]). Knowledge base and concept satisfiability serve the reasoning problem of validation, while instance checking and subsumption serve the reasoning problem of deduction.

4.2.3

Concrete Domains

In practical applications it is often desired to incorporate concrete entities like numbers or strings into the knowledge represented trough abstract domain objects and their classes. To account for such features, description logics have been extended by so-called concrete domains [7] that allow for additional predicates with a predefined interpretation to represent typical datatypes and their values known from e.g. software development or database design. An example for a numerical concrete domain would be the set of natural numbers N with predicates like = or < defined on them. The concept expression Flight ∃ routeLengthKm. ≥1000 , for example, denotes all flights with a route length of at least 1000 km.11 The interpretation of datatypes and their values includes an additional interpretation domain ΔD (the concrete domain) disjoint from the abstract domain ΔI . Additional concrete roles are interpreted as subsets of ΔI × ΔD , connecting abstract objects with concrete data values. Predefined predicates for ΔD have an extension that is determined extra-logically, e.g. by the laws of arithmetics in case of N. In the naming scheme for description logics, the inclusion of concrete domains is indicated by a parameter D, such as in SHOIN (D), the underlying logic for OWL-DL. For details on DLs with concrete domains we refer to [95]. While the current OWL standard has only limited support for concrete domains, there have been proposals to extend OWL by richer datatype support, such as [113], which is also considered in ongoing standardisation efforts for OWL 1.112 . 11 Notice that the concrete domain predicate ≥1000 is different from the use of number restrictions on roles. The expression ≥ 1000 routeLengthKm would denote all things with at least 1000 values for the respective role. 12 http://owl1 1.cs.manchester.ac.uk

48

Chapter 4: OWL and Description Logics

Part II

Nonmonotonic Reasoning in the Semantic Web

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Chapter 5

Nonmonotonic Description Logics Description logics are typically fragments of first-order predicate logic and inherit a classical model-theoretic semantics. In the literature, however, various attempts have been made to extend description logics by non-classical features that result in nonmonotonic formalisms. In this chapter, we address Objective 2 by demonstrating how nonmonotonic extensions to description logics can be used to realise various forms of common-sense reasoning in the context of the Semantic Web. By this, we also transfer results from the rather theoretical and technical literature to practical applications and lay the basis for an intuitive view on notions of nonmonotonic reasoning for their use in matchmaking in Part III. We will study different formalisms for this purpose, namely autoepistemic DLs in Section 5.1, circumscriptive DLs in Section 5.2 and terminological defaults in Section 5.3. In Section 5.4, we will briefly discuss the characteristics of these approaches.

5.1

Autoepistemic Description Logics

Autoepistemic logic [102, 4] is a formalism concerned with the notions of “knowledge” and “belief”. Besides statements about the domain of discourse, it also allows for statements about what a knowledge-based agent knows or beliefs, by means of epistemic operators for referring to entailments within the logical language in an introspective way. Various forms of epistemic operators with slightly different semantics, denoted by K, B or L, have been investigated primarily in the context of propositional or first-order predicate logic, where they were either applied to predicates or even to formulas. In [36, 38, 126], epistemic operators K and A have been incorporated into the description logic framework to express what a knowledge base knows or assumes. While in [36, 38] the basic DL ALC was considered for an autoepistemic extension, in [126] also more expressive DLs were extended that capture more features of OWL-DL. Intuitively, a concept like KVegetarianDish captures all things that are known to be vegetarian dishes. In contrast to its classical counterpart VegetarianDish, this epistemic form of a concept would be unsatisfiable with respect to a knowledge base in which there is no known instance of a vegetarian dish. On the other hand, a concept like AVegetarianDish captures all things that are assumed to be vegetarian dishes, meaning that additional knowledge is

52

Chapter 5: Nonmonotonic Description Logics

required to justify this assumption. A knowledge base with an axiom like  AVegetarianDish that fails to justify the assumption by lack of evidence for each of its individuals to be a vegetarian dish becomes unsatisfiable. Hence, by means of epistemic operators local closure can be imposed on predicates, assuming full knowledge about a predicate’s extension. Reasoning then becomes nonmonotonic, as adding new evidence can contradict the assumption about full knowledge and formerly drawn conclusions are retracted. In this section, we will describe the formal semantics of autoepistemic description logics as a basis for nonmonotonic reasoning with epistemic operators in the context of matchmaking. We will also demonstrate how different forms of reasoning with epistemic operators can be applied in a Semantic Web setting by means of examples.

5.1.1

Formal Semantics for Autoepistemic DLs

The formal framework of autoepistemic DLs is tightly integrated with the classical modeltheory of conventional description logics and extends it by a possible-worlds semantics for epistemic operators in the style of modal logics.1 We present this formal framework in the following paragraphs, addressing syntax and semantics, intuition on the use of epistemic operators and the definition of reasoning tasks. Formal Syntax and Semantics — In [38] the basic DL ALC has been extended by two operators, K and A , reflecting the notions of “knowledge” and “assumption”. The following ˙ C˙ i denote concepts, A rules define the syntax of the resulting language ALCKN F , where C, denotes an atomic concept and r, ˙ r denote roles. C˙ 1 , C˙ 2 r˙

−→ −→

A |  | ⊥ | C˙ 1 C˙ 2 | C˙ 1  C˙ 2 | ¬C˙ | ∀ r. ˙ C˙ | ∃ r. ˙ C˙ | KC | AC r | Kr | Ar

An epistemic concept C˙ is a complex concept with potential occurrences of K-operators ˙ Similarly, an epistemic role r˙ is a role with in front of any concepts and roles within C. occurrences of epistemic operators. In DLs without complex role constructors, an epistemic role has the form Kr or Ar. We refer to the union of both epistemic concepts and epistemic roles by epistemic predicates, and we call classical predicates that do not contain any epistemic operators non epistemic. An epistemic axiom is an axiom that contains epistemic concepts or roles, and an epistemic knowledge base contains such epistemic axioms. The formal semantics of autoepistemic DLs is defined similarly to that of classical DLs introduced in Chapter 4, with the difference that first-order interpretations are replaced by epistemic interpretations. An epistemic interpretation is a triple (I, WK , WA ) where I = (ΔI , ·I ) is a first-order interpretation with interpretation domain ΔI and interpretation function ·I , and WK , WA are sets of first order interpretations, seen as possible worlds for the two modalities K and A in the sense of modal logics. For atomic concepts and roles, epistemic interpretations work as first order interpretations, mapping them to subsets of ΔI and ΔI × ΔI , respectively. Also for the conventional constructors they work as in the classical case, without the sets WK and WA taking any effect. For epistemic operators, 1

See also [6] and [126] for the relation between autoepistemic DLs and modal logics.

5.1 Autoepistemic Description Logics

(I,WK ,WA ) A(I,WK ,WA ) (C˙ 1 C˙ 2 )(I,WK ,WA ) (C˙ 1  C˙ 2 )(I,WK ,WA ) ˙ (I,WK ,WA ) (¬C) ˙ (I,WK ,WA ) (∀ r. ˙ C) ˙ (I,WK ,WA ) (∃ r. ˙ C) ˙ (I,WK ,WA ) (KC) (Kr)(I,WK ,WA ) ˙ (I,WK ,WA ) (AC) (Ar)(I,WK ,WA )

53

= ΔI , ⊥(I,WK ,WA ) = ∅ I I = A ⊆Δ , r(I,WK ,WA ) = rI ⊆ ΔI × ΔI (I,W ,W ) (I,W ,W ) = C˙ 1 K A ∩ C˙ 2 K A (I,W ,W ) (I,W ,W ) = C˙ 1 K A ∪ C˙ 2 K A = ΔI \ C˙ (I,WK ,WA ) = {a ∈ ΔI | ∀b.(a, b) ∈ r˙ (I,WK ,WA ) → b ∈ C˙ (I,WK ,WA ) } = {a ∈ ΔI | ∃b.(a, b) ∈ r˙ (I,WK ,WA ) ∧ b ∈ C˙ (I,WK ,WA ) }  = C˙ (J ,WK ,WA ) J ∈WK (J ,W ,W ) K A = r J ∈WK ˙ (J ,W ,W ) K A = C J ∈WA (J ,W ,W ) K A = J ∈WA r

Table 5.1: Formal semantics of ALCKN F however, the sets WK and WA are used to realise a possible world semantics that breaks the locality of considering a single first-order interpretation. Table 5.1 shows how epistemic predicates are interpreted in the autoepistemic description logic ALCKN F . Atomic concepts are interpreted as subsets of ΔI , and atomic roles as subsets of ΔI × ΔI . The boolean connectives and existential and universal role quantification are interpreted in terms of set operations on ΔI , as in classical DL. Epistemic concepts KC and AC are interpreted as the sets of all individuals which belong to the concept C in all first-order interpretations in WK and WA , respectively. Similarly, epistemic roles Kr and Ar are interpreted as the pairs of individuals that belong to the role r in all possible worlds in WK and WA . Notice, that for the case of non-epistemic predicates the semantics is defined as for conventional DLs, and thus, autoepistemic DLs fully embed their classical counterparts. (I,W ,W ) An epistemic interpretation (I, WK , WA ) satisfies an inclusion axiom C˙ 1 C˙ 2 if C˙ 1 K A (I,W ,W ) K A I (I,W ˙ K ,WA ) or ⊆ C˙ 2 , and it satisfies an assertion axiom C(a) or r(a, ˙ b) if a ∈ C˙ I I (I,W ,W ) K A , respectively. An epistemic model for an epistemic knowledge base KB (a , b ) ∈ r˙ is a non-empty set M of first-order interpretations such that, for each I ∈ M, the epistemic interpretation (I, M, M) satisfies all axioms in KB and there is no set M of first-order interpretations such that M ⊂ M and the epistemic interpretation (I, M , M) also satisfies all axioms in KB . As a special case, a non-epistemic knowledge base has a single epistemic model, which is just the set of all its first order models, as captured by the following proposition due to [38]. Proposition 5.1. Let KB be a non epistemic knowledge base. If KB is classically satisfiable then the set M(KB ) of all first order models of KB is its single unique epistemic model. Intuition of Epistemic Operators — The semantics of both epistemic operators, K and A, is defined as an intersection of concept/role extensions over sets of first order in terpretations WK , WA , seen as possible worlds. Therefore they both ensure statements to

54

Chapter 5: Nonmonotonic Description Logics

constantly hold in all possible worlds in these sets. The difference between K and A lies in the restrictions about which worlds belong to WK and WA , respectively. To see this difference, consider the knowledge bases KB = {∃ r.C(a)}, KB K = {∃ r.KC(a)} and KBA = {∃ r.AC(a)}. Due to Proposition 5.1 M(KB ) is the unique epistemic model for KB . However, M(KB ) is not an epistemic model for KB K , since it contains first-order interpretations in which the r-successors of a do not constantly belong to C over all J ∈ M(KB ). The use of the K-operator in KB K requires the existence of an r-successor for a that belongs to C in all possible worlds, i.e. which is known to be in the extension of C. The set Mx ⊂ M(KB ), defined by {I : I |= r(a, x) ∧ C(x)} for some x ∈ ΔI , fulfils this condition. It is an epistemic model for KB K , since the epistemic interpretation (I, Mx , Mx ) satisfies the axiom in KB K whereas (I, Mx ∪ {I  }, Mx ) does not, for any I  ∈ M(KB ) \ Mx . In this sense K can be paraphrased as “known”. Conversely, neither any Mx nor any other set of first order interpretations is an epistemic model for KBA . To see this, consider any set M of first-order interpretations for which (I, M, M) satisfies KBA . To verify M as being maximal, (I, M , M) must not satisfy KBA for any set M ⊃ M. However, the choice of M does not affect the modality A. The set M could only be an epistemic model if it would already be maximal, such that there is no such set M . In this sense, the use of the A-operator in KBA refers to individuals that are assumed to be in the extension of C already, and A can therefore be paraphrased as “assumed”. If this assumption is not justified by other facts then the knowledge base becomes unsatisfiable. The A-operator is directly related to the operator not for negation as failure: AC maps to ¬ not C, which means that any individual assumed to be in C belongs to the complement of those individuals that cannot be proven to be in C. Reasoning Tasks — The reasoning tasks for epistemic knowledge bases are defined analogously to the classical case, but with respect to epistemic models instead of first-order models. The following definition captures the standard reasoning tasks that are typically considered in the literature [38, 126]. Definition 5.2 (reasoning tasks for epistemic knowledge bases). Let KB be an epis˙ C˙ i be epistemic concepts and a be an individual. temic knowledge base. Furthermore, let C, The following reasoning tasks are defined for KB . • knowledge base satisfiability – KB is satisfiable if it has an epistemic model. ˙ • instance checking – a is an instance of C˙ with respect to KB , denoted by KB |= C(a), if for all epistemic models M of KB the epistemic interpretation (I, M, M) satisfies ˙ C(a) for all first order interpretations I ∈ M. • subsumption – C˙ 1 is subsumed by C˙ 2 with respect to KB , denoted by KB |= C˙ 1 C˙ 2 , if for all epistemic models M of KB the epistemic interpretation (I, M, M) satisfies C˙ 1 C˙ 2 for all first order interpretations I ∈ M. A simplified form of reasoning with epistemic operators is epistemic querying, for which epistemic concepts are considered with respect to a non epistemic knowledge base. The task of querying is often considered as the retrieval of all known instances for a concept C in

5.1 Autoepistemic Description Logics

55

a knowledge base KB , and the query is represented through the concept C.2 For the case of an epistemic concept C˙ and a non-epistemic knowledge base KB , C˙ is also called an epistemic query. This form of querying can be reduced to the reasoning task of instance ˙ checking, verifying the entailment of concept assertions C(a) for all known individuals a in KB . Another form of epistemic querying is to check the concept C˙ for satisfiability with respect to KB . Reasoning according to Definition 5.2 considers all the epistemic models of the knowledge base KB . However, since here KB is non-epistemic, it has the single epistemic model M(KB ) due to Proposition 5.1 (or no model at all). Moreover, a characteristics for the case of epistemic querying is that outside a knowledge base, i.e. rather in queries than in axioms, the two operators K and A show the same behaviour, which is captured in the following proposition [38]. Proposition 5.3. Let KB be a non epistemic knowledge base and C˙ be an epistemic con ˙ cept. Furthermore, let C[A|K] denote the epistemic concept that is obtained by replacing any occurrence of an A-operator in C˙ by a K-operator. Then, the following holds: ˙ 1. C[A|K] is satisfiable with respect to KB if and only if C˙ is satisfiable with respect to KB ˙ ˙ 2. for all individuals a ∈ σ(KB ), KB |= C[A|K](a) if and only if KB |= C(a) Due to Proposition 5.3, we only use the K-operator in epistemic queries, and an epistemic interpretation can be reduced to a pair (I, WK ) considering only the set of possible worlds for the modality K. Hence, epistemic querying is based on a simplified form of reasoning, defined as follows. Definition 5.4 (epistemic querying). Let KB be a non-epistemic knowledge base, C˙ be an epistemic concept and a be an individual. The following two reasoning tasks are forms of epistemic querying regarding an epistemic concept with respect to a non-epistemic knowledge base. • epistemic concept satisfiability – C˙ is satisfiable with respect to KB if there is a firstorder interpretation I ∈ M(KB ) such that C˙ (I,M(KB )) = ∅. • epistemic instance checking – a is an instance of C˙ with respect to KB , denoted by KB |= ˙ C(a), if for all first-order interpretations I ∈ M(KB ) the epistemic interpretation ˙ (I, M(KB )) satisfies C(a). While we investigate different forms of reasoning with epistemic knowledge bases as well as epistemic queries within this chapter, we will exploit the reasoning task of epistemic concept satisfiability in the context of matchmaking in Part III. 2 This is a simpler form of conjunctive queries, which in general also allow for the connection of several concepts via roles (see e.g. [128]).

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Chapter 5: Nonmonotonic Description Logics

always belong to the concept extension for these models, in this case normalChili, mildChili and margarita. The negated expression ¬KSpicyDish therefore refers to exactly those individuals that are not known to be spicy dishes. Analogously, for the epistemic concept K∀ topping.¬Chili those individuals are eliminated that are not excluded from having chili toppings, leaving only vesufo and margarita. Hence, the assertion Q(margarita) is also satisfied. In general, epistemic queries can be used to make conjectures on the side of a Semantic Web agent, in settings where the original ontologies involved shall be left untouched. In such a setting each agent can then make its own conjectures when querying shared ontologies. Default Reasoning — A default rule, according to [123], has the form α : β / γ and is read as “ if α is true and it is consistent to assume that β is true then conclude that γ is true ”. In [38] it has been shown that such a default rule can be formalised as the epistemic axiom Kα ¬A¬β Kγ .3 Default rules provide a means to incorporate conjectures into the domain knowledge. In our example scenario, the designers of the domain ontology OPizza could decide to make the conjecture “pizzas with chili toppings are typically spicy, whereas pizzas without chili toppings are typically non-spicy” part of the domain knowledge for pizzas by means of the following default rules. DP izza = { Da = K∃ topping.Chili ¬A¬SpicyDish KSpicyDish , Db = K∀ topping.¬Chili ¬ASpicyDish K¬SpicyDish } By this they would achieve that pizzas, for which there is no evidence of whether they are spicy or not in OPizza , are concluded to be spicy or non-spicy in OPizza ∪ DP izza by default, depending on whether they are known to have chili toppings or non-chili toppings only. In a joint ontology OPizza ∪ DP izza ∪ OGiovanni ∪ OAlberto we would intuitively like these default rules to be applied on the pizzas normalChili and margarita, concluding that normalChili is spicy and that margarita is not. Contrarily, we would not like the default rules to be applied on the pizzas mildChili and vesufo, since we already know about their spiciness. In order to verify the appropriate application of the default rules, we will determine the epistemic models of the ontologies involved. For sake of simplicity, we will only consider the knowledge base KB := OPizza ∪ OAlberto together with the default rule Db . To obtain candidates for epistemic models of KB ∪{Db }, let M1 and M2 be two partitions for all first-order models in KB , such that M1 = {I ∈ M(KB ) : I |= ¬SpicyDish(margarita)} and M2 = {I ∈ M(KB ) : I |= SpicyDish(margarita)}. Interpretations I ∈ M(KB ) can be ruled out, since they do not satisfy KB , and other candidate sets M12 , containing inthe inclusion axiom in Db because terpretations from both M1 and M2 , do not satisfy   margarita is in J ∈M12 ∀ topping.¬Chili(J ,M12 ,M12 ) , not in J ∈M12 SpicyDish(J ,M12 ,M12 ) but not  in J ∈M12 ¬SpicyDish(J ,M12 ,M12 ) , making the inclusion false. We verify that only M1 is an epistemic model of KB ∪ {Db } using Table 5.4, which shows the extensions of the epistemic concepts involved in the inclusion from Db for different epistemic interpretations. The epistemic interpretation (I, M in Db is true for both 1 , M1 ) satisfies KB ∪{Db }, since the inclusion  individuals: margarita is in J ∈M1 ∀ topping.¬Chili(J ,M1 ,M1 ) , not in J ∈M1 SpicyDish(J ,M1 ,M1 ) 3

We exclude prerequisite-free defaults (no presence of α) and cases where α=, see [38]

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The integrity constraint in IC P izza says that any individual that is known to be a pizza can either be assumed to be spicy or assumed to be non-spicy. Recall that such an assumption, expressed through the A-operator, requires a justification by other facts in a knowledge base. Both the pizzas normalChili and margarita fail to be determined as either spicy or nonspicy, which results in both OPizza ∪ IC P izza ∪ OGiovanni and OPizza ∪ IC P izza ∪ OAlberto being unsatisfiable. To exemplarily verify this unsatisfiability for KB := OPizza ∪ IC P izza ∪ OAlberto , consider a set of first-order interpretations M1 = {I ∈ M(KB ) : I |= SpicyDish(margarita)}, in which the pizza margarita is constantly spicy. The epistemic interpretation (I, M1 , M1 ) satisfies KB , since margarita is in Pizza(J ,M1 ,M1 ) and also in SpicyDish(J ,M1 ,M1 ) for all J ∈ M1 . However, for any set M1 ⊃ M1 the epistemic interpretation (I, M1 , M1 ) also satisfies KB , since margarita  is still in SpicyDish(J ,M1 ,M1 ) for all J ∈ M1 . A similar reasoning can be done for a set of first-order models in which margarita is constantly non-spicy, and hence KB is unsatisfiable. In general, integrity constraints can be used in cases where conjectures cannot be safely made on either side and where modelers should be forced to explicate certain information. Observe, that in classical DLs there is no way to express such an integrity constraint allowing to detect the improper modelling in Giovanni’s and Alberto’s ontologies.

5.2

Circumscriptive Description Logics

Besides autoepistemic logic, circumscription [98] is another prominent historic approach to local closed world reasoning. In essence, it rests on the idea of closing knowledge by enforcing certain extensional minimality conditions on interpretations. We follow the recent work [18] which incorporates these ideas into description logics. The actual description logic used in this case was ALCQIO, which is basically SHOIN (D) without the use of datatypes and role hierarchies, but extended with a slight modification of the ≥ and ≤ constructors. Intuitively, minimisation of predicates imposes a local closure by keeping the number of instances in the predicate extension to a minimum according to the given background knowl edge. For example, if the concept VegetarianDish is minimised then it is only satisfiable with respect to some knowledge base if this knowledge base contains evidence for the existence of any vegetarian dish. With respect to the empty knowledge base, it is unsatisfiable. Moreover, any individual which cannot be concluded to be a vegetarian dish is automatically derived to be non-vegetarian. As adding evidence for an individual to be a vegetarian dish at a later stage falsifies such previously drawn conclusions, reasoning becomes nonmonotonic. This is a desirable inferencing behaviour in many situations, e.g. when the ordering of a non-vegetarian dish shall be avoided in a situation with incomplete information about the menu. In this section, we will describe the formal semantics of circumscriptive description logics as a basis for nonmonotonic reasoning with circumscribed knowledge bases in the context of matchmaking. We will furthermore demonstrate how different forms of nonmonotonic rea soning are realised by means of concept minimisation with a particular focus on various kinds of defeat for conclusions drawn based on assumptions. Again we will use the Semantic Web setting from Section 5.1.2 to demonstrate how common-sense conjectures can be incorporated in circumscribed knowledge bases to realise defeasible inference.

5.2 Circumscriptive Description Logics

5.2.1

61

Formal Semantics for Circumscriptive DLs

The formal framework of circumscriptive DLs builds on the semantics of classical description logics and additionally allows for the circumscription of a knowledge base for the minimisa tion of predicate extensions. In terms of a preference-model semantics, some of the classical models are ignored for reasoning to yield additional conclusions. We present this formal framework in the following paragraphs, addressing syntax and semantics, intuition on predicate minimisation and the definition of reasoning tasks. Formal Syntax and Semantics — In contrast to autoepistemic DLs, circumscriptive DLs do not provide an additional syntactical language construct like epistemic operators. In stead, an external circumscription pattern is used to indicate the specifics of the minimisation to be performed. Similar to [18], we define a circumscription pattern as follows.4 Definition 5.5 (circumscription pattern,