An Introduction to Description logic.pdf

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Half Title

Title Page

Contents

1 Introduction

1.1 What are DLs and where do they come from?

1.2 What are they good for and how are they used?

1.3 A brief history of description logic

1.4 How to use this book

2 A Basic Description Logic

2.1 The concept language of the DL ALC

2.2 ALC knowledge bases

2.2.1 ALC TBoxes

2.2.2 ALC ABoxes

2.2.3 Restricted TBoxes and concept definitions

2.3 Basic reasoning problems and services

2.4 Using reasoning services

2.5 Extensions of the basic DL ALC

2.5.1 Inverse roles

2.5.2 Number restrictions

2.5.3 Nominals

2.5.4 Role hierarchies

2.5.5 Transitive roles

2.6 DLs and other logics

2.6.1 DLs as decidable fragments of first-order logic

2.6.2 DLs as cousins of modal logic

2.7 Historical context and literature review

3 A Little Bit of Model Theory

3.1 Bisimulation

3.2 Expressive power

3.3 Closure under disjoint union

3.4 Finite model property

3.5 Tree model property

3.6 Historical context and literature review

4 Reasoning in DLs with Tableau Algorithms

4.1 Tableau basics

4.2 A tableau algorithm for ALC

4.2.1 ABox consistency

4.2.2 Acyclic knowledge base consistency

4.2.3 General knowledge base consistency

4.3 A tableau algorithm for ALCIN

4.3.1 Inverse roles

4.3.2 Number restrictions

4.3.3 Combining inverse roles and number restrictions

4.4 Some implementation issues

4.4.1 Or-branching

4.4.2 And-branching

4.4.3 Classification

4.5 Historical context and literature review

5 Complexity

5.1 Concept satisfiability in ALC

5.1.1 Acyclic TBoxes and no TBoxes

5.1.2 General TBoxes

5.2 Concept satisfiability beyond ALC

5.2.1 ALC with inverse roles and nominals

5.2.2 Further adding number restrictions

5.3 Undecidable extensions of ALC

5.3.1 Role value maps

5.3.2 Concrete domains

5.4 Historical context and literature review

6 Reasoning in the εL Family of Description Logics

6.1 Subsumption in εL

6.1.1 Normalisation

6.1.2 The classification procedure

6.2 Subsumption in εLI

6.2.1 Normalisation

6.2.2 The classification procedure

6.3 Comparing the two subsumption algorithms

6.3.1 Comparing the classification rules

6.3.2 A more abstract point of view

6.4 Historical context and literature review

7 Query Answering

7.1 Conjunctive queries and FO queries

7.2 FO-rewritability and DL-Lite

7.2.1 Introducing DL-Lite

7.2.2 Universal models

7.2.3 FO-rewritability in DL-Lite

7.3 Datalog-rewritability in εL and εLI

7.3.1 Fundamentals of Datalog

7.3.2 Datalog-rewritings in εLI

7.3.3 Short Datalog-rewritings in εL

7.4 Complexity aspects

7.5 Historical context and literature review

8 Ontology Languages and Applications

8.1 The OWL ontology language

8.1.1 OWL and RDF

8.1.2 OWL and SROIQ

8.1.3 OWL ontologies

8.1.4 Non-DL features

8.1.5 OWL profiles

8.2 OWL tools and applications

8.2.1 The OWL API

8.2.2 OWL reasoners

8.2.3 Ontology engineering tools

8.2.4 OWL applications

Appendix: Description Logic Terminology

A.1 Syntax and semantics of concept and role constructors 228

A.2 Syntax and semantics of knowledge bases

A.3 Naming schemes for description logics

References

Index

An Introduction to Description Logic Description logic (DL) has a long tradition in computer science and knowledge representation, being designed so that domain knowledge can be described and so that computers can reason about this knowledge. DL has recently gained increased importance since it forms the logical basis of widely used ontology languages, in particular the web ontology language OWL. Written by four renowned experts, this is the first textbook on Description Logic. It is suitable for self-study by graduates and as the basis for a university course. Starting from a basic DL, the book introduces the reader to its syntax, semantics, reasoning problems and model theory, and discusses the computational complexity of these reasoning problems and algorithms to solve them. It then explores a variety of different description logics, reasoning techniques, knowledge-based applications and tools, and describes the relationship between DLs and OWL.

An Introduction to Description Logic FRANZ BAADER Technische Universität, Dresden IAN HORROCKS University of Oxford CARSTEN LUTZ Universität Bremen ULI SATTLER University of Manchester

CAMBRIDGE UNIVERSITY PRESS University Printing House, Cambridge CB2 8BS, United Ringdom One Liberty Plaza, 20th Floor, New York, NY 10006, USA 477 Williamstown Road, Port Melbourne, VIC 3207, Australia 4843/24, 2nd Floor, Ansari Road, Daryaganj, Delhi – 110002, India 79 Anson Road, #06-04/06, Singapore 079906 Cambridge University Press is part of the University of Cambridge. It furthers the University’s mission by disseminating knowledge in the pursuit of education, learning, and research at the highest international levels of excellence. www.cambridge.org Information on this title: www.cambridge.org/9780521873611 DOI: 10.1017/9781139025355 © Franz Baader, Ian Horrocks, Carsten Lutz and Uli Sattler 2017 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 2017 Printed in the United Ringdom by Clays, St Ives pic A catalogue record for this publication is available from the British Library. ISBN 978-0-521-87361-1 Hardback ISBN 978-0-521-69542-8 Paperback Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party Internet Web sites referred to in this publication and does not guarantee that any content on such Web sites is, or will remain, accurate or appropriate.

Contents 1 Introduction 1.1 1.2 1.3 1.4 What are DLs and where do they come from? What are they good for and how are they used? A brief history of description logic How to use this book 2 A Basic Description Logic ALC TBoxes ALC ABoxes Restricted TBoxes and concept definitions The concept language of the DL ALC ALC knowledge bases 2.2.1 2.2.2 2.2.3 Basic reasoning problems and services Using reasoning services Extensions of the basic DL ALC 2.5.1 2.5.2 2.5.3 2.5.4 2.5.5 DLs and other logics DLs as decidable fragments of first-order logic 2.6.1 2.6.2 DLs as cousins of modal logic Historical context and literature review Inverse roles Number restrictions Nominals Role hierarchies Transitive roles 2.1 2.2 2.3 2.4 2.5 2.6 2.7 3.1 3.2 3.3 3.4 3.5 3.6 3 A Little Bit of Model Theory Bisimulation Expressive power Closure under disjoint union Finite model property Tree model property Historical context and literature review 4 Reasoning in DLs with Tableau Algorithms 4.1 4.2 Tableau basics A tableau algorithm for ALC 4.2.1 4.2.2 4.2.3 ABox consistency Acyclic knowledge base consistency General knowledge base consistency

4.3 4.4 4.5 Inverse roles Number restrictions Combining inverse roles and number restrictions A tableau algorithm for ALCIN 4.3.1 4.3.2 4.3.3 Some implementation issues 4.4.1 4.4.2 4.4.3 Historical context and literature review Or-branching And-branching Classification 5 Complexity Acyclic TBoxes and no TBoxes General TBoxes Concept satisfiability in ALC 5.1.1 5.1.2 Concept satisfiability beyond ALC 5.2.1 5.2.2 Undecidable extensions of ALC 5.3.1 5.3.2 Historical context and literature review Role value maps Concrete domains ALC with inverse roles and nominals Further adding number restrictions Normalisation The classification procedure Subsumption in EL 6.1.1 6.1.2 Subsumption in ELI 6.2.1 6.2.2 Comparing the two subsumption algorithms Comparing the classification rules 6.3.1 6.3.2 A more abstract point of view Historical context and literature review Normalisation The classification procedure 6 Reasoning in the EL Family of Description Logics 5.1 5.2 5.3 5.4 6.1 6.2 6.3 6.4 7.1 7.2 7.3 7 Query Answering Conjunctive queries and FO queries FO-rewritability and DL-Lite Introducing DL-Lite 7.2.1 Universal models 7.2.2 FO-rewritability in DL-Lite 7.2.3 Datalog-rewritability in EL and ELI 7.3.1 7.3.2 7.3.3 Fundamentals of Datalog Datalog-rewritings in ELI Short Datalog-rewritings in EL

7.4 7.5 Complexity aspects Historical context and literature review 8 Ontology Languages and Applications 8.1 8.2 OWL and RDF OWL and SROIQ OWL ontologies Non-DL features OWL profiles The OWL ontology language 8.1.1 8.1.2 8.1.3 8.1.4 8.1.5 OWL tools and applications 8.2.1 8.2.2 8.2.3 8.2.4 The OWL API OWL reasoners Ontology engineering tools OWL applications Appendix: Description Logic Terminology A.1 A.2 A.3 Syntax and semantics of concept and role constructors 228 Syntax and semantics of knowledge bases Naming schemes for description logics References Index

1 Introduction This is, to the best of our knowledge, the first textbook dedicated solely to Description Logic (DL), a very active research area in logic-based knowledge representation and reasoning that goes back to the late 1980s and that has a wide range of applications in knowledge-intensive information systems. In this introductory chapter we will sketch what DLs are, how they are used and where they come from historically. We will also explain how to use this book. 1.1 What are DLs and where do they come from? Description logics (DLs) are a family of knowledge representation languages that can be used to represent knowledge of an application domain in a structured and well-understood way.1 The name description logics is motivated by the fact that, on the one hand, the important notions of the domain are represented by concept descriptions, i.e., expressions that are built from atomic concepts (unary predicates) and atomic roles (binary predicates) using the concept and role constructors provided by the particular DL; on the other hand, DLs differ from their predecessors, such as semantic networks and frames, in that they are equipped with a logic-based semantics which, up to some differences in notation, is actually the same semantics as that of classical first-order logic. Description logics typically separate domain knowledge into two components, a terminological part called the TBox and an assertional part called the ABox, with the combination of a TBox and an ABox being called a knowledge base (KB). The TBox represents knowledge about the structure of the domain (similar to a database schema), while the ABox represents knowledge about a concrete situation (similar to a database instance). TBox statements capturing knowledge about a university domain might include, e.g., a teacher is a person who teaches a course, a student is a person who attends a course and students do not teach, while ABox statements from the same domain might include Mary is a person, CS600 is a course and Mary teaches CS600. As already mentioned, a crucial feature of DLs is that such statements have a formal, logic-based semantics. In fact the above statements can be rendered as sentences in first-order logic as follows: Equivalently, these statements can be written in description logic syntax as follows:

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