An Introduction to Description Logic

✍ Scribed by Franz Baader, Ian Horrocks, Carsten Lutz, Uli Sattler

• Publisher: Cambridge University Press
• Year: 2017
• Tongue: English
• Leaves: 265
• Edition: 1
• Category: Library

✦ Synopsis

Description logics (DLs) have 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. DLs have recently gained increased importance since they form 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 logics. 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 their 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 reasoning techniques, knowledge-based applications and tools and it describes the relationship between DLs and OWL.

✦ Table of Contents

Contents
1 Introduction page
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 EL Family of Description Logics
6.1 Subsumption in EL
6.1.1 Normalisation
6.1.2 The classification procedure
6.2 Subsumption in ELI
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 EL and ELI
7.3.1 Fundamentals of Datalog
7.3.2 Datalog-rewritings in ELI
7.3.3 Short Datalog-rewritings in EL
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
A.2 Syntax and semantics of knowledge bases
A.3 Naming schemes for description logics
References
Index