THE DESCRIPTION LOGIC HANDBOOK: Theory, implementation, and applications Edited by Franz Baader Deborah L. McGuinness Daniele Nardi Peter F. Patel-Schneider Contents List of contributors page 1 1 An Introduction to Description Logics D. Nardi, R. J. Brach- man 5 1.1 Introduction 5 1.2 From networks to Description Logics 8 1.3 Knowledge representation in Description Logics 16 1.4 From theory to practice: Description Logics systems 20 1.5 Applications developed with Description Logics systems 24 1.6 Extensions of Description Logics 34 1.7 Relationship to other fields of Computer Science 40 1.8 Conclusion 43 Part one: Theory 45 2 Basic Description Logics F. Baader, W. Nutt 47 2.1 Introduction 47 2.2 Definition of the basic formalism 50 2.3 Reasoning algorithms 78 2.4 Language extensions 95 3 Complexity of Reasoning F. M. Donini 101 3.1 Introduction 101 3.2 OR-branching: finding a model 105 3.3 AND-branching: finding a clash 112 3.4 Combining sources of complexity 119 3.5 Reasoning in the presence of axioms 121 3.6 Undecidability 127 3.7 Reasoning about individuals in ABoxes 133 3.8 Discussion 137 3.9 A list of complexity results for subsumption and satisfiability 138 iii iv Contents 4 Relationships with other Formalisms U. Sattler, D. Cal- vanese, R. Molitor 142 4.1 AI knowledge representation formalisms 142 4.2 Logical formalisms 154 4.3 Database models 166 5 Expressive Description Logics D. Calvanese, G. De Giacomo184 5.1 Introduction 184 5.2 Correspondence between Description Logics and Propositional Dy- namic Logics 185 5.3 Functional restrictions 192 5.4 Qualified number restrictions 200 5.5 Objects 204 5.6 Fixpoint constructs 207 5.7 Relations of arbitrary arity 211 5.8 Finite model reasoning 215 5.9 Undecidability results 222 6 Extensions to Description Logics F. Baader, R. K¨usters, F. Wolter 226 6.1 Introduction 226 6.2 Language extensions 227 6.3 Non-standard inference problems 257 Part two: Implementation 269 7 From Description Logic Provers to Knowledge Representation Systems D. L. McGuinness, P. F. Patel-Schneider 271 7.1 Introduction 271 7.2 Basic access 273 7.3 Advanced application access 276 7.4 Advanced human access 280 7.5 Other technical concerns 286 7.6 Public relations concerns 286 7.7 Summary 287 8 Description Logics Systems R. M¨oller, V. Haarslev 289 8.1 New light through old windows? 289 8.2 The first generation 290 8.3 Second generation Description Logics systems 298 8.4 The next generation: Fact , Dlp and Racer 308 8.5 Lessons learned 310 Contents v 9 Implementation and Optimisation Techniques I. Horrocks 313 9.1 Introduction 313 9.2 Preliminaries 315 9.3 Subsumption testing algorithms 320 9.4 Theory versus practice 324 9.5 Optimisation techniques 330 9.6 Discussion 354 Part three: Applications 357 10 Conceptual Modeling with Description Logics A. Borgida, R. J. Brachman 359 10.1 Background 359 10.2 Elementary Description Logics modeling 361 10.3 Individuals in the world 363 10.4 Concepts 365 10.5 Subconcepts 368 10.6 Modeling relationships 371 10.7 Modeling ontological aspects of relationships 373 10.8 A conceptual modeling methodology 378 10.9 The ABox: modeling specific states of the world 379 10.10 Conclusions 381 11 Software Engineering C. Welty 382 11.1 Introduction 382 11.2 Background 382 11.3 Lassie 383 11.4 CodeBase 388 11.5 CSIS and CBMS 389 12 Configuration D. L. McGuinness 397 12.1 Introduction 397 12.2 Configuration description and requirements 399 12.3 The Prose and Questar family of configurators 412 12.4 Summary 413 13 Medical Informatics A. Rector 415 13.1 Background and history 416 13.2 Example applications 419 13.3 Technical issues in medical ontologies 425 13.4 Ontological issues in medical ontologies 431 13.5 Architectures: terminology servers, views, and change management 434 13.6 Discussion: key lessons from medical ontologies 435 vi Contents 14 Digital Libraries and Web-Based Information Systems I. Horrocks, D. L. McGuinness, C. Welty 436 14.1 Background and history 436 14.2 Enabling the Semantic Web: DAML 441 14.3 OIL and DAML+OIL 443 14.4 Summary 457 15 Natural Language Processing E. Franconi 460 15.1 Introduction 460 15.2 Semantic interpretation 461 15.3 Reasoning with the logical form 465 15.4 Knowledge-based natural language generation 470 16 Description Logics for Data Bases A. Borgida, M. Lenzerini, R. Rosati 472 16.1 Introduction 472 16.2 Data models and Description Logics 475 16.3 Description Logics and database querying 484 16.4 Data integration 488 16.5 Conclusions 493 1 Description Logic Terminology F. Baader 495 A1.1 Notational conventions 495 A1.2 Syntax and semantics of common Description Logics 496 A1.3 Additional constructors 501 A1.4 A note on the naming scheme for Description Logics 504 1 An Introduction to Description Logics Daniele Nardi Ronald J. Brachman Abstract This introduction presents the main motivations for the development of Description Logics (DL) as a formalism for representing knowledge, as well as some important basic notions underlying all systems that have been created in the DL tradition. In addition, we provide the reader with an overview of the entire book and some guidelines for reading it. We first address the relationship between Description Logics and earlier seman- tic network and frame systems, which represent the original heritage of the field. We delve into some of the key problems encountered with the older efforts. Subse- quently, we introduce the basic features of Description Logic languages and related reasoning techniques. Description Logic languages are then viewed as the core of knowledge represen- tation systems, considering both the structure of a DL knowledge base and its associated reasoning services. The development of some implemented knowledge representation systems based on Description Logics and the first applications built with such systems are then reviewed. Finally, we address the relationship of Description Logics to other fields of Com- puter Science. We also discuss some extensions of the basic representation language machinery; these include features proposed for incorporation in the formalism that originally arose in implemented systems, and features proposed to cope with the needs of certain application domains. 1.1 Introduction Research in the field of knowledge representation and reasoning is usually focused on methods for providing high-level descriptions of the world that can be effectively used to build intelligent applications. In this context, “intelligent” refers to the abil- 5 6 D. Nardi, R. J. Brachman ity of a system to find implicit consequences of its explicitly represented knowledge. Such systems are therefore characterized as knowledge-based systems. Approaches to knowledge representation developed in the 1970’s—when the field enjoyed great popularity—are sometimes divided roughly into two categories: logic- based formalisms, which evolved out of the intuition that predicate calculus could be used unambiguously to capture facts about the world; and other, non-logic-based representations. The latter were often developed by building on more cognitive notions—for example, network structures and rule-based representations derived from experiments on recall from human memory and human execution of tasks like mathematical puzzle solving. Even though such approaches were often developed for specific representational chores, the resulting formalisms were usually expected to serve in general use. In other words, the non-logical systems created from very specific lines of thinking (e.g., early Production Systems) evolved to be treated as general purpose tools, expected to be applicable in different domains and on different types of problems. On the other hand, since first-order logic provides very powerful and general ma- chinery, logic-based approaches were more general-purpose from the very start. In a logic-based approach, the representation language is usually a variant of first-order predicate calculus, and reasoning amounts to verifying logical consequence. In the non-logical approaches, often based on the use of graphical interfaces, knowledge is represented by means of some ad hoc data structures, and reasoning is accomplished by similarly ad hoc procedures that manipulate the structures. Among these spe- cialized representations we find semantic networks and frames. Semantic Networks were developed after the work of Quillian [1967], with the goal of characterizing by means of network-shaped cognitive structures the knowledge and the reasoning of the system. Similar goals were shared by later frame systems [Minsky, 1981], which rely upon the notion of a “frame” as a prototype and on the capability of expressing relationships between frames. Although there are significant differences between se- mantic networks and frames, both in their motivating cognitive intuitions and in their features, they have a strong common basis. In fact, they can both be regarded as network structures, where the structure of the network aims at representing sets of individuals and their relationships. Consequently, we use the term network-based structures to refer to the representation networks underlying semantic networks and frames (see [Lehmann, 1992] for a collection of papers concerning various families of network-based structures). Owing to their more human-centered origins, the network-based systems were often considered more appealing and more effective from a practical viewpoint than the logical systems. Unfortunately they were not fully satisfactory because of their usual lack of precise semantic characterization. The end result of this was that every system behaved differently from the others, in many cases despite virtually identical- An Introduction to Description Logics 7 looking components and even identical relationship names. The question then arose as to how to provide semantics to representation structures, in particular to semantic networks and frames, which carried the intuition that, by exploiting the notion of hierarchical structure, one could gain both in terms of ease of representation and in terms of the efficiency of reasoning.