In Praise of Knowledge Representation and Reasoning This book clearly and concisely distills decades of work in AI on representing information in an efficient and general manner. The information is valuable not only for AI researchers, but also for people working on logical databases, XML, and the semantic web: read this book, and avoid reinventing the wheel! Henry Kautz, University of Washington Brachman and Levesque describe better than I have seen elsewhere, the range of formalisms between full first order logic at its most expressive and formalisms that compromise expressiveness for computation speed. Theirs are the most even-handed explanations I have seen. John McCarthy, Stanford University This textbook makes teaching my KR course much easier. It provides a solid foundation and starting point for further studies. While it does not (and cannot) cover all the topics that I tackle in an advanced course on KR, it provides the basics and the background assumptions behind KR research. Together with current research literature, it is the perfect choice for a graduate KR course. Bernhard Nebel, University of Freiburg This is a superb, clearly written, com- prehensive overview of nearly all the major issues, ideas, and techniques of this important branch of artificial intelligence, written by two of the masters of the field. The examples are well chosen, and the explanations are illuminating. Thank you for giving me this opportunity to review and praise a book that has sorely been needed by the KRR community. William J. Rapaport, State University of New York at Buffalo A concise and lucid exposition of the major topics in knowledge representation, from two of the leading authorities in the field. It provides a thorough grounding, a wide variety of useful examples and exercises, and some thought-provoking new ideas for the expert reader. Stuart Russell, UC Berkeley No other text provides a clearer introduc- tion to the use of logic in knowledge representation, reasoning, and planning, while also covering the essential ideas underlying practical methodologies such as production systems, description logic-based systems, and Bayesian networks. Lenhart Schubert, University of Rochester Brachman and Levesque have laid much of the foundations of the field of knowledge representation and reasoning. This textbook provides a lucid and comprehensive introduction to the field. It is written with the same clarity and gift for exposition as their many research publications. The text will become an invaluable resource for students and researchers alike. Bart Selman, Cornell University KR&R is known as “core AI” for a reason — it embodies some of the most basic con- ceptualizations and technical approaches in the field. And no researchers are more qualified to provide an in-depth introduction to the area than Brachman and Levesque, who have been at the forefront of KR&R for two decades. The book is clearly written, and is intelligently comprehensive. This is the definitive book on KR&R, and it is long overdue. Yoav Shoham, Stanford University This Page Intentionally Left Blank K NOWLEDGE R EPRESENTATION AND R EASONING About the Authors Ron Brachman has been doing influential work in knowledge representation since the time of his Ph.D. thesis at Harvard in 1977, the result of which was the KL-ONE system, which initiated the entire line of research on description logics. For the majority of his career he served in research management at AT&T, first at Bell Labs and then at AT&T Labs, where he was Communications Services Research Vice President, and where he built one of the premier research groups in the world in Artificial Intelligence. He is a Founding Fellow of the American Association for Artificial Intelligence (AAAI), and also a Fellow of the Association for Computing Machinery (ACM). He is currently President of the AAAI. He served as Secretary- Treasurer of the International Joint Conferences on Artificial Intelligence (IJCAI) for nine years. With more than 60 technical publications in knowledge representation and related areas to his credit, he has led a number of important knowledge representation systems efforts, including the CLASSIC project at AT&T, which resulted in a commercially deployed system that processed more than $5 billion worth of equipment orders. Brachman is currently Director of the Information Processing Technology Office at the U.S. Defense Advanced Research Projects Agency (DARPA), where he is leading a new national-scale initiative in cognitive systems. Hector Levesque has been teaching knowledge representation and reasoning at the Univer- sity of Toronto since joining the faculty there in 1984. He has published over 60 research papers in the area, including three that have won best-paper awards. He has also co-authored a book on the logic of knowledge bases and the widely used TELL–ASK interface that he pioneered in his Ph.D. thesis. He and his collaborators have initiated important new lines of research on a number of topics, including implicit and explicit belief, vivid reasoning, new methods for satisfiability, and cognitive robotics. In 1985, he became the first non-American to receive the Computers and Thought Award given by IJCAI. He was the recipient of an E.W.R. Steacie Memorial Fellowship from the Natural Sciences and Engineering Research Council of Canada for 1990–1991. He was also a Fellow of the Canadian Institute for Advanced Research from 1984 to 1995, and is a Founding Fellow of the AAAI. He was elected to the Executive Council of the AAAI, and is on the editorial board of five journals. In 2001, Levesque was the Conference Chair of the IJCAI-01 conference, and is currently Past President of the IJCAI Board of Trustees. Brachman and Levesque have been working together on knowledge representation and rea- soning for more than 25 years. In their early collaborations at BBN and Schlumberger, they produced widely read work on key issues in the field, as well as several well-known knowledge representation systems, including KL-ONE , KRYPTON , and KANDOR . They presented a tutorial on knowledge representation at the International Joint Conference on Artificial Intelligence in 1983. In 1984, they coauthored a prize-winning paper at the National Conference on Artificial Intelligence that is generally regarded as the impetus for an explosion of work in description logics and which inspired many new research efforts on the tractability of knowledge rep- resentation systems, including hundreds of research papers. The following year, they edited a popular collection, Readings in Knowledge Representation , the first text in the area. With Ray Reiter, they founded and chaired the international conferences on Principles of Knowl- edge Representation and Reasoning in 1989; these conferences continue on to this day. Since 1992, they have worked together on the course in knowledge representation at the University of Toronto that is the basis for this book. K NOWLEDGE R EPRESENTATION AND R EASONING ■ ■ ■ Ronald J. Brachman Hector J. Levesque with a contribution by Maurice Pagnucco AMSTERDAM • BOSTON • HEIDELBERG • LONDON NEW YORK • OXFORD • PARIS • SAN DIEGO SAN FRANCISCO • SINGAPORE • SYDNEY • TOKYO Morgan Kaufmann is an imprint of Elsevier Publishing Director: Diane Cerra Senior Editor: Denise E. M. Penrose Publishing Services Manager: Andre Cuello Production Manager: Brandy Palacios Production Management: Graphic World Publishing Services Editorial Assistant: Valerie Witte Design Manager: Cate Barr Cover Design: Dick Hannus, Hannus Design Associates Cover Image: “Trout River Hills 6: The Storm Passing”, 1999, Oil on board, 80" × 31¾". Private Collection. Copyright Christopher Pratt Text Design: Graphic World Publishing Services Composition: Cepha Imaging Pvt. Ltd. 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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, or otherwise—without written permission of the publishers. Permissions may be sought directly from Elsevier’s Science & Technology Rights Department in Oxford, UK: phone: (+44) 1865 843830, fax: (+44) 1865 853333, e-mail: permissions@elsevier.com.uk. You may also complete your request on-line via the Elsevier homepage (http://elsevier.com) by selecting “Customer Support” and then “Obtaining Permissions.” Library of Congress Cataloging-in-Publication Data Brachman, Ronald J., 1949- Knowledge representation and reasoning / Ronald J. Brachman, Hector J. Levesque. p. cm. Includes bibliographical references and index. ISBN: 1-55860-932-6 1. Knowledge representation (Information theory) 2. Reasoning. I. Levesque, Hector J., 1951- II. Title. Q387.B73 2003 006.3 ′ 32 ′ —dc22 2004046573 For information on all Morgan Kaufmann publications, visit our website at www.mkp.com Printed in the United States of America 04 05 06 07 5 4 3 2 1 To Gwen, Rebecca, and Lauren; and Pat, Michelle, and Marc — because a reasoning mind still needs a loving heart. This Page Intentionally Left Blank ■ C ONTENTS ■ ■ Preface xvii Acknowledgments xxvii 1 Introduction 1 1.1 The Key Concepts: Knowledge, Representation, and Reasoning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Why Knowledge Representation and Reasoning? . . . . . . . . . 5 1.2.1 Knowledge-Based Systems . . . . . . . . . . . . . . . . . . . 6 1.2.2 Why Knowledge Representation? . . . . . . . . . . . . . . 7 1.2.3 Why Reasoning? . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.3 The Role of Logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.4 Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2 The Language of First-Order Logic 15 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.2 The Syntax . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.3 The Semantics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.3.1 Interpretations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.3.2 Denotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.3.3 Satisfaction and Models . . . . . . . . . . . . . . . . . . . . . . 22 2.4 The Pragmatics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.4.1 Logical Consequence . . . . . . . . . . . . . . . . . . . . . . . . 23 2.4.2 Why We Care . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.5 Explicit and Implicit Belief . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.5.1 An Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.5.2 Knowledge-Based Systems . . . . . . . . . . . . . . . . . . . 27 2.6 Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 ix x Contents 3 Expressing Knowledge 31 3.1 Knowledge Engineering . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.2 Vocabulary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 3.3 Basic Facts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.4 Complex Facts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.5 Terminological Facts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.6 Entailments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.7 Abstract Individuals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 3.8 Other Sorts of Facts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 3.9 Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 3.10 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 4 Resolution 49 4.1 The Propositional Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.1.1 Resolution Derivations . . . . . . . . . . . . . . . . . . . . . . 52 4.1.2 An Entailment Procedure . . . . . . . . . . . . . . . . . . . . 53 4.2 Handling Variables and Quantifiers . . . . . . . . . . . . . . . . . . . 55 4.2.1 First-Order Resolution . . . . . . . . . . . . . . . . . . . . . . . 58 4.2.2 Answer Extraction . . . . . . . . . . . . . . . . . . . . . . . . . . 61 4.2.3 Skolemization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 4.2.4 Equality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 4.3 Dealing with Computational Intractability . . . . . . . . . . . . . . 67 4.3.1 The First-Order Case . . . . . . . . . . . . . . . . . . . . . . . . 67 4.3.2 The Herbrand Theorem . . . . . . . . . . . . . . . . . . . . . . 68 4.3.3 The Propositional Case . . . . . . . . . . . . . . . . . . . . . . 69 4.3.4 The Implications . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 4.3.5 SAT Solvers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 4.3.6 Most General Unifiers . . . . . . . . . . . . . . . . . . . . . . . 71 4.3.7 Other Refinements . . . . . . . . . . . . . . . . . . . . . . . . . . 72 4.4 Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 4.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 5 Reasoning with Horn Clauses 85 5.1 Horn Clauses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 5.1.1 Resolution Derivations with Horn Clauses . . . . . . . . 86 5.2 SLD Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 5.2.1 Goal Trees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 5.3 Computing SLD Derivations . . . . . . . . . . . . . . . . . . . . . . . . 91 5.3.1 Backward Chaining . . . . . . . . . . . . . . . . . . . . . . . . . 91 5.3.2 Forward Chaining . . . . . . . . . . . . . . . . . . . . . . . . . . 93 5.3.3 The First-Order Case . . . . . . . . . . . . . . . . . . . . . . . . 94 Contents xi 5.4 Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 5.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 6 Procedural Control of Reasoning 99 6.1 Facts and Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 6.2 Rule Formation and Search Strategy . . . . . . . . . . . . . . . . . . 101 6.3 Algorithm Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 6.4 Specifying Goal Order . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 6.5 Committing to Proof Methods . . . . . . . . . . . . . . . . . . . . . . . 104 6.6 Controlling Backtracking . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 6.7 Negation as Failure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 6.8 Dynamic Databases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 6.8.1 The PLANNER Approach . . . . . . . . . . . . . . . . . . . . . . . 111 6.9 Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 6.10 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 7 Rules in Production Systems 117 7.1 Production Systems: Basic Operation . . . . . . . . . . . . . . . . . 118 7.2 Working Memory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 7.3 Production Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 7.4 A First Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 7.5 A Second Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 7.6 Conflict Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 7.7 Making Production Systems More Efficient . . . . . . . . . . . . . 127 7.8 Applications and Advantages . . . . . . . . . . . . . . . . . . . . . . . . 129 7.9 Some Significant Production Rule Systems . . . . . . . . . . . . . 130 7.10 Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 7.11 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 8 Object-Oriented Representation 135 8.1 Objects and Frames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 8.2 A Basic Frame Formalism . . . . . . . . . . . . . . . . . . . . . . . . . . 136 8.2.1 Generic and Individual Frames . . . . . . . . . . . . . . . . 136 8.2.2 Inheritance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 8.2.3 Reasoning with Frames . . . . . . . . . . . . . . . . . . . . . . 140 8.3 An Example: Using Frames to Plan a Trip . . . . . . . . . . . . . . 141 8.3.1 Using the Example Frames . . . . . . . . . . . . . . . . . . . 146 8.4 Beyond the Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 8.4.1 Other Uses of Frames . . . . . . . . . . . . . . . . . . . . . . . 149 xii Contents 8.4.2 Extensions to the Frame Formalism . . . . . . . . . . . . 150 8.4.3 Object-Driven Programming with Frames . . . . . . . . 151 8.5 Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 8.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 9 Structured Descriptions 155 9.1 Descriptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 9.1.1 Noun Phrases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 9.1.2 Concepts, Roles, and Constants . . . . . . . . . . . . . . . . 157 9.2 A Description Language . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 9.3 Meaning and Entailment . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 9.3.1 Interpretations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 9.3.2 Truth in an Interpretation . . . . . . . . . . . . . . . . . . . . 161 9.3.3 Entailment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 9.4 Computing Entailments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 9.4.1 Simplifying the Knowledge Base . . . . . . . . . . . . . . . 164 9.4.2 Normalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 9.4.3 Structure Matching . . . . . . . . . . . . . . . . . . . . . . . . . 167 9.4.4 The Correctness of the Subsumption Computation . 168 9.4.5 Computing Satisfaction . . . . . . . . . . . . . . . . . . . . . . 169 9.5 Taxonomies and Classification . . . . . . . . . . . . . . . . . . . . . . . 171 9.5.1 A Taxonomy of Atomic Concepts and Constants . . . 172 9.5.2 Computing Classification . . . . . . . . . . . . . . . . . . . . . 173 9.5.3 Answering the Questions . . . . . . . . . . . . . . . . . . . . . 175 9.5.4 Taxonomies versus Frame Hierarchies . . . . . . . . . . 175 9.5.5 Inheritance and Propagation . . . . . . . . . . . . . . . . . . 176 9.6 Beyond the Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 9.6.1 Extensions to the Language . . . . . . . . . . . . . . . . . . . 177 9.6.2 Applications of Description Logics . . . . . . . . . . . . . . 179 9.7 Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 9.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 10 Inheritance 187 10.1 Inheritance Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188 10.1.1 Strict Inheritance . . . . . . . . . . . . . . . . . . . . . . . . . . 189 10.1.2 Defeasible Inheritance . . . . . . . . . . . . . . . . . . . . . . . 190 10.2 Strategies for Defeasible Inheritance . . . . . . . . . . . . . . . . . . 192 10.2.1 The Shortest Path Heuristic . . . . . . . . . . . . . . . . . . . 192 10.2.2 Problems with Shortest Path . . . . . . . . . . . . . . . . . . 194 10.2.3 Inferential Distance . . . . . . . . . . . . . . . . . . . . . . . . . 195 10.3 A Formal Account of Inheritance Networks . . . . . . . . . . . . . 196 10.3.1 Extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 10.3.2 Some Subtleties of Inheritance Reasoning . . . . . . . . 201 Contents xiii 10.4 Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202 10.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203 11 Defaults 205 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 11.1.1 Generics and Universals . . . . . . . . . . . . . . . . . . . . . 206 11.1.2 Default Reasoning . . . . . . . . . . . . . . . . . . . . . . . . . . 207 11.1.3 Nonmonotonicity . . . . . . . . . . . . . . . . . . . . . . . . . . 209 11.2 Closed-World Reasoning . . . . . . . . . . . . . . . . . . . . . . . . . . . 209 11.2.1 The Closed-World Assumption . . . . . . . . . . . . . . . . . 210 11.2.2 Consistency and Completeness of Knowledge . . . . . 211 11.2.3 Query Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 11.2.4 Consistency and a Generalized Assumption . . . . . . . 212 11.2.5 Quantifiers and Domain Closure . . . . . . . . . . . . . . . 213 11.3 Circumscription . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 11.3.1 Minimal Entailment . . . . . . . . . . . . . . . . . . . . . . . . 216 11.3.2 The Circumscription Axiom . . . . . . . . . . . . . . . . . . . 219 11.3.3 Fixed and Variable Predicates . . . . . . . . . . . . . . . . . 219 11.4 Default Logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 11.4.1 Default Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 11.4.2 Default Extensions . . . . . . . . . . . . . . . . . . . . . . . . . . 223 11.4.3 Multiple Extensions . . . . . . . . . . . . . . . . . . . . . . . . . 224 11.5 Autoepistemic Logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 11.5.1 Stable Sets and Expansions . . . . . . . . . . . . . . . . . . . 228 11.5.2 Enumerating Stable Expansions . . . . . . . . . . . . . . . 230 11.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232 11.7 Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 11.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 12 Vagueness, Uncertainty, and Degrees of Belief 237 12.1 Noncategorical Reasoning . . . . . . . . . . . . . . . . . . . . . . . . . . 238 12.2 Objective Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 12.2.1 The Basic Postulates . . . . . . . . . . . . . . . . . . . . . . . . 240 12.2.2 Conditional Probability and Independence . . . . . . . 241 12.3 Subjective Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 12.3.1 From Statistics to Belief . . . . . . . . . . . . . . . . . . . . . 244 12.3.2 A Basic Bayesian Approach . . . . . . . . . . . . . . . . . . . 245 12.3.3 Belief Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246 12.3.4 An Example Network . . . . . . . . . . . . . . . . . . . . . . . . 247 12.3.5 Influence Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . 250 12.3.6 Dempster–Shafer Theory . . . . . . . . . . . . . . . . . . . . . 251 xiv Contents 12.4 Vagueness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253 12.4.1 Conjunction and Disjunction . . . . . . . . . . . . . . . . . . 255 12.4.2 Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255 12.4.3 A Bayesian Reconstruction . . . . . . . . . . . . . . . . . . . 259 12.5 Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262 12.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263 13 Explanation and Diagnosis 267 13.1 Diagnosis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268 13.2 Explanation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269 13.2.1 Some Simplifications . . . . . . . . . . . . . . . . . . . . . . . . 270 13.2.2 Prime Implicates . . . . . . . . . . . . . . . . . . . . . . . . . . . 271 13.2.3 Computing Explanations . . . . . . . . . . . . . . . . . . . . . 272 13.3 A Circuit Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 13.3.1 Abductive Diagnosis . . . . . . . . . . . . . . . . . . . . . . . . 275 13.3.2 Consistency-Based Diagnosis . . . . . . . . . . . . . . . . . . 277 13.4 Beyond the Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279 13.4.1 Extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279 13.4.2 Other Applications . . . . . . . . . . . . . . . . . . . . . . . . . . 280 13.5 Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281 13.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282 14 Actions 285 14.1 The Situation Calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286 14.1.1 Fluents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286 14.1.2 Precondition and Effect Axioms . . . . . . . . . . . . . . . . 287 14.1.3 Frame Axioms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288 14.1.4 Using the Situation Calculus . . . . . . . . . . . . . . . . . . 289 14.2 A Simple Solution to the Frame Problem . . . . . . . . . . . . . . . 291 14.2.1 Explanation Closure . . . . . . . . . . . . . . . . . . . . . . . . 292 14.2.2 Successor State Axioms . . . . . . . . . . . . . . . . . . . . . . 292 14.2.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294 14.3 Complex Actions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295 14.3.1 The Do Formula . . . . . . . . . . . . . . . . . . . . . . . . . . . 295 14.3.2 GOLOG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297 14.3.3 An Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 298 14.4 Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299 14.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301 15 Planning 305 15.1 Planning in the Situation Calculus . . . . . . . . . . . . . . . . . . . . 306 Contents xv 15.1.1 An Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307 15.1.2 Using Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . 308 15.2 The STRIPS Representation . . . . . . . . . . . . . . . . . . . . . . . . . . 312 15.2.1 Progressive Planning . . . . . . . . . . . . . . . . . . . . . . . . 314 15.2.2 Regressive Planning . . . . . . . . . . . . . . . . . . . . . . . . . 315 15.3 Planning as a Reasoning Task . . . . . . . . . . . . . . . . . . . . . . . 316 15.3.1 Avoiding Redundant Search . . . . . . . . . . . . . . . . . . 317 15.3.2 Application-Dependent Control . . . . . . . . . . . . . . . . 318 15.4 Beyond the Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320 15.4.1 Hierarchical Planning . . . . . . . . . . . . . . . . . . . . . . . 320 15.4.2 Conditional Planning . . . . . . . . . . . . . . . . . . . . . . . . 321 15.4.3 “Even the Best-Laid Plans . . . ” . . . . . . . . . . . . . . . . . 322 15.5 Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322 15.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323 16 The Tradeoff between Expressiveness and Tractability 327 16.1 A Description Logic Case Study . . . . . . . . . . . . . . . . . . . . . . 329 16.1.1 Two Description Logic Languages . . . . . . . . . . . . . . 329 16.1.2 Computing Subsumption . . . . . . . . . . . . . . . . . . . . . 330 16.2 Limited Languages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332 16.3 What Makes Reasoning Hard? . . . . . . . . . . . . . . . . . . . . . . . 334 16.4 Vivid Knowledge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336 16.4.1 Analogues, Diagrams, Models . . . . . . . . . . . . . . . . . 337 16.5 Beyond Vivid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339 16.5.1 Sets of Literals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339 16.5.2 Incorporating Definitions . . . . . . . . . . . . . . . . . . . . . 340 16.5.3 Hybrid Reasoning . . . . . . . . . . . . . . . . . . . . . . . . . . 340 16.6 Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342 16.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343 Bibliography 349 Index 377 This Page Intentionally Left Blank ■ P REFACE ■ ■ Knowledge representation and reasoning is the area of Artificial Intelli- gence (AI) concerned with how knowledge can be represented symboli- cally and manipulated in an automated way by reasoning programs. More informally, it is the part of AI that is concerned with thinking, and how thinking contributes to intelligent behavior. There are, of course, many ways to approach the topic of intelligence and intelligent behavior : We can, for example, look at the neuroscience, the psychology, the evolution, and even the philosophy of the concepts involved. What does knowledge representation have to offer here? As a field of study it suggests an approach to understanding intelligent behav- ior that is radically different from the others. Instead of asking us to study humans or other animals very carefully (their biology, their nervous sys- tems, their psychology, their sociology, their evolution, or whatever), it argues that what we need to study is what humans know . It is taken as a given that what allows humans to behave intelligently is that they know a lot of things about a lot of things and are able to apply this knowledge as appropriate to adapt to their environment and achieve their goals. So in the field of knowledge representation and reasoning we focus on the knowledge, not on the knower. We ask what any agent—human, animal, electronic, mechanical—would need to know to behave intelligently, and what sorts of computational mechanisms might allow its knowledge to be made available to the agent as required. This book is the text for an introductory course in this area of research. REPRESENTATION AND REASONING TOGETHER The easiest book to have written might have been one that simply surveyed the representation languages and reasoning systems currently popular with researchers pushing the frontiers of the field. Instead, we have taken a definite philosophical stance about what we believe matters in the research, and then looked at the key concepts involved from this perspec- tive. What has made the field both intellectually exciting and relevant to practice, in our opinion, is the interplay between representation and reason- ing . It is not enough, in other words, to write down what needs to be known xvii xviii Preface in some formal representation language; nor is it enough to develop rea- soning procedures that are effective for various tasks. Although both of these are honorable enterprises, knowledge representation and reasoning is best understood as the study of how knowledge can at the same time be represented as comprehensively as possible and be reasoned with as effectively as possible. There is a tradeoff between these two concerns, which is an implicit theme throughout the book and one that becomes explicit in the final chapter. Although we start with first-order logic as our representation language and logical entailment as the specification for reasoning, this is just the starting point, and a somewhat simplistic one at that. In sub- sequent chapters we wander from this starting point, looking at various representation languages and reasoning schemes with different intuitions and emphases. In some cases, the reasoning procedure may be less than ideal; in other cases, it might be the representation language. In still other cases, we wander far enough from the starting point that it is hard to even see the logic involved. However, in all cases, we take as fundamental the impact that needing to reason with knowledge structures has on the form and scope of the languages used to represent a system’s knowledge. OUR APPROACH We believe that it is the job of an introductory course (and an introductory textbook) to lay a solid foundation, enabling students to understand in a deep and intuitive way novel work that they may subsequently encounter and putting them in a position to tackle their own later research. This foundation does not depend on current systems or the approaches of spe- cific researchers. Fundamental concepts like knowledge bases, implicit belief, mechanized inference using sound deductive methods, control of reasoning, nonmonotonic and probabilistic extensions to inference, and the formal and precise representation of actions and plans are so basic to the understanding of AI that we believe that the right approach is to teach them in a way that parallels the teaching of elementary physics or economics. This is the approach that we have taken here. We start with very basic assumptions of the knowledge representation enterprise and build on them with simplified but pedagogically digestible descriptions of mechanisms and “laws.” This will ultimately leave the student grounded in all of the important basic concepts and fully prepared to study and understand current and advanced work in the field. This book takes a strong stand on this. We have taken it as our goal to cover most of the key principles underlying work in knowledge representa- tion and reasoning in a way that is, above all else, accessible to the student, Preface xix and in a sequence that allows later concepts to regularly build directly on earlier ones. In other words, pedagogical clarity and the importance of the material were our prime drivers. For well more than ten years we have taught this material to early graduate students and some fourth-year undergraduates, and in that time we have tried to pay close attention to what best prepared the students to jump directly from our course into the active research literature. Over the years we have tuned and refined the material to match the needs and feedback of the students; we believe that this has resulted in a very successful one-semester course, and one that is unique in its focus on core principles and fundamental mechanisms with- out being slanted toward our own technical work or interests of the week. Based on our experience with the course, we approached the construction of the book in a top-down way: We first outlined the most important topics in what we felt was the ideal sequence, and then worked to determine the appropriate relative weight (i.e., chapter length) of each set of concepts in the overall book. As we wrote, we worked hard to stay within the structure and bounds that we had initially set, despite the frequent temptation to just keep writing about certain topics. We will have to leave it to you, our reader, to judge, but we feel that the relative emphases and scope of the chapters are important contributions to the value of the book. Perhaps it would have been nice to have written the comprehensive and up-to-the-minute book that might have become the “bible” of the field, and we may someday tilt at that windmill. But that is not the book we set out to write. By adhering to the approach outlined here, we have created something that fits very well in a one-semester course on the prin- ciples and mechanisms that underlie most of the important work going on in the field. In a moment, we will discuss other courses that could be built on top of this textbook, but we feel that it is important for you to know that the book you hold in your hands is first and foremost about the basics. It is intended to put students and practitioners on a firm enough foundation that they can build substantial later work on top of what they learn here. OVERVIEW OF THE BOOK The text is organized as follows. The first chapter provides an overview and motivation for the area of knowledge representation and reason- ing and defines the core concepts on which the rest of the book is built. It also spells out the fundamental relationships between knowledge, rep- resentation, and reasoning that underlie the rest of the material in the text. Chapters 2 through 4 are concerned with the basic techniques of