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Cambridge University Press 978-0-521-51900-7 - Artificial Intelligence: Foundations of Computational Agents David L. Poole and Alan K. Mackworth Frontmatter More information Artificial Intelligence Foundations of Computational Agents Artificial Intelligence: Foundations of Computational Agents is about the science of artificial intelligence (AI). It presents AI as the study of the design of intelligent computational agents. The book is structured as a textbook, but it is accessible to a wide audience of professionals and researchers. The past decades have witnessed the emergence of AI as a serious science and engineering discipline. This book provides the first accessible synthesis of the field aimed at undergraduate and graduate students. It provides a coherent vision of the foundations of the field as it is today, in terms of a multidimensional design space that has been partially explored. As with any science worth its salt, AI has a coherent, formal theory and a rambunctious experimental wing. The book balances theory and experiment, showing how to link them intimately together. It develops the science of AI together with its engineering applications. David L. Poole is Professor of Computer Science at the University of British Columbia. He is a coauthor of Computational Intelligence: A Logical Approach (1998), cochair of the Twenty-Fourth AAAI Conference on Artificial Intelligence (AAAI-10), and coeditor of the Proceedings of the Tenth Conference in Uncertainty in Artificial Intelligence (1994). Poole is a former associate editor of the Journal of Artificial Intelligence Research. He is an associate editor of Artificial Intelligence and on the editorial boards of AI Magazine and AAAI Press. He is the secretary of the Association for Uncertainty in Artificial Intelligence and is a Fellow of the Association for the Advancement of Artificial Intelligence. Alan K. Mackworth is Professor of Computer Science and Canada Research Chair in Artificial Intelligence at the University of British Columbia. He has authored more than 100 papers and coauthored the text Computational Intelligence: A Logical Approach. He was President and Trustee of International Joint Conferences on AI (IJCAI) Inc. Mackworth was vice president and president of the Canadian Society for Computational Studies of Intelligence (CSCSI). He has served as president of the AAAI. He also served as the founding director of the UBC Laboratory for Computational Intelligence. He is a Fellow of the Canadian Institute for Advanced Research, AAAI, and the Royal Society of Canada. © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-51900-7 - Artificial Intelligence: Foundations of Computational Agents David L. Poole and Alan K. Mackworth Frontmatter More information Artificial Intelligence Foundations of Computational Agents David L. Poole University of British Columbia Alan K. Mackworth University of British Columbia © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-51900-7 - Artificial Intelligence: Foundations of Computational Agents David L. Poole and Alan K. Mackworth Frontmatter More information CAMBRIDGE UNIVERSITY PRESS Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo, Delhi, Dubai, Tokyo Cambridge University Press 32 Avenue of the Americas, New York, NY 10013-2473, USA www.cambridge.org Information on this title: www.cambridge.org/9780521519007 C David L. Poole and Alan K. Mackworth 2010 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 2010 Printed in the United States of America A catalog record for this publication is available from the British Library. Library of Congress Cataloging in Publication data Poole, David L. (David Lynton), 1958– Artificial intelligence : foundations of computational agents / David L. Poole, Alan K. Mackworth. p. cm. Includes bibliographical references and index. ISBN 978-0-521-51900-7 (hardback) 1. Computational intelligence – Textbooks. 2. Artificial intelligence – Textbooks. I. Mackworth, Alan K. II. Title. Q342.P66 2010 006.3 – dc22 2009039895 ISBN 978-0-521-51900-7 Hardback 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. © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-51900-7 - Artificial Intelligence: Foundations of Computational Agents David L. Poole and Alan K. Mackworth Frontmatter More information To our families for their love, support, and patience Jennifer, Alexandra, and Shannon Marian and Bryn © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-51900-7 - Artificial Intelligence: Foundations of Computational Agents David L. Poole and Alan K. Mackworth Frontmatter More information Contents Preface xiii I Agents in the World: What Are Agents and How Can They Be Built? 1 Artificial Intelligence and Agents 1.1 What Is Artificial Intelligence? . 1.2 A Brief History of AI . . . . . . . 1.3 Agents Situated in Environments 1.4 Knowledge Representation . . . 1.5 Dimensions of Complexity . . . . 1.6 Prototypical Applications . . . . 1.7 Overview of the Book . . . . . . 1.8 Review . . . . . . . . . . . . . . . 1.9 References and Further Reading 1.10 Exercises . . . . . . . . . . . . . . 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3 6 10 11 19 29 39 40 40 42 2 Agent Architectures and Hierarchical Control 2.1 Agents . . . . . . . . . . . . . . . . . . . 2.2 Agent Systems . . . . . . . . . . . . . . . 2.3 Hierarchical Control . . . . . . . . . . . 2.4 Embedded and Simulated Agents . . . 2.5 Acting with Reasoning . . . . . . . . . . 2.6 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 43 44 50 59 60 65 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-51900-7 - Artificial Intelligence: Foundations of Computational Agents David L. Poole and Alan K. Mackworth Frontmatter More information viii Contents 2.7 2.8 References and Further Reading . . . . . . . . . . . . . . . . . Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II Representing and Reasoning 3 States and Searching 3.1 Problem Solving as Search . . . . 3.2 State Spaces . . . . . . . . . . . . 3.3 Graph Searching . . . . . . . . . 3.4 A Generic Searching Algorithm . 3.5 Uninformed Search Strategies . . 3.6 Heuristic Search . . . . . . . . . . 3.7 More Sophisticated Search . . . . 3.8 Review . . . . . . . . . . . . . . . 3.9 References and Further Reading 3.10 Exercises . . . . . . . . . . . . . . 66 66 69 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 71 72 74 77 79 87 92 106 106 107 4 Features and Constraints 4.1 Features and States . . . . . . . . . . . . . . 4.2 Possible Worlds, Variables, and Constraints 4.3 Generate-and-Test Algorithms . . . . . . . 4.4 Solving CSPs Using Search . . . . . . . . . 4.5 Consistency Algorithms . . . . . . . . . . . 4.6 Domain Splitting . . . . . . . . . . . . . . . 4.7 Variable Elimination . . . . . . . . . . . . . 4.8 Local Search . . . . . . . . . . . . . . . . . . 4.9 Population-Based Methods . . . . . . . . . 4.10 Optimization . . . . . . . . . . . . . . . . . 4.11 Review . . . . . . . . . . . . . . . . . . . . . 4.12 References and Further Reading . . . . . . 4.13 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 111 113 118 119 120 125 127 130 141 144 151 151 152 . . . . . . . . . . 157 157 163 174 185 193 199 204 206 207 208 . . . . . . . . . . 5 Propositions and Inference 5.1 Propositions . . . . . . . . . . . . . 5.2 Propositional Definite Clauses . . 5.3 Knowledge Representation Issues 5.4 Proving by Contradictions . . . . . 5.5 Complete Knowledge Assumption 5.6 Abduction . . . . . . . . . . . . . . 5.7 Causal Models . . . . . . . . . . . . 5.8 Review . . . . . . . . . . . . . . . . 5.9 References and Further Reading . 5.10 Exercises . . . . . . . . . . . . . . . © in this web service Cambridge University Press . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . www.cambridge.org Cambridge University Press 978-0-521-51900-7 - Artificial Intelligence: Foundations of Computational Agents David L. Poole and Alan K. Mackworth Frontmatter More information ix Contents 6 Reasoning Under Uncertainty 6.1 Probability . . . . . . . . . . . . . 6.2 Independence . . . . . . . . . . . 6.3 Belief Networks . . . . . . . . . . 6.4 Probabilistic Inference . . . . . . 6.5 Probability and Time . . . . . . . 6.6 Review . . . . . . . . . . . . . . . 6.7 References and Further Reading 6.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III Learning and Planning 219 219 232 235 248 266 274 274 275 281 7 Learning: Overview and Supervised Learning 7.1 Learning Issues . . . . . . . . . . . . . . . . 7.2 Supervised Learning . . . . . . . . . . . . . 7.3 Basic Models for Supervised Learning . . . 7.4 Composite Models . . . . . . . . . . . . . . 7.5 Avoiding Overfitting . . . . . . . . . . . . . 7.6 Case-Based Reasoning . . . . . . . . . . . . 7.7 Learning as Refining the Hypothesis Space 7.8 Bayesian Learning . . . . . . . . . . . . . . 7.9 Review . . . . . . . . . . . . . . . . . . . . . 7.10 References and Further Reading . . . . . . 7.11 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283 284 288 298 313 320 324 327 334 340 341 342 8 Planning with Certainty 8.1 Representing States, Actions, and Goals 8.2 Forward Planning . . . . . . . . . . . . . 8.3 Regression Planning . . . . . . . . . . . 8.4 Planning as a CSP . . . . . . . . . . . . . 8.5 Partial-Order Planning . . . . . . . . . . 8.6 Review . . . . . . . . . . . . . . . . . . . 8.7 References and Further Reading . . . . 8.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349 350 356 357 360 363 366 367 367 9 Planning Under Uncertainty 9.1 Preferences and Utility . . . . . . . . . 9.2 One-Off Decisions . . . . . . . . . . . . 9.3 Sequential Decisions . . . . . . . . . . 9.4 The Value of Information and Control 9.5 Decision Processes . . . . . . . . . . . 9.6 Review . . . . . . . . . . . . . . . . . . 9.7 References and Further Reading . . . 9.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371 373 381 386 396 399 412 413 413 © in this web service Cambridge University Press . . . . . . . . www.cambridge.org Cambridge University Press 978-0-521-51900-7 - Artificial Intelligence: Foundations of Computational Agents David L. Poole and Alan K. Mackworth Frontmatter More information x Contents 10 Multiagent Systems 10.1 Multiagent Framework . . . . . . . . . . . . . . 10.2 Representations of Games . . . . . . . . . . . . 10.3 Computing Strategies with Perfect Information 10.4 Partially Observable Multiagent Reasoning . . 10.5 Group Decision Making . . . . . . . . . . . . . 10.6 Mechanism Design . . . . . . . . . . . . . . . . 10.7 Review . . . . . . . . . . . . . . . . . . . . . . . 10.8 References and Further Reading . . . . . . . . 10.9 Exercises . . . . . . . . . . . . . . . . . . . . . . 11 Beyond Supervised Learning 11.1 Clustering . . . . . . . . . . . . . 11.2 Learning Belief Networks . . . . 11.3 Reinforcement Learning . . . . . 11.4 Review . . . . . . . . . . . . . . . 11.5 References and Further Reading 11.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423 423 425 430 433 445 446 449 449 450 . . . . . . 451 451 458 463 485 486 486 IV Reasoning About Individuals and Relations 12 Individuals and Relations 12.1 Exploiting Structure Beyond Features . . . . . 12.2 Symbols and Semantics . . . . . . . . . . . . . 12.3 Datalog: A Relational Rule Language . . . . . 12.4 Proofs and Substitutions . . . . . . . . . . . . . 12.5 Function Symbols . . . . . . . . . . . . . . . . . 12.6 Applications in Natural Language Processing . 12.7 Equality . . . . . . . . . . . . . . . . . . . . . . 12.8 Complete Knowledge Assumption . . . . . . . 12.9 Review . . . . . . . . . . . . . . . . . . . . . . . 12.10 References and Further Reading . . . . . . . . 12.11 Exercises . . . . . . . . . . . . . . . . . . . . . . 13 Ontologies and Knowledge-Based Systems 13.1 Knowledge Sharing . . . . . . . . . . . . . . . . 13.2 Flexible Representations . . . . . . . . . . . . . 13.3 Ontologies and Knowledge Sharing . . . . . . 13.4 Querying Users and Other Knowledge Sources 13.5 Implementing Knowledge-Based Systems . . . 13.6 Review . . . . . . . . . . . . . . . . . . . . . . . 13.7 References and Further Reading . . . . . . . . 13.8 Exercises . . . . . . . . . . . . . . . . . . . . . . © in this web service Cambridge University Press 489 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 491 492 493 494 506 512 520 532 537 541 542 542 . . . . . . . . 549 549 550 563 576 579 591 591 592 www.cambridge.org Cambridge University Press 978-0-521-51900-7 - Artificial Intelligence: Foundations of Computational Agents David L. Poole and Alan K. Mackworth Frontmatter More information xi Contents 14 Relational Planning, Learning, and Probabilistic Reasoning 14.1 Planning with Individuals and Relations . . . . . . . . 14.2 Learning with Individuals and Relations . . . . . . . . 14.3 Probabilistic Relational Models . . . . . . . . . . . . . . 14.4 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.5 References and Further Reading . . . . . . . . . . . . . 14.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 597 598 606 611 618 618 620 V The Big Picture 623 15 Retrospect and Prospect 15.1 Dimensions of Complexity Revisited . . . . . . . . . . . . . . . 15.2 Social and Ethical Consequences . . . . . . . . . . . . . . . . . 15.3 References and Further Reading . . . . . . . . . . . . . . . . . 625 625 629 632 A Mathematical Preliminaries and Notation A.1 Discrete Mathematics . . . . . . . . . . . . . . . . . . . . . . . . A.2 Functions, Factors, and Arrays . . . . . . . . . . . . . . . . . . A.3 Relations and the Relational Algebra . . . . . . . . . . . . . . . 633 633 634 635 Bibliography 637 Index 653 © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-51900-7 - Artificial Intelligence: Foundations of Computational Agents David L. Poole and Alan K. Mackworth Frontmatter More information Preface Artificial Intelligence: Foundations of Computational Agents is a book about the science of artificial intelligence (AI). The view we take is that AI is the study of the design of intelligent computational agents. The book is structured as a textbook, but it is designed to be accessible to a wide audience. We wrote this book because we are excited about the emergence of AI as an integrated science. As with any science worth its salt, AI has a coherent, formal theory and a rambunctious experimental wing. Here we balance theory and experiment and show how to link them intimately together. We develop the science of AI together with its engineering applications. We believe the adage “There is nothing so practical as a good theory.” The spirit of our approach is captured by the dictum “Everything should be made as simple as possible, but not simpler.” We must build the science on solid foundations; we present the foundations, but only sketch, and give some examples of, the complexity required to build useful intelligent systems. Although the resulting systems will be complex, the foundations and the building blocks should be simple. The book works as an introductory text on AI for advanced undergraduate or graduate students in computer science or related disciplines such as computer engineering, philosophy, cognitive science, or psychology. It will appeal more to the technically minded; parts are technically challenging, focusing on learning by doing: designing, building, and implementing systems. Any curious scientifically oriented reader will benefit from studying the book. Previous experience with computational systems is desirable, but prior study of the foundations on which we build, including logic, probability, calculus, and control theory, is not necessary, because we develop the concepts as required. xiii © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-51900-7 - Artificial Intelligence: Foundations of Computational Agents David L. Poole and Alan K. Mackworth Frontmatter More information xiv Preface The serious student will gain valuable skills at several levels ranging from expertise in the specification and design of intelligent agents to skills for implementing, testing, and improving real software systems for several challenging application domains. The thrill of participating in the emergence of a new science of intelligent agents is one of the attractions of this approach. The practical skills of dealing with a world of ubiquitous, intelligent, embedded agents are now in great demand in the marketplace. The focus is on an intelligent agent acting in an environment. We start with simple agents acting in simple, static environments and gradually increase the power of the agents to cope with more challenging worlds. We explore nine dimensions of complexity that allow us to introduce, gradually and with modularity, what makes building intelligent agents challenging. We have tried to structure the book so that the reader can understand each of the dimensions separately, and we make this concrete by repeatedly illustrating the ideas with four different agent tasks: a delivery robot, a diagnostic assistant, a tutoring system, and a trading agent. The agent we want the student to envision is a hierarchically designed agent that acts intelligently in a stochastic environment that it can only partially observe – one that reasons about individuals and the relationships among them, has complex preferences, learns while acting, takes into account other agents, and acts appropriately given its own computational limitations. Of course, we can’t start with such an agent; it is still a research question to build such agents. So we introduce the simplest agents and then show how to add each of these complexities in a modular way. We have made a number of design choices that distinguish this book from competing books, including the earlier book by the same authors: • We have tried to give a coherent framework in which to understand AI. We have chosen not to present disconnected topics that do not fit together. For example, we do not present disconnected logical and probabilistic views of AI, but we have presented a multidimensional design space in which the students can understand the big picture, in which probabilistic and logical reasoning coexist. • We decided that it is better to clearly explain the foundations on which more sophisticated techniques can be built, rather than present these more sophisticated techniques. This means that a larger gap exists between what is covered in this book and the frontier of science. It also means that the student will have a better foundation to understand current and future research. • One of the more difficult decisions we made was how to linearize the design space. Our previous book (Poole, Mackworth, and Goebel, 1998) presented a relational language early and built the foundations in terms of this language. This approach made it difficult for the students to appreciate work that was not relational, for example, in reinforcement © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-51900-7 - Artificial Intelligence: Foundations of Computational Agents David L. Poole and Alan K. Mackworth Frontmatter More information Preface xv learning that is developed in terms of states. In this book, we have chosen a relations-late approach. This approach probably reflects better the research over the past few decades in which there has been much progress in feature-based representations. It also allows the student to understand that probabilistic and logical reasoning are complementary. The book, however, is structured so that an instructor can present relations earlier. This book uses examples from AIspace.org (http://www.aispace.org), a collection of pedagogical applets that we have been involved in designing. To gain further experience in building intelligent systems, a student should also experiment with a high-level symbol-manipulation language, such as LISP or Prolog. We also provide implementations in AILog, a clean logic programming language related to Prolog, designed to demonstrate many of the issues in this book. This connection is not essential to an understanding or use of the ideas in this book. Our approach, through the development of the power of the agent’s capabilities and representation language, is both simpler and more powerful than the traditional approach of surveying and cataloging various applications of AI. However, as a consequence, some applications, such as the details of computational vision or computational linguistics, are not covered in this book. We have chosen not to present an encyclopedic view of AI. Not every major idea that has been investigated is presented here. We have chosen some basic ideas on which other, more sophisticated, techniques are based and have tried to explain the basic ideas in detail, sketching how these can be expanded. Figure 1 (page xvi) shows the topics covered in the book. The solid lines give prerequisites. Often the prerequisite structure does not include all subtopics. Given the medium of a book, we have had to linearize the topics. However, the book is designed so that the topics can be taught in any order satisfying the prerequisite structure. The references given at the end of each chapter are not meant to be comprehensive: we have referenced works that we have directly used and works that we think provide good overviews of the literature, by referencing both classic works and more recent surveys. We hope that no researchers feel slighted by their omission, and we are happy to have feedback where someone feels that an idea has been misattributed. Remember that this book is not a survey of AI research. We invite you to join us in an intellectual adventure: building a science of intelligent agents. David Poole Alan Mackworth © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-51900-7 - Artificial Intelligence: Foundations of Computational Agents David L. Poole and Alan K. Mackworth Frontmatter More information xvi Preface 1: AI & Agents 2: Architecture & Control 3: States & Searching 4: Features & Constraints 5: Propositions & Inference 6: Uncertainty 7: Supervised Learning 8: Planning 9: Planning Under Uncertainty 10: Multi agent systems 11: Beyond Supervised Learning 12: Individuals & Relations 13: Ontologies & KBS 14: Relational Planning Learning & Probability Figure 1: Overview of chapters and dependencies © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-51900-7 - Artificial Intelligence: Foundations of Computational Agents David L. Poole and Alan K. Mackworth Frontmatter More information Preface xvii Acknowledgments Thanks to Randy Goebel for valuable input on this book. We also gratefully acknowledge the helpful comments on earlier drafts of this book received from Giuseppe Carenini, Cristina Conati, Mark Crowley, Pooyan Fazli, Holger Hoos, Manfred Jaeger, Mohammad Reza Khojasteh, Jacek Kisyński, Bob Kowalski, Kevin Leyton-Brown, Marian Mackworth, Gabriel Murray, Alessandro Provetti, Marco Valtorta, and the anonymous reviewers. Thanks to the students who pointed out many errors in earlier drafts. Thanks to Jen Fernquist for the web site design, and to Tom Sgouros for hyperlatex fixes. We are grateful to James Falen for permission to quote his poem on constraints. Thanks to our editor Lauren Cowles and the staff at Cambridge University Press for all their support, encouragement, and help. All the mistakes remaining are ours. © in this web service Cambridge University Press www.cambridge.org