Human and Machine Problem Solving

Human and Machine Problem Solving

Edited by K. J. Gilhooly

Universify of Aberdeen Aberdeen, United Kingdom

Plenum Press • New York and London

ubrary of Congress Cataloging in Publication Data

Human and machine problem solving.

Includes bibliographies and index. 1. Problem solving. 2. Problem solving-Data processing. J. Cognitive science. J.

Gilhooly, K. J. BF449.H86 1989 15H' J 88·J1628

I S B N 9 78-1-468 4-801 7 - 7 00110. 10071978- 1-4 684-801 5-3

IS ON 978- 1-4684-80 15-3 (cOook)

© 1989 Plenum p~, New York Soncover reprinl of the hardcover 1$1 edilion 1989

A Division of Plenum Publishing Corporation BJ Spring Street, New York. N.Y. 10013

AI! rights reserved

No part of this book may be reproduced. stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical. photocopying. microfilming.

recording. or otherwise. without written permission from the Publisher

Contributors

J. L. ALTY, Turing Institute, George House, 36 North Hanover Street, Glasgow Gl 2AD, United Kingdom

I. BRATKO, E. Kardelj University, Faculty of Electrical Engineering, and J. Stefan Institute, 61000 Ljubljana, Yugoslavia

M. T. H. CHI, Learning Research and Development Center, University of Pittsburgh, Pittsburgh, Pennsylvania 15260

M. R. B. CLARKE, Department of Computer Science, Queen Mary Col­lege, University of London, London El 4NS, United Kingdom

BENEDICT DU BOULAY, School of Cognitive Sciences, University of Sus­sex, Brighton BNl 9QN, United Kingdom

MICHAEL W. EYSENCK, Department of Psychology, Royal Holloway and Bedford New College, University of London, Egham, Surrey TW20 OEX, United Kingdom .

R. A. FROST, School of Computer Science, University of Windsor, Windsor, Ontario N9B 3P4, Canada

ANGUS R. H. GELLATLY, Department of Psychology, University of Keele, Keele, Staffordshire STS SBG, United Kingdom

K. J. GILHOOLY, Department of Psychology, University of Aberdeen, Aberdeen AB9 2UB, United Kingdom

DENNIS H. HOLDING, Department of Psychology, University of Louis­ville, Louisville, Kentucky 40292

RICHARD E. MAYER, Department of Psychology, University of Califor­nia, Santa Barbara, California 93106

v

vi CONTRIBUTORS

P. REIMANN, Psychology Institute, University of Freiburg, D-7800 Frei­burg, West Germany

J. C. THOMAS, AI Laboratory, NYNEX Corporation, White Plains, New York 10604

Preface

Problem solving is a central topic for both cognitive psychology and artificial intelligence (AI). Psychology seeks to analyze naturally occur­ring problem solving into hypothetical processes, while AI seeks to synthesize problem-solving performance from well-defined processes. Psychology may suggest possible processes to AI and, in turn, AI may suggest plausible hypotheses to psychology. It should be useful for both sides to have some idea of the other's contribution-hence this book, which brings together overviews of psychological and AI re­search in major areas of problem solving.

At a more general level, this book is intended to be a contribution toward comparative cognitive science. Cognitive science is the study of intelligent systems, whether natural or artificial, and treats both organ­isms and computers as types of information-processing systems. Clearly, humans and typical current computers have rather different functional or cognitive architectures. Thus, insights into the role of cognitive ar­chitecture in performance may be gained by comparing typical human problem solving with efficient machine problem solving over a range of tasks.

Readers may notice that there is little mention of connectionist ap­proaches in this volume. This is because, at the time of writing, such approaches have had little or no impact on research at the problem­solving level. Should a similar volume be produced in ten years or so, of course, a very different story may need to be told.

Thanks are due to the following people who helped solve the problem of producing this book: to the secretarial staff of my depart­ment for expert word processing and reprocessing; to P. Bates, for many of the figures; to Professor E. A. Salzen, my head of department, for providing a good working environment at Aberdeen; to Professors

vii

viii PREFACE

Sanford and Oatley, and P. J. O'Donnell, who provided me with facil­ities to work on this book during a visiting fellowship at the Psychol­ogy Department of Glasgow University; to Ben du Boulay, for much advice; and to Ken Derham, senior editor at Plenum Press, who greatly assisted the transition from initial proposal to final product.

K. J. Gilhooly Aberdeen

Contents

CHAPTER 1 Human and Machine Problem Solving: Toward a Comparative Cognitive Science

K. J. GILHOOLY

1. Introduction ............................................... 1 2. Problem Solving. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 2

2.1. Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 2 2.2. Solving. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 5

3. Perspectives ............................................... 6 3.1. Psychological Perspective ............................... 6 3.2. Machine Perspective .................................... 8 3.3. Interaction of Human and Machine Perspectives .......... 9

4. Some Issues .............................................. 11 5. References ................................................ 11

CHAPTER 2 Nonadversary Problem Solving by Machine

BENEDICT DU BOULAY

1. Introduction .............................................. 13 1.1. Problem-Solving Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 15 1.2. State Space Search and Problem Reduction .............. 17 1.3. Blind Search and Heuristic Search. . . . . . . . . . . . . . . . . . . . . .. 18 1.4. Graphs and Trees ..................................... 19

2. State Space Representation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 20 2.1. The Graph Traverser. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 21 2.2. Blind Search .......................................... 22 2.3. Heuristic Search ....................................... 25

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3. Problem Reduction Representation: And/or Graphs. . . . . . . . . .. 27 3.1. Blind Search .......................................... 28 3.2. Heuristic Search. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 28 3.3. MeanslEnds Analysis .................................. 29

4. Planning.................................................. 29 4.1. Theorem-Proving Approaches .......................... 31 4.2. STRIPs-like Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 32 4.3. Hierarchical and Nonlinear Planners .................... 35

5. Conclusions ............................................... 36 6. References ................................................ 37

CHAPTER 3 Human Nonadversary Problem Solving

RICHARD E. MAYER

1. Introduction .............................................. 39 1.1. Definitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 39 1.2. Types of Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 41 1.3. Analysis of Problem Solving. . . . . . . . . . . . . . . . . . . . . . . . . . .. 42

2. Constraints on a Model of Human Nonadversary Problem Solving. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 45 2.1. Humans Systematically Distort the Problem To Be

Consistent with Prior Knowledge . . . . . . . . . . . . . . . . . . . . . .. 45 2.2. Humans Focus on Inappropriate Aspects of the

Problem .............................................. 47 2.3. Humans Change the Problem Representation during

Problem Solving. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 49 2.4. Humans Apply Procedures Rigidly and Inappropriately. .. 50 2.5. Humans Are Intuitive and Insightful and Creative. . . . . . .. 51 2.6. Humans Let Their Beliefs Guide Their Approach to

Problem Solving. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 53 3. Conclusion ............................................... 54 4. References................................................ 55

CHAPTER 4 Adversary Problem Solving by Machine

M. R. B. CLARKE

1. Introduction .............................................. 57 2. Search Techniques for Two-Person Games ................... 58 3. Minimaxing with an Evaluation Function . . . . . . . . . . . . . . . . . . .. 59

CONTENTS xi

4. The Alpha-Beta Algorithm ................................. 60 5. Refinements of the Basic Alpha-Beta Rule. . . . . . . . . . . . . . . . . .. 63 6. Theoretical Analyses of Alpha-Beta and Its Variants .......... 64 7. Other Problem-Independent Adversary Search Methods ...... 66 8. Selective Search, Evaluation Functions, and Quiescence. . . . . .. 67 9. A Short History of Game-Playing Programs .................. 68

10. Example of Implementation Method for Chess ............... 70 11. Knowledge-Based Selective Search .......................... 73 12. Exact Play in Chess Endgames .............................. 74 13. Other Nonprobabilistic Games. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 76 14. Games of Imperfect Information, Game Theory .............. 77 15. Conclusion-Likely Future Trends .......................... 78 16. References ................................................ 79 17. Further Reading ........................................... 80

CHAPTER 5 Adversary Problem Solving by Humans

DENNIS H. HOLDING

1. Adversary Games ......................................... 83 1.1. Games Research. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 84 1.2. Memory and Skill ..................................... 85 1.3. The Need for Alternative Explanations .................. 87

2. Dealing with the Adversary ................................ 88 2.1. Predicting Opponent Moves. . . . . . . . . . . . . . . . . . . . . . . . . . .. 90 2.2. The Opponent's Intentions ............................. 91

3. Characteristics of the Search Process ........................ 92 3.1. Problem Behavior Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 93 3.2. Progress through the Tree .............................. 95

4. Plans and Knowledge. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 97 4.1. Using Plans ........................................... 97 4.2. Using Knowledge ..................................... 99 4.3. Knowledge and Skill .................................. 100

5. Evaluation Functions ..................................... 101 5.1. Material and Positional Evaluations .................... 102 5.2. Judgment and Skill. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 103 5.3. Comparison with Computers .......................... 105

6. Projecting Ahead. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 107 6.1. Following One Line of Moves ......................... 107 6.2. Anticipation through a Tree. . . . . . . . . . . . . . . . . . . . . . . . . .. 109 6.3. Human Minimaxing .................................. 111

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7. Humans versus Computers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 112 7.1. Knowledge, Search, and Evaluation .................... 113 7.2. Experimental Comparisons. . . . . . . . . . . . . . . . . . . . . . . . . . .. 115 7.3. Playing against Computers ............................ 116

8. Overview ................................................ 117 8.1. Unresolved Issues .................................... 117 8.2. Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 118

9. References............................................... 120

CHAPTER 6 Machine Expertise

]. L. ALTY

1. The Automation of Problem Solving-Continuing a Tradition ................................................ 123

2. Problem-Solving Knowledge Representation ................ 124 3. The Nature of Expert Knowledge . . . . . . . . . . . . . . . . . . . . . . . . .. 126 4. Knowledge Representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 127 5. Problems with the Traditional Approach. . . . . . . . . . . . . . . . . . .. 128 6. Architectures for Representing Machine Expertise ... . . . . . . .. 129

6.1. The Production System Approach. . . . . . . . . . . . . . . . . . . . .. 130 6.2. Multiple Experts and Mixed Reasoning Strategies. . . . . . .. 131 6.3. The Set-Covering Approach (or Frame Abduction) ....... 132 6.4. Multiple Paradigms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 132

7. The Rule-Based Approach-MYCIN, PROSPECTOR, and XCON ... 133 7.1. The MYCIN System .................................... 133 7.2. The XC ON System (Rl) ................................. 136 7.3. The PROSPECTOR System. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 138

8. The Blackboard Approach (HEARSAY) ....................... 141 9. The Set-Covering Approach (Frame Abduction) ............. 142

9.1. The Inference Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 143 9.2. System D-An Example ............................... 145 9.3. The INTERNIST System ................................ 147

10. Multiple Paradigm Approaches ............................ 149 10.1. The COMPASS System ................................ 150

11. Expert System Shells. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 152 11.1. The Shell Concept. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 154 11.2. What Does a Shell Provide? .......................... 154 11.3. What Sorts of Shells Exist? ........................... 155

12. Recent Developments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 156 12.1. Nonmonotonic Reasoning. . . . . . . . . . . . . . . . . . . . . . . . . . .. 156 12.2. Deep Knowledge. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 157 12.3. Commonsense Reasoning and Causality. . . . . . . . . . . . . .. 157

CONTENTS xiii

12.4. Better Tools ......................................... 158 13. Conclusions .............................................. 158 14. References ............................................... 159

CHAPTER 7 Human Expertise

P. REIMANN and M. CHI

1. Introduction ............................................. 161 2. The Theoretical Framework: Information-Processing

Theory of Problem Solving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 161 3. The Construction of a Problem Representation . . . . . . . . . . . . .. 165 4. The Role of Schemata in Problem Solving ............. ; . . . .. 171 5. Problem-Solving Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 178

5.1. Interaction of Different Problem-Solving Strategies. . . . . .. 180 5.2. Switching Problem-Solving Strategy. . . . . . . . . . . . . . . . . . .. 183

6. The Development of Expertise. . . . . . . . . . . . . . . . . . . . . . . . . . . .. 184 6.1. Acquisition of Episodic Knowledge Structures. . . . . . . . . .. 184 6.2. Acquisition of Procedural Knowledge .................. 186

7. Conclusion .............................................. 188 8. References ............................................... 189

CHAPTER 8 Machine Inference

R. A. FROST

1. Input of Knowledge ...................................... 193 1.1. Formal Languages .................................... 193 1.2. Recognition and Parsing .............................. 197 1.3. Translation .......................................... 200 1.4. Summary of Input of Knowledge ...................... 200

2. Machine Inference Based on Logic ......................... 201 2.1. Introduction ......................................... 201 2.2. Classical Propositional Logic ........................... 202 2.3. Automatic Inference in Classical Propositional Logic ..... 206 2.4. Summary of Machine Inference Based on Logic ......... 213

3. The Production-Rule-Based Approach to Inference ........... 214 3.1. What Is a Production-Rule-Based System? .............. 214 3.2. Origins of the Production-Rule-Based Approach ......... 214 3.3. Rule Application ..................................... 215 3.4. Accommodating Uncertainty .......................... 216 3.5. Summary of the Production-Rule-Based Approach to

Inference ............................................ 217

xiv CONTENTS

4. The Frame-Based Approach to Inference .................... 217 4.1. Some Definitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 218 4.2. Matching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 222 4.3. Finding the Best Match ............................... 223 4.4. Inference in the Frame-Based Approach . . . . . . . . . . . . . . .. 224 4.5. Summary of the Frame-Based Approach to Inference .... 225

5. The Current Status of Machine Inference ... . . . . . . . . . . . . . . .. 226 5.1. The Status of the Logic-Based Approach to Inference . . .. 227 5.2. The Status of the Production-Rule-Based Approach to

Inference ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228 5.3. The Status of the Frame-Based Approach to Inference ... 229 5.4. Integration of Techniques from All Three Approaches ... 229

6. References ............................................... 230

CHAPTER 9 Human Inference

ANGUS R. H. GELLATLY

1. Introduction ............................................. 233 1.1. What Is an Inference? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 235 1.2. Implicit and Explicit Inferences ........................ 236 1.3. Logic and Comprehension ............................ 237

2. The Mental Logic Approach. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 239 2.1. Henle's Argument .................................... 239 2.2. Mental Logic and Propositional Reasoning .............. 241 2.3. Other Arguments and Evidence for Mental Logic. . . . . . .. 244

3. The Mental Models Approach .... . . . . . . . . . . . . . . . . . . . . . . . .. 246 3.1. Simulation by Mental Model ........................... 247 3.2. Truth-Functional Reasoning . . . . . . . . . . . . . . . . . . . . . . . . . .. 248 3.3. Propositional Reasoning with Mental Models ........... 250 3.4. Reasoning with Syllogisms . . . . . . . . . . . . . . . . . . . . . . . . . . .. 252

4. The Nature of Inference. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 256 4.1. The Argument from Observation ...................... 256 4.2. Analytical Comprehension Revisited ................... 259 4.3. Conclusion .......................................... 261

5. References ............................................... 261

CHAPTER 10 Machine Learning

I. BRATKO

1. Introduction ............................................. 265 2. Learning Concepts from Examples: Problem Statement. . . . . .. 266

CONTENTS xv

2.1. Concepts as Sets ..................................... 266 2.2. Description Languages for Objects and Concepts. . . . . . .. 267 2.3. The Problem of Learning from Examples ............... 268 2.4. Criteria of Success. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 269

3. Learning Concepts by Induction: A Detailed Example ........ 270 4. Learning Decision Trees and Coping with Noise ............ 275

4.1. The TDIDT Family of Learning Programs . . . . . . . . . . . . . .. 275 4.2. Tree Pruning in TDIDT Programs ...................... 281 4.3. How Pruning Affects Accuracy and Transparency

of Decision Trees. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 283 5. Other Approaches to Learning and Bibliographical Remarks.. 284 6. References ............................................... 286

CHAPTER 11 Human Learning

MICHAEL W. EYSENCK

1. Introduction ............................................. 289 2. Schemata, Scripts, and Frames ............................. 292 3. Amnesia ................................................. 298 4. Retrieval from Long-Term Memory ......................... 305 5. Concept Learning ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 309 6. Conclusions .............................................. 312 7. References ............................................... 313

CHAPTER 12 Problem Solving by Human-Machine Interaction

J. C. THOMAS

1. Problem Solving for the Real World ........................ 317 1.1. What Is Problem Solving? . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 317 1.2. The Importance of Problem Solving. . . . . . . . . . . . . . . . . . .. 319 1.3. How Can Computers Help People Solve Problems? . . . . .. 320

2. Problem Solving Reconsidered from a Human Factors Perspective .............................................. 321 2.1. The Importance of the Task ........................... 321 2.2. The Importance of the User ........................... 322 2.3. The Importance of the Interface ........................ 323 2.4. Recommendations for Human-Computer Problem

Solving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324 3. Stages of the Problem-Solving Process. . . . . . . . . . . . . . . . . . . . .. 324

3.1. Problem Finding ..................................... 327 3.2. Problem Formulation ................................. 328

xvi CONTENTS

3.3. Idea Generation ...................................... 331 3.4. Idea Evaluation ...................................... 332 3.5. Solution Match with Goal . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 333 3.6. Solution Match with Environment ..................... 334 3.7. Idea Integration ...................................... 336 3.8. Acceptance or Modification. . . . . . . . . . . . . . . . . . . . . . . . . . .. 337 3.9. Planning for Implementation .......................... 338 3.10. Measuring the Outcome ............................. 338 3.11. Evaluating the Process ............................... 339

4. Human-Computer Problem Solving: Cases . . . . . . . . . . . . . . . .. 340 4.1. Speech Synthesis as an Interface Problem. . . . . . . . . . . . . .. 340 4.2. The Computer as an Active Communications Medium. .. 344

5. A Retrospective Example. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 348 5.1. Designing a Strategy for Human Factors. . . . . . . . . . . . . . .. 348 5.2. The Actual Use of Computers in Solving This Problem ... 350 5.3. The Potential for Human-Computer Problem Solving. . .. 352

6. Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 358 7. References ............................................... 359 8. Further Reading. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 360

CHAPTER 13 Human and Machine Problem Solving: A Comparative Overview

K. J. GILHOOLY

1. Introduction ............................................. 363 2. Nonadversary Problems ................................... 363 3. Adversary Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 365 4. Expertise ................................................ 366 5. Inference ................................................ 368 6. Learning ................................................. 368 7. Solving Problems by Human-Computer Interaction ......... 369 8. Concluding Comments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... 370 9. References............................................... 371

Author Index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 373

Subject Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 381

Human and Machine Problem Solving