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
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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
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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
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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