Qualitative Representations: How People Reason and Learn about the Continuous World

441 Pages·2019·33.394 MB·English

by  Kenneth D Forbus

Qualitative Repre sen ta tions

Qualitative Repre sen ta tions
How People Reason and Learn about the Continuous World
Kenneth D. Forbus
The MIT Press
Cambridge, Mas sa chu setts
London, England
© 2018 Kenneth D. Forbus
All rights reserved. No part of this book may be reproduced in any form by any
electronic or mechanical means (including photocopying, recording, or information
storage and retrieval) without permission in writing from the publisher.
This book was set in Stone Serif by Westchester Publishing Ser vices. Printed and
bound in the United States of Amer i ca.
Library of Congress Cataloging- in- Publication Data
Names: Forbus, Kenneth D., author.
Title: Qualitative repre sen ta tions: how people reason and learn about the
continuous world / Kenneth D. Forbus.
Description: Cambridge, MA : MIT Press, [2018] | Includes bibliographical
references and index.
Identifiers: LCCN 2018010193 | ISBN 9780262038942 (hardcover : alk. paper)
Subjects: LCSH: Cognition. | Reasoning. | Space perception.
Classification: LCC BF311 .F6297 2018 | DDC 153.4—d c23
LC rec ord available at https:// lccn. loc . gov / 2018010193
10 9 8 7 6 5 4 3 2 1
To Dedre Gentner, my best collaborator in all aspects of life

Contents
Preface xv
I Introduction and Preliminaries 1
1 Introduction 3
1.1 Some Examples of Everyday Qualitative Reasoning 4
1.1.1 Heating Water 4
1.1.2 Does Cold Water Freeze Faster Than Warm W ater? 5
1.1.3 The Seasons 5
1.1.4 Will These Collide? 6
1.1.5 Raven’s Progressive Matrices 7
1.1.6 Moral Decision Making 8
1.2 The Importance of Qualitative Reasoning in Human Cognition 8
1.3 Overview of the Book 10
2 Repre sen ta tion: An Overview 13
2.1 The Importance of Structured, Relational Repre sen ta tions 13
2.2 Logic, Formalism, and Precision 14
2.2.1 Syntax 14
2.3 Schemas, Frames, and Cases 19
2.4 Ontologies and Knowledge Bases 20
2.5 Richness and Structure of Predicate Vocabularies 22
2.6 Summary: Evaluating Repre sen ta tions 23
3 Reasoning: An Overview 25
3.1 Computational Complexity and Tractability 25
3.2 Deduction, Abduction, and Induction 27
3.3 Pattern Matching and Unification 32
3.3.1 Storing and Retrieving Knowledge 33
viii Contents
3.4 Closed- World Assumptions 33
3.5 Probability 34
4 Analogy 35
4.1 Some Psychologically Motivated Repre sen ta tion Conventions 35
4.2 Structure- Mapping Theory 36
4.3 Psychological Support for Structure- Mapping Theory 42
4.4 Computational Models of Analogical Pro cessing 43
4.4.1 Matching 43
4.4.2 Retrieval 46
4.4.3 Generalization 48
4.5 The Centrality of Analogy in Human Cognition 50
II Dynamics 53
5 Quantity 55
5.1 The Reals 56
5.2 Finite Approximations to the Reals 58
5.3 Finite Algebras and Fuzzy Logic 59
5.4 Signs 60
5.5 Ordinal Relations 61
5.6 Numerical Intervals 62
5.7 Order of Magnitude 63
5.8 Infinitesimals 64
5.9 Status Values 65
5.10 Summary 67
6 Relationships between Quantities 69
6.1 Why Qualitative Mathe matics? 69
6.1.1 Soundness 70
6.1.2 Minimal Knowledge 71
6.1.3 Causality 72
6.2 Qualitative Mathe matics in QP Theory 73
6.2.1 Direct Influences 73
6.2.2 Indirect Influences 75
6.2.3 Compositionality and Graceful Extension of Knowledge 77
6.2.4 Specifying Additional Information about Relationships 79
6.3 Naturalness 81
6.4 Expressiveness 82
6.5 Confluences and Causal Ordering 85
6.6 Summary 87
Contents ix
7 Qualitative Pro cess Theory 89
7.1 Modeling the Modeling Pro cess 90
7.2 Model Fragments 92
7.3 The Ontology of QP Theory 95
7.4 Basic Inferences of QP Theory 98
7.4.1 Model Formulation 98
7.4.2 Determining Activity 99
7.4.3 Resolving Influences 100
7.4.4 Limit Analy sis 103
7.5 Encapsulated Histories 110
7.6 Summary 111
8 Examples Using QP Theory 113
8.1 Modeling Fluids 113
8.2 Existence and Why It Matters 114
8.3 Representing Contained Liquids 118
8.4 Representing Gases 120
8.5 Phase Changes 123
8.6 Boiling Water and Its Consequences 128
8.7 Ice Cubes in Freezers, Revisited 131
8.8 Modeling Motion 133
8.9 Modeling Materials 136
8.10 Modeling an Oscillator 144
8.11 Analyzing Stability 148
8.12 Discussion 151
9 Causality 153
9.1 What Is Causality? 153
9.2 Causality in QP Theory 156
9.3 Causality via Propagation 160
9.3.1 Causality in Confluence Models 160
9.3.2 Causal Ordering 161
9.4 Other Notions of Causality in Cognitive Science 163
9.5 Summary 164
10 Qualitative Simulation and Reasoning about Change 165
10.1 Qualitative Simulation 165
10.2 Existence and Continuity 168
10.3 Correctness of Qualitative Reasoning 171
10.3.1 Phase Space 172