A P P L I E D L O G I C S E R I E S
34
Rigid Flexibility
The Logic of Intelligence
Pei Wang
Rigid Flexibility
APPLIED LOGIC SERIES
VOLUME 34
Managing Editor
Dov M. Gabbay, Department of Computer Science, King’s College, London,
U.K.
Co-Editor
Jon Barwise†
Editorial Assistant
Jane Spurr, Department of Computer Science, King’s College, London, U.K.
SCOPE OF THE SERIES
Logic is applied in an increasingly wide variety of disciplines, from the traditional subjects
of philosophy and mathematics to the more recent disciplines of cognitive science, computer
science, artificial intelligence, and linguistics, leading to new vigor in this ancient subject.
Kluwer, through its Applied Logic Series, seeks to provide a home for outstanding books and
research monographs in applied logic, and in doing so demonstrates the underlying unity and
applicability of logic.
The titles published in this series are listed at the end of this volume.
Rigid Flexibility
The Logic of Intelligence
by
Pei Wang
Temple University, Philadelphia, USA
A C.I.P. Catalogue record for this book is available from the Library of Congress.
ISBN-10 1-4020-5044-5 (HB)
ISBN-13 978-1-4020-5044-2 (HB)
ISBN-10 1-4020-5045-3 (e-book)
ISBN-13 978-1-4020-5045-3 (e-book)
Published by Springer,
P.O. Box 17, 3300 AA Dordrecht, The Netherlands.
www.springer.com
Printed on acid-free paper
All Rights Reserved
© 2006 Springer
No part of this work 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, with the exception
of any material supplied specifically for the purpose of being entered
and executed on a computer system, for exclusive use by the purchaser of the work.
Printed in the Netherlands
Contents
Preface
Acknowledgment
I Theoretical Foundation
xi
xv
1
1 The Goal of Artificial Intelligence
3
1.1 To define intelligence . . . . . . . . . . . . . . . . . . . .
3
1.2 Various schools in AI research . . . . . . . . . . . . . . . 11
1.3 AI as a whole . . . . . . . . . . . . . . . . . . . . . . . . 20
2 A New Approach Toward AI
29
2.1 To define AI . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.2
Intelligent reasoning systems . . . . . . . . . . . . . . . . 37
2.3 Major design issues of NARS . . . . . . . . . . . . . . . 42
II Non-Axiomatic Reasoning System
47
3 The Core Logic
49
3.1 NAL-0: binary inheritance . . . . . . . . . . . . . . . . . 49
3.2 The language of NAL-1 . . . . . . . . . . . . . . . . . . . 57
3.3 The inference rules of NAL-1 . . . . . . . . . . . . . . . . 69
4 First-Order Inference
91
4.1 Compound terms . . . . . . . . . . . . . . . . . . . . . . 91
4.2 NAL-2: sets and variants of inheritance . . . . . . . . . . 92
v
vi
Contents
4.3 NAL-3: intersections and differences . . . . . . . . . . . . 100
4.4 NAL-4: products, images,
and ordinary relations
. . . . . . . . . . . . . . . . . . . 109
5 Higher-Order Inference
115
5.1 NAL-5: statements as terms . . . . . . . . . . . . . . . . 115
5.2 NAL-6: statements with variables . . . . . . . . . . . . . 127
5.3 NAL-7: temporal statements . . . . . . . . . . . . . . . . 134
5.4 NAL-8: procedural statements . . . . . . . . . . . . . . . 138
6 Inference Control
149
6.1 Task management . . . . . . . . . . . . . . . . . . . . . . 150
6.2 Memory structure . . . . . . . . . . . . . . . . . . . . . . 158
6.3
. . . . . . . . . . . . . . . . . . . . . 162
Inference processes
. . . . . . . . . . . . . . . . . . . . . 165
6.4 Budget assessment
III Comparison and Discussion
171
7 Semantics
173
7.1 Experience vs. model
. . . . . . . . . . . . . . . . . . . . 174
7.2 Extension and intension . . . . . . . . . . . . . . . . . . 183
7.3 Meaning of term . . . . . . . . . . . . . . . . . . . . . . 189
7.4 Truth of statement . . . . . . . . . . . . . . . . . . . . . 195
8 Uncertainty
201
8.1 The non-numerical approaches . . . . . . . . . . . . . . . 201
8.2 The fuzzy approach . . . . . . . . . . . . . . . . . . . . . 206
8.3 The Bayesian approach . . . . . . . . . . . . . . . . . . . 219
8.4 Other probabilistic approaches . . . . . . . . . . . . . . . 236
8.5 Unified representation of uncertainty . . . . . . . . . . . 241
9 Inference Rules
245
9.1 Deduction . . . . . . . . . . . . . . . . . . . . . . . . . . 245
9.2
Induction . . . . . . . . . . . . . . . . . . . . . . . . . . 253
9.3 Abduction . . . . . . . . . . . . . . . . . . . . . . . . . . 263
9.4
Implication . . . . . . . . . . . . . . . . . . . . . . . . . 265
Contents
vii
10 NAL as a Logic
271
10.1 NAL as a term logic
. . . . . . . . . . . . . . . . . . . . 271
10.2 NAL vs. predicate logic . . . . . . . . . . . . . . . . . . . 278
. . . . . . . . . . . . . . . . . . . . . . . . 285
10.3 Logic and AI
11 Categorization and Learning
297
11.1 Concept and categorization . . . . . . . . . . . . . . . . 297
11.2 Learning in NARS . . . . . . . . . . . . . . . . . . . . . 310
12 Control and Computation
319
12.1 NARS and theoretical computer science . . . . . . . . . . 319
12.2 Various assumptions about resources
. . . . . . . . . . . 331
12.3 Dynamic natures of NARS . . . . . . . . . . . . . . . . . 338
IV Conclusions
345
13 Current Results
347
13.1 Theoretical foundation . . . . . . . . . . . . . . . . . . . 347
13.2 Formal model
. . . . . . . . . . . . . . . . . . . . . . . . 351
13.3 Computer implementation . . . . . . . . . . . . . . . . . 354
14 NARS in the Future
357
14.1 Next steps of the project . . . . . . . . . . . . . . . . . . 357
14.2 What NARS is not . . . . . . . . . . . . . . . . . . . . . 364
. . . . . . . . . . . . . . . . . . . . 367
14.3 General implications
Bibliography
Index
371
399