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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
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