Artificial Intelligence

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1 SYMBOLIC COMPUTATION Artificial Intelligence Managing Editor: D.W. Loveland Editors: S. Amarel A. Biermann A. Bundy H. Gallaire A. Joshi D. Lenat E. Sandewall J. Siekmann R. Reiter L. Bolc P. Hayes A. Mackworth W. Wahlster

2 Springer Series SYMBOLIC COMPUTATION - Artificial Intelligence N.J. Nilsson: Principles of Artificial Intelligence. XV, 476 pages, 139 figs., 1982 J.H. Siekmann, G. Wrightson (Eds.): Automation of Reasoning 1. Classical Papers on Computational Logic XII, 525 pages, 1983 J.H. Siekmann, G. Wrightson (Eds.): Automation of Reasoning 2. Classical Papers on Computational Logic XII, 637 pages, 1983 L. Bolc (Ed.): The Design of Interpreters, Compilers, and Editors for Augmented Transition Networks. XI, 214 pages, 72 figs., 1983 M.M. Botvinnik: Computers in Chess. Solving Inexact Search Problems. XIV, 158 pages, 48 figs., 1984 L. Bolc (Ed.): Natural Language Communication with Pictorial Information Systems. VII, 327 pages, 67 figs., 1984 R.S. Michalski, J.G. Carbonell, T.M. Mitchell (Eds.): Machine Learning. An Artificial Intelligence Approach. XI, 572 pages, 1984 A. Bundy (Ed.): Catalogue of Artificial Intelligence Tools. Second, Revised Edition. XVII, 168 pages, 1986 C. Blume, W. Jakob: Programming Languages for Industrial Robots. XIII, 376 pages, 145 figs., 1986 J.W. Lloyd: Foundations of Logic Programming. Second, Extended Edition. XII, 212 pages, 1987 L. Bolc (Ed.): Computational Models of Learning. IX, 208 pages, 34 figs., 1987 L. Bolc (Ed.): Natural Language Parsing Systems. XVIII, 367 pages, 151 figs., 1987 N. Cercone, G. McCalla (Eds.): The Knowledge Frontier, Essays in the Representation of Knowledge. XXXV, 512 pages, 93 figs., 1987 continued after index

3 Yun Peng James A. Reggia Abductive Inference Models for Diagnostic Problem-Solving With 25 Illustrations Springer Science+Business Media, LLC

4 Yun Peng University of Maryland Department of Computer Science College Park, Maryland 20742, USA The Institute of Software Academia Sinica Beijing, China James A. Reggia University of Maryland Department of Computer Science College Park, Maryland USA Library of Congress Cataloging-in-Publication Data Peng, Yun. Abductive inference models for diagnostic problem-solving I Yun Peng, James A. Reggia. p. cm.-(symbolic computation. Artificial intelligence) Includes bibliographical references and index. 1. Problem solving. 2. Artificial inteliigence. 3. Problem solving. 4. Abduction (Logic) 5. Reasoning. 1. Reggia, James A. II. Title. III. Series. Q335.P dc Printed on acid-free paper 1990 Springer Science+Business Media New York Originally published by Springer-Verlag New York Inc in 1990 Softcover reprint ofthe hardcover lst edition 1990 AII rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer-Verlag New York, Inc., 175 Fifth Avenue, New York, NY 10010, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use of general descriptive names, trade names, trademarks, etc., in this publication, even if the former are not especially identified, is not to be taken as a sign that such names, as understood by the Trade Marks and Merchandise Marks Act, may accordingly be used freely by anyone. Camera-ready copy provided by the authors using troff on UNIX ISBN ISBN (ebook) DOI /

5 Preface Making a diagnosis when something goes wrong with a natural or manmade system can be difficult. In many fields, such as medicine or electronics, a long training period and apprenticeship are required to become a skilled diagnostician. During this time a novice diagnostician is asked to assimilate a large amount of knowledge about the class of systems to be diagnosed. In contrast, the novice is not really taught how to reason with this knowledge in arriving at a conclusion or a diagnosis, except perhaps implicitly through ease examples. This would seem to indicate that many of the essential aspects of diagnostic reasoning are a type of intuitionbased, common sense reasoning. More precisely, diagnostic reasoning can be classified as a type of inference known as abductive reasoning or abduction. Abduction is defined to be a process of generating a plausible explanation for a given set of observations or facts. Although mentioned in Aristotle's work, the study of formal aspects of abduction did not really start until about a century ago. The emergence of computational models for various abduetive inference applications in artificial intelligence (AI) and cognitive science is even more recent, having begun little more than a decade ago. Considering the importance of abduetive inference and how widely it is used in everyday life and in numerous special fields, the late emergence of formal and computational models of abduction is somewhat surprising. This is particularly true when contrasted with the maturity of some deductive inference models, such as first order predicate calculus. This book is about reasoning with causal associations during diagnostic problem-solving. It is an attempt to formalize the currently vague notions of abductive inference in the context of diagnosis. The material brings together and synthesizes the efforts of a ten year period of research by the authors and others. The core results were initially developed as a formal theory of diagnostic inference called parsimonious covering theory, and were then extended to incorporate probability theory. Within parsimonious covering theory, various diagnostic problems are formally defined, properties of diagnostic problem-solving are identified and analyzed, and algorithms for finding plausible explanations in different situations are given along with proofs of their correctness. Parsimonious covering theory captures in a precise form many of the important features of the imprecise, intuitive concept of abduction. It not only forms a good theoretical foundation for automated diagnostic problem-solving, but also provides a useful framework for examining other

6 vi Prefuce non-diagnostic applications characterized as abductive problems. Practically, this theory may provide important guiding principles for constructing various diagnostic knowledge-based systems capable of handling a broad range of problems. Of course, the theory developed in this book does not represent a complete theory of abduction, even for diagnostic problem-solving. Nevertheless, we believe it represents a substantial step forward in formalizing some aspects of diagnostic reasoning in a general, application-independent fashion. This book is intended for readers with a background in artificial intelligence or cognitive science. While some of the material involves mathematical derivations, only basic knowledge of elementary set theory, logic and probability theory is assumed. Our emphasis is on developing an intuitive understanding rather than on mathematical rigor. Thus, the intuitions behind the results presented in this book are explained and stressed in the text, while their formal proofs are given in appendices at the ends of appropriate chapters. These appendices can be skipped by those whose primary interests are the methods of parsimonious covering theory and how to apply them to various problems rather than the mathematical develop- ment of the theory. This book is not only suitable for self-study, but could also be used as a text for graduate courses in AI, knowledge engineering, or cognitive science that include material on abductive inference. This book could also be used as a reference source for professionals in these and other related areas. The material in this book is organized as follows. Chapters 1 and 2 informally introduce the reader to the basic characteristics of abductive inference and diagnostic problem-solving. Some computational diagnostic problem-solving systems based on parsimonious covering theory and examples of problem-solving with these systems are presented. This approach is contrasted to other existing computational models of diagnostic reasoning, both to motivate the intuitions behind the theory and to demonstrate its basic features. Chapter 3 presents the basic model of parsimonious covering theory. Diagnostic problems and their solutions are defined in unambiguous mathematical terms, and formal algorithms for finding problem solutions are then developed. This formulation, although based on very simple causal networks, is seen to capture the essence of abductive diagnostic reasoning and can provide a theoretical foundation for a variety of real-world applications. The basic framework of parsimonious covering theory can be extended in various ways to accommodate different types of information. Some of these theoretical extensions are presented in Chapters 4 and 5 where probability theory is incorporated into basic parsimonious covering theory, capturing information about the uncertainty of causal relations. Other extensions are given in Chapter 6 where more general causal networks involving intermediate states and "causal chaining" are used. These

7 vii Preface extensions greatly enhance the breadth and power of parsimonious covering theory and its potential practical applications. One difficulty that arises in developing parsimonious covering theory and other models of abductive diagnosis is the computational complexity involved. For example, in some situations, finding the most probable causative hypothesis for a given set of symptoms/manifestations may take time exponential to the size of the causal network if multiple disorders may occur simultaneously. To circumvent this potentially formidable difficulty, an approximation algorithm based on connectionist modeling is presented in Chapter 7. This model, taking advantage of highly parallel computations, requires a more or less constant amount of time for problem-solving, yet yields very accurate results. It offers an attractive alternative to traditional AI sequential search in diagnostic problemsolving. Finally, Chapter 8 closes the book with concluding remarks about non-diagnostic abduction and future research directions. The development of parsimonious covering theory has benefited from contributions from a number of individuals. These contributions are referenced in the text, including those from Sanjeev Ahuja, Bill Chu, Venu Dasigi, C. Lynne D'Autrechy, Sharon Goodall, Dana Nau, Barry Perricone, Srinivasan Sekar, Malle Tagamets, Stanley Tuhrim, and Pearl Wang. We have been very fortunate in working with such talented collaborators. Finally, we wish to express our thanks to the staff at Springer-Verlag, especially Gerhard Rossbach and Donna Moore, for their help in bringing this book to completion. Yun Peng James A. Reggia College Park, Maryland January, 1990

8 Contents Preface 1 Abduction and Diagnostic Inference 1.1 Abductive Inference 1.2 Abduction as a Class of Logic 1.3 Diagnostic Problem-Solving 1.4 Overview of What Follows Computational Models for Diagnostic Problem Solving 2.1 Knowledge-Based Problem-Solving Systems Structural (Symbolic) and Probabilistic (Numeric) Knowledge Statistical Pattern Classification Production (Rule-Based) Systems 2.2 Association-Based Abductive Models Basic Concepts Parsimonious Covering Theory: An Informal Preview An Example: Chemical Spill! A More Substantial Example of Medical Diagnosis Description of the System An Example Solution 2.3 Some Issues What Is Parsimony? Question Generation and Termination Criteria Contextual Information and Ranking of Hypotheses Answer Justification II II Basics of Parsimonious Covering Theory 49

9 x Contents 3.1 Problem Formulation Diagnostic Problems Solutions for Diagnostic Problems 3.2 Properties of Diagnostic Problems 3.3 An Algebra of Generator-Sets 3.4 Problem-Solving Algorithmic Solution Answer Justification in Parsimonious Covering Theory Problem Decomposition 3.5 Relevance to Abductive Diagnostic Systems Multiple Simultaneous Disorders Assumption Single Disorder Assumption 3.6 Comparison to Other Formalisms Reiter's Theory of Diagnosis from First Principles De Kleer and Williams' GDE Model Josephson et al's Assembly of Composite Hypotheses 3.7 Conclusions 3.8 Appendix Summarizing Set Notation 3.9 Mathematical Appendix Probabilistic Causal Model 4.1 Definitions and Assumptions 4.2 A Probability Calculus Single Disorder Multiple Disorders Relative Likelihood Measures for Hypotheses 4.3 Properties of the Probabilistic Causal Model Relationship to Basic Parsimonious Covering Interdependence Among Disorders and Manifestations Non-Monotonic Evidence Accumulation Relationship to Traditional Bayesian Classification Method 4.4 Comparison to Related Work 4.5 Mathematical Appendix Diagnostic Strategies in the Probabilistic Causal Model 149

10 xi Contents 5.1 Closed Problem-Solving Bounding a Hypothesis An Algorithm for Closed Problems Correctness of Algorithm SEARCH 5.2 Open Problem-Solving Formulation Algorithm and Correctness 5.3 The Quality of Problem Solutions Comfort Measure and Estimating Posterior Probabilities Problem-Solving Strategy Correctness of Algorithms Efficiency Considerations 5.4 Comparison to Related Work Cooper's NESTOR Pearl's Belief Networks 5.5 Mathematical Appendix Causal Chaining 6.1 Problem Formulation and Taxonomy of Causal Networks Diagnostic Problems with Causal Chaining Solutions for Diagnostic Problems 6.2 Solving Layered and Hyper-Bipartite Problems Transitivity of Sets of Irredundant Covers Algorithm LAYERED and Its Correctness Pseudo-Layers in Hyper-Bipartite Problems Algorithm HYPER-BIPARTITE and Its Correctness 6.3 Volunteered Partial Solutions 6.4 Mathematical Appendix Parallel Processing for Diagnostic Problem-Solving 7.1 Connectionist Models and Diagnosis Basics of Connectionist Models Connectionist Modeling of Diagnostic Problem-Solving 7.2 A Specific Connectionist Model Architecture

11 xii Contents 7.3 Equations for Updating Node Activations Optimization Problem Updating m~{t) Updating di(t) 7.4 Experiments and Analysis Basic Experimental Methods and Results Resettling Process Convergence with Multiple-Winners- Take-All Altered Activation Rule Using A Sigmoid Function 7.5 A Medical Application Example 7.6 Summary 7.7 Mathematical Appendix 7.8 Appendix of Experimental Networks Conclusion 8.1 A Summary of Parsimonious Covering Theory 8.2 Generality of the Theory: Non-Diagnostic Application 8.3 Future Research Directions 8.4 A Final Note Bibliography 269 Index 279

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