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Language, %X<N « / X Partiality, Modality, and Nonmonotonicity edited by Patrick Doherty The European Association for Logic, Language and information Partiality, Modality, and Nonmonotonicity Studies in Logic, Language and Information The Studies in Logic, Language and Information book series is the official book series of the European Association for Logic, Language and Infor mation (FoLLI). The scope of the book series is the logical and computational foun dations of natural, formal, and programming languages, as well as the different forms of human and mechanized inference and information processing. It covers the logical, linguistic, psychological and informa tion-theoretic parts of the cognitive sciences as well as mathematical tools for them. The emphasis is on the theoretical and interdiscipli nary aspects of these areas. The series aims at the rapid dissemination of research monographs, lecture notes and edited volumes at an affordable price. Managing editor: Robin Cooper, University of Edinburgh Executive editor: Maarten de Rijke, University of Warwick Editorial board: Peter Aczel, Manchester University Nicholas Asher, The University of Austin, Texas Jon Barwise, Indiana University, Bloominton John Etchemendy, CSLI, Stanford University Dov Gabbay, Imperial College, London Hans Kamp, Universitat Stuttgart Godehard Link, Universitat Miinchen Fernando Pereira, AT&T Bell Laboratories, Murray Hill Dag Westerstahl, Stockholm University Partiality, Modality, and Nonm onotonicity Patrick Doherty CSLI Publications Center for the Study of Language and Information Stanford, California & FoLLI The European Association for Logic, Language and Information Copyright ©1996 CSLI Publications Center for the Study of Language and Information Leland Stanford Junior University Printed in the United States 99 98 97 96 5 4 3 2 1 Library of Congress Cataloging-in-Publication Data Partiality, modality, and nonmonotonicity / [edited by] Patrick Doherty. p. cm. — (Studies in logic, language, and information) Includes bibliographical references and index. ISBN 1-57586-031-7 (he : alk. paper). — ISBN 1-57586-030-9 (pbk : alk. paper) 1. Modality (Logic) 2. —Formal languages. 3. Commonsense reasoning. I. Doherty, Patrick, 1957 - . II. Series. QA9.46.P37 1996 006.3'3—dc20 95-50863 CIP © The acid-free paper used in this book meets the minimum requirements of the American National Standard for Information Sciences—Permanence of Paper for Printed Library Materials, ANSI Z39.48-1984. Contents Contributors vii Preface ix Part I Foundations 1 1 How Different is Partial Logic? 3 Tore Langholm 2 Sequent Formalizations of Three-Valued Logic 45 Douglas Busch 3 Modalities for Reasoning about Knowledge and Uncertainties 77 WlEBE VAN DER HOEK AND JOHN-JULES MEYER 4 Fundamentals of Partial Modal Logic 111 Jan Jaspars and Elias Thijsse Part II Case Studies 143 5 A Study in Modal Embeddings of NML3 145 Patrick Doherty and Witold Lukaszewicz 6 A Model-based Approach to Predictive Causal Reasoning 169 John Bell 7 Partial Semantics for Truth Maintenance 197 Cees Witteveen 8 Combining Partial and Classical Semantics. A Hybrid Approach to Belief and Awareness 223 Elias Thijsse V vi / Contents 9 Autoepistemic Logic as a Basis for Automating Nonmonotonic Reasoning 251 Ilkka Niemela Name Index 291 Subject Index 295 Contributors John Bell is a lecturer at the Department of Computer Science, Queen Mary and Westfield College, Mile End Road, London El 4NS, England. Email: [email protected] Douglas Busch is an associate professor at the Department of Computer and System Sciences (DSV), Stockholm University and KTH, Elektrum 230, S-164 40 Kista, Sweden. URL: http://www.dsv.su.se/~dbu/ Email: [email protected] Patrick Doherty is an associate professor at the Department of Com puter and Information Science, Linkoping University, S-581 83 Linkoping, Sweden. URL: http://www.ida.liu.se/labs/rkllab/people/patdo/ Email: [email protected] Wiebe van der Hoek is an assistant professor at the Department of Computer Science, Utrecht University, P.O. Box 80089, 3508 TB Utrecht, the Netherlands. Email: [email protected] Jan Jaspars is a post-doc researcher at the Centre for Mathematics and Computer Science (CWI), P.O. Box 94079, 1090 GB Amsterdam, the Netherlands. Email: [email protected] Tore Langholm is an associate professor at the Department of Informat ics, University of Bergen, Hpyteknologisenteret, 5020 Bergen, Norway. Email: [email protected] Witold Lukaszewicz is a professor at the Institute of Informatics, War saw University, 00-913 Warsaw 59, ul. Banacha 2, Poland. E-mail: witlu@mimuw. edu. pi Vll viii / Contributors John-Jules Meyer is a professor at the Department of Computer Science, Utrecht University, P.O. Box 80089, 3508 TB Utrecht, the Netherlands. Email: [email protected] Ilkka Niemela is an assistant professor at the Department of Computer Science, Helsinki University of Technology, Otakaari 1, FIN-02150 Espoo, Finland. Email: [email protected] Elias Thijsse is a lecturer at the Faculty of Arts, Institute for Language Technology & AI (ITK), Tilburg University, P.O. Box 90153, 5000 LE Tilburg, the Netherlands. Email: [email protected] Cees Witteveen is an assistant professor at the Department of Mathe matics and Computer Science, Delft University of Technology, Julianalaan 132, 2628 BL Delft, The Netherlands. Email: [email protected] Preface This volume contains a collection of articles of both a tutorial and case- study nature. The original idea for such a collection crystalized during a combined summer school and workshop on Partial Logics, Modalities, and Nonmonotonic Reasoning, which took place in May, 1992, and was spon sored in part by both the Nordiska Forskerutbildningsakademin (NorFA) and the Department of Information and Computer Science, Linkoping Uni versity, Sweden. During the workshop, it became clear to the participants that there was an interesting body of work being pursued which combined and integrated a number of specialized approaches to modeling commonsense reasoning. The central problem which was the focus of the workshop and summer school is the formal modeling of reasoning with incomplete information. More specifically, the topic of interest was the use and inte gration of partial logics, modal logics and nonmonotonic logics for knowl edge representation. The approaches described in this volume compare and integrate the use of partial, modal, and nonmonotonic logics for knowledge representation. Each of the articles was written especially for this volume. The volume contains two parts. In Part I, which consists of chapters 1-4, the authors provide articles of a more general tutorial or survey nature, describing partiality, multi-valued logics, the implicit use of modal logic to capture partiality, and finally an integration of modal and partial logics. In Part II, which consists of chapters 5-9, specialized articles are presented which can be viewed as case studies reflecting on particular issues discussed in Part I. In Part II, partial, modal, nonmonotonic, or combinations of these logics, are used to model knowledge representation topics such as default reasoning, theories of action and change, reason maintenance, awareness, and automation of nonmonotonic reasoning. A fair amount of time has been allocated for integrating the various chapters, even though each chapter is self-contained with its own notation and references. Each of the chapters contains a summary and references IX