Partiality, Modality, and Nonmonotonicity

312 Pages·1996·13.356 MB·Studies in Logic, Language and Information

by  Patrick Doherty

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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: [e-mail]
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: [e-mail]
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: [e-mail]
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: [e-mail]
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: [e-mail]
Tore Langholm is an associate professor at the Department of Informat­
ics, University of Bergen, Hpyteknologisenteret, 5020 Bergen, Norway.
Email: [e-mail]
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: [e-mail]
Ilkka Niemela is an assistant professor at the Department of Computer
Science, Helsinki University of Technology, Otakaari 1, FIN-02150 Espoo,
Finland.
Email: [e-mail]
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: [e-mail]
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: [e-mail]
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 common-
sense 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