Proof Theory of Modal Logic
Proof Theory of Modal Logic is devoted to a thorough study of proof systems for modal logics, that is, logics of necessity, possibility, knowledge, belief, time, computations etc. It contains many new technical results and presentations of novel proof pro
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APPLIED LOGIC SERIES VOLUME 2
Managing Editor
Dov M. Gabbay, Department of Computing, Imperial College, London, U.K. Co-Editor Jon Barwise, Department of Philosophy, Indiana University, Bloomington, IN, U.S.A.
Editorial Assistant Jane Spurr, Department of Computing, Imperial 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.
Proof Theory of Modal Logic edited by
HEINRICH WANSING University ofLeipvg, Institute ofLogic and Philosophy ofScience
SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.
Library of Congress Cataloging-in-Publication Data Proof theory of modal logic 1 ed1ted by Heinr1ch Wans1ng. p. cm. -- Proceed1ngs of a workshop held at the Univers1ty of Hamburg. Nov. 19-20, 1993.
Includes index. ISBN 978-90-481-4720-5 ISBN 978-94-017-2798-3 (eBook) DOI 10.1007/978-94-017-2798-3
1. Modal log1c--congresses. 2. Proof theory--Congresses. I. Wansing, H. II. Series. OA9.46.P76 1996 511.3--dc20
96-9019
ISBN 978-90-481-4720-5
Logo design by L. Rivlin
Printed on acid-free paper
All Rights Reserved
1996 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 1996 No part of the material protected by this copyright notice may be reproduced or utilized in any fonn or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without written pennission from the copyright owner.
©
EDITORIAL PREFACE The editors of the Applied Logic Series are pleased to present the second volume in the series, this one on Proof Theory and Modal Logic. In recent years the topic of multi-modal logics has had significant applications in a variety of disciplines, including Artificial Intelligence, theoretical computer science, philosophy, linguistics, Peano arithmetic, and generalized quantifiers. In this volume, leading researchers examine the proof theory of this rich and active field. The Editors
CONTENTS
Preface
ix
I Standard Proof Systems JORG HUDELMAIER A Contraction-free Sequent Calculus for S4
3
GRIGORI MINTS, VLADIMIR OREVKOV AND TANEL TAMMET Transfer of Sequent Calculus Strategies to Resolution for S4
17
HAROLD SCHELLINX A Linear Approach to Modal Proof Theory
33
TOMASZ SKURA Refutations and Proofs in S4
45
II Extended Formalisms EWA ORLOWSKA Relational Proof Systems for Modal Logics
55
NUELBELNAP The Display Problem
79
MARCUS KRACHT Power and Weakness of the Modal Display Calculus
93
HEINRICH WANSING A Proof-theoretic Proof of Functional Completeness for Many Modal and Tense Logics 123
viii RAJEEVGORE On the Completeness of C
