Handbook of Philosophical Logic Volume III: Alternatives in Classica
This volume presents a number of systems of logic which can be considered as alternatives to classical logic. The notion of what counts as an alternative is a somewhat problematic one. There are extreme views on the matter of what is the 'correct' logical
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PHILOSOPHICAL LOGIC Volume 111: Alternatives in Classical Logic Eäited by
D. GABBAY Department 0/ Computing, Imperial College, London, England
and
F. GUENTHNER FNS, University o[ Tuebingen, West Germany
SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.
Library of Congress Cataloging-in-Publication Data Main entry under title: Alternatives in c1assicallogic. (Handbook of philosophical logic ; v. 3) (Synthese Iibrary ; v. 166) Inc1udes bibliographies and indexes. 1. Logic - Addresses, essays, lectures. 1. Gabbay, Dov M., 1945 . H. Guenthner, Franz. III. Series. IV. Series: Synthese Iibrary ; v. 166. BC71.A56 1985 160 85-25692 ISBN 978-94-010-8801-5 ISBN 978-94-009-5203-4 (eBook) DOI 10.1007/978-94-009-5203-4
All Rights Reserved © 1986 by Springer Science+Business Media Dordrecht Originally published by D. Reidel Publishing Company in 1986 Softcover reprint of the hardcover 1st edition 1986 No part Qf the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, inc1uding photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner
CONTENTS TO VOLUME III
ACKNOWLEDGEMENTS
~
PREFACE
~
A NOT EON NOT A T IO N
xi
III.I. III.2. II1.3. I1I.4. 111.5.
STEPHEN BLAMEY / Partial Logic ALA SDA IR U R QU H ART / Many-valued Logic
J. M I C H A E L DUN N / Relevance Logic and Entailment D IRK V AND ALE N / Intuitionistic Logic
71 117 225
W A L TE R FE L S CH E R / Dialogues as a Foundation for
Intuitionistic Logic 111.6. ERMANNO BENCIVENGA / Free Logics IIL7. MARIA LUISA DALLA CHIARA / Quantum Logic III.8. GO RAN SUN D H 0 L M / Proof Theory and Meaning
341 373 427 471
NAME INDEX
507
SUBJECT INDEX
513
TAB LEO F CON TEN T S TO VOL U M E S I , II, AND IV
521
ACKNOWLEDGEMENTS
The preparation of the Handbook of Philosophical Logic was generously supported by the Lady Davis Fund at Bar-Han University, Ramat-Gan, Israel and the Werner-Reimers-Stiftung, Bad Homburg, West Germany, which provided us with the chance of discussing the chapters in the Handbook at various workshops with the contributors. It is a great pleasure to acknowledge the assistance of these institutions during the preparation of this collection. We benefitted further from the editorial and personal advice and help from the publisher. Most important of all, we would like to express our thanks to all the contributors to the Handbook for their unlimited goodwill, their professional counsel, as well as their friendly support. They have made the preparation of this collection a stimulating and gratifying enterprise.
(Imperial College, London) GUENTHNER (University of Tuebingen) D. GABBA Y
F.
PREFACE
This volume presents a number of systems of logic which can be considered as alternatives to classical logic. The notion of what counts as an alternative is a somewhat problematic one. There are extreme views on the matter of what is the 'correct' logical system and whether one logical system (e.g. classical logic) can rep
