Handbook of Philosophical Logic

such questions for centuries (unrestricted by the capabilities of any hard ware). The principles governing the interaction of several processes, for example, are abstract an similar to principles governing the cooperation of two large organisation. A det

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HANDBOOK ОР PHILOSOPHICAL LOGIC 2nd Edition Volume 6 edited Ьу D.M. Gabbay andF. Guenthncr

HANDBOOK OF PHILOSOPHICAL LOGIC 2nd EDITION VOLUME 6 Edited by

D.M.GABBAY King's College, London,

u.K.

and

F. GUENTHNER Centrumfur lnformations- und Sprachverarbeitung, Ludwig-Maximilians-Universitiit Munchen, Germany

,

~.

SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.

A c.I.P. Catalogue record for this book is available from the Library of Congress.

ISBN 978-90-481-6004-4 ISBN 978-94-017-0460-1 (eBook) DOI 10.1007/978-94-017 -0460-1

Printed on acid-free paper

AII Rights Reserved

© 2002 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 2002 Softcover reprint of the hardcover 2nd edition 2002 No part of this work may be reproduced, stored in a retrieval system, Of transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publishef, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work.

CONTENTS

Editorial Preface Dov M. Gabbay Relevance Logic Mike Dunn and Greg Restall

Vll

1

Quantum Logics Maria-Luisa Dalla Chiara and Roberto Giuntini

129

Combinators, Proofs and Implicational Logics Martin Bunder

229

Paraconsistent Logic Graham Priest

287

Index

395

PREFACE

ТО ТНЕ

SECOND EDITION

It is with great pleasure that we аге presenting to the community the second edition of this extraordinary handbook. It has been over 15 уеагв since the publication of the first edition and there have been great changes in the landscape of philosophical logic since then. The first edition has proved invaluable to generations of students and researchers in formal philosophy and language, ав well as to consumers of logic in тanу applied areas. The main logic article in the Encyclopaedia Britannica 1999 has described the first edition as 'the best starting point for exploring any of the topics in logic'. We are confident that the second edition will prove to Ье just ав good! The first edition was the second handbook published for the logic сотти nity. It followed the North Holland one volume Handbook о/ Mathematical Logic, published in 1977, edited Ьу the late Jon Barwise. The four volume Handbook о/ Philosophical Logic, published 1983-1989 сате at а fortunate temporal junction at the evolution of logic. ТЫв was the time when logic was gaining ground in computer science and artificial intelligence circles. These агеав were under increasing commercial pressure to provide devices which help and/or replace the human in Ыв daily activity. ТЫв pressure required the иве of logic in the modelling of human activity and organisation оп the one hand and to provide the theoretical basis for the computer prograт constructs оп the other. The result was that the Handbook о/ Philosophical Logic, which covered most of the агеав needed from logic for these active communities, Ьесате their bible