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HANDBOOK OF PHILOSOPHICAL LOGIC 2nd Edition Volume 2 edited by D.M. Gabbay andF. Guenthner

Volume 1- ISBN 0-7923-7018-X Volume 2 - ISBN 0-7923-7126-7

HANDBOOK OF PHILOSOPHICAL LOGIC 2nd EDITION

VOLUME2 Edited by

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

u.K.

and

F. GUENTHNER Centrum für Informations- und Sprachverarbeitung, Ludwig-Maximilians-Universität München, Germany

,~ SPRINGER-SCIENCE+BUSINESS MEDIA B.V.

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

ISBN 978-94-017-0452-6 (eBook) ISBN 978-90-481-5753-2 DOI 10.1007/978-94-017-0452-6

Printed on acid-free paper

All Rights Reserved © 2001 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 2001 Softcover reprint ofthe hardcover 2nd edition 2001 No part of 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

Editorial Preface Dov M. Gabbay Systems of Deduction Göran Sundholm Alternatives to Standard First-order Semantics Hugues Leblanc

Vll

1 53

Algebraic Logic Hajnal Andreka, Istvan N emeti and Ildiko Sain

133

Basic Many-valued Logic Alisdair U rquhart

249

Advanced Many-valued Logics Reiner Hähnle

297

Index

397

PREFACE TO THE SECOND EDITION It is with great pleasure that we are presenting to the community the second edition of this extraordinary handbook. It has been over 15 years 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, as weIl as to consumers of logic in many applied areas. The main logic artiele in the Encyelopaedia 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 be just as good.! The first edition was the second handbook published for the logic community. It followed the North Holland one volume Handbook 0/ Mathematical Logic, published in 1977, edited by the late Jon Barwise. The four volume Handbook 0/ Philosophical Logic, published 1983-1989 came at a fortunate temporal junction at the evolution of logic. This was the time when logic was gaining ground in computer science and artificial intelligence cireles. These areas were under increasing commercial pressure to provide devices which help andjor replace the human in his daily activity. This pressure required the use of logic in the modelling of human activity and organisation on the one hand and to provide the theoretical basis for the computer program constructs on the other. The result was that the Handbook 0/ Philosophical Logic, which covered most of the areas needed from logic for these active communities, became their bible. The increased demand