Substructural Logics: A Primer
Substructural logics are by now one of the most prominent branches of the research field usually labelled as "nonclassical logics" - and perhaps of logic tout court. Over the last few decades a vast amount of research papers and even some books have been
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TRENDS IN LOGIC Studia Logica Library VOLUME 13 Managing Editor
Ryszard W6jcicki, Institute of Philosophy and Sociology, Polish Academy of Sciences, Warsaw, Poland Editors
Daniele Mundici, Department of Computer Sciences, University of Milan, Italy Ewa Odowska, National Institute of Telecommunications, Warsaw, Poland
Graham Priest, Department of Philosophy, University of Queensland, Brisbane, Australia
Krister Segerberg, Department of Philosophy, Uppsala University, Sweden
Alasdair Urquhart, Department of Philosophy, University of Toronto, Canada Heinrich Wansing, Institute of Philosophy, Dresden University of Technology, Germany
SCOPE OF THE SERIES Trends in Logic is a bookseries covering essentially the same area as the journal Studia Logica - that is, contemporary formal logic and its applications and
relations to other disciplines. These include artificial intelligence, informatics, cognitive science, philosophy of science, and the philosophy of language. However, this list is not exhaustive, moreover, the range of applications, comparisons and sources of inspiration is open and evolves over time. Volume Editor
Heinrich Wansing
The titles published in this series are listed at the end of this volume.
FRANCESCO PAOLI Universita di Cagliari, Italy
SUB STRUCTURAL LOGICS:
A PRIMER
SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.
A C.I.p. Catalogue record for this book is available from the Library of Congress.
ISBN 978-90-481-6014-3
ISBN 978-94-017-3179-9 (eBook)
DOI 10.1007/978-94-017-3179-9
Printed on acid-free paper
All Rights Reserved © 2002 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 2002 Softcover reprint of the hardcover 1st edition 2002 No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise. without written permission from the Publisher. 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
Preface ....................................................................................................... ix
Part I: The philosophy of substructurallogics Chapter 1. The role of structural rules in sequent calculi .......................... .3
1. The "inferential approach" to logical calculus......................................... 3 1.1 Structural rules, operational rules, and meaning .......................... 5 1.2 Discovering the effects of structural rules .................................. 11 2. Reasons for dropping structural rules.................................................... 15 2.1 Reasons for dropping structural rules altogether ........................ 15 2.2 Reasons for dropping (or eliminating) the cut rule..................... 17 2.3 Reasons for dropping the weakening rules ................................. 21 2.4 Reasons for dropping the contraction rules ..............
