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TEMPORAL LOGIC
Studies in Linguistics and Philosophy
Volume 57
Managing Editors
GENNARO CHIERCHIA, University of Milan
PAULINE JACOBSON, Brown University
FRANCIS J. PELLETIER, University of Alberta
Editorial Board
JOHAN VAN BENTHEM, University of Amsterdam
GREGORY N. CARLSON, University of Rochester
DAVID DOWTY, Ohio State University, Columbus
GERALD GAZDAR, University of Sussex, Brighton
IRENE HEIM, M./.T., Cambridge
EWAN KLEIN, University of Edinburgh
BILL LADUSAW, University of California at Santa Cruz
TERRENCE PARSONS, University of California, lrvine
The titles published in this series are listed at the end of this volume.
TEMPORAL LOGIC
From Ancient Ideas to Artificial Intelligence
by
PETER OHRSTROM
Department of Communication,
Aalborg University, Denmark
and
PER F. V. HASLE
Department of Information Science,
University of Aarhus, Denmark
KLUWER ACADEMIC PUBLISHERS
DORDRECHT
/ BOSTON / LONDON
Library of Congress Cataloging-in-Publication Data
~hrstrem, Peter.
Temporal
logic :
From
ancient ideas to artlflclal Intelligence
/
by Peter Ohrstrem and Per F.V. Hasle.
p. cm. -- (Studles in linguist~cs and philosophy
;
v. 57)
Includes bibliographical references and index.
ISBN 0-7923-3586-4 (hb . alk. paper)
1. Tense (Logic) 2. Logic, Symbolic and mathematical. 3. Time.
I. Haste, Per F. V. II. Title. III. Series.
BC199.T4037 1995
160--dc20 95-22191
ISBN 0-7923-3586-4
Published by Kluwer Academic Publishers,
P.O. Box 17, 3300 AA Dordrecht, The Netherlands.
Kluwer Academic Publishers incorporates
the publishing programmes of
D. Reidel, Martinus Nijhoff, Dr W. Junk and MTP Press.
Sold and distributed in the U.S.A. and Canada
by Kluwer Academic Publishers,
101 Philip Drive, Norwell, MA 02061, U.S.A.
In all other countries, sold and distributed
by Kluwer Academic Publishers Group,
P.O. Box 322, 3300 AH Dordrecht, The Netherlands.
Printed on acid-free paper
All Rights Reserved
© 1995 Kluwer Academic Publishers
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,
including photocopying, recording or by any information storage and
retrieval system, without written permission from the copyright owner.
Printed in the Netherlands
TABLE OF CONTENTS
PREFACE .............................................................................................................. ~i
INTRODUCTION ........................................................................................................ 1
PART 1.
1.1.
1.2.
1.3.
1.4.
1.5.
1.6.
1.7.
1.8.
1.9.
1.10.
1.11.
PART 2.
2.1.
2.2.
2.3.
2.4.
2.5.
2.6.
2.7.
2.8.
2.9.
TIMEAND IA~C ........................................................................... 6
The Sea-fight Tomorrow ........................................................ 10
The Master Argument of Diodorus Cronus ................. 15
The Study of Tenses in the Middle Ages ......................... 33
Temporal Ampliation ............................................................... 39
The Duration of the Present ................................................. 43
The Logic of Beginning and Ending ................................. 52
Time and Consequentia .......................................................... 65
Temporalis - the Logic of"While'. ....................................... 71
Human Freedom and Divine Foreknowledge ............ 87
The Downfall of Medieval Tense-logic .......................... 109
Logic as a Timeless Science ................................................. 114
TIME AND LOGIC REUNITED ............................................. 118
The 19th century and Boolean logic .............................. 122
C.S. Peirce on Time and Modality ................................... 128
Lukasiewicz's Contribution to Temporal logic .......... 149
A Three-Point Structure of Tenses ................................. 155
A. N. Prior's Tense-logic ........................................................ 167
The Idea of Branching Time .............................................. 180
Tense Logic and Special Relativity .................................. 197
Some Basic Systems of Temporal Logic ........................ 203
Four Grades of Tense-Logical Involvement .............. 216
V
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