Dynamic Epistemic Logic
Dynamic Epistemic Logic is the logic of knowledge change. This is not about one logical system, but about a whole family of logics that allows us to specify static and dynamic aspects of multi-agent systems. This book provides various logics to support su
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SYNTHESE LIBRARY STUDIES IN EPISTEMOLOGY, LOGIC, METHODOLOGY, AND PHILOSOPHY OF SCIENCE
Editors-in-Chief:
VINCENT F. HENDRICKS, Roskilde University, Roskilde, Denmark JOHN SYMONS, University of Texas at El Paso, U.S.A.
Honorary Editor: JAAKKO HINTIKKA, Boston University, U.S.A.
Editors: DIRK VAN DALEN, University of Utrecht, The Netherlands THEO A.F. KUIPERS, University of Groningen, The Netherlands TEDDY SEIDENFELD, Carnegie Mellon University, U.S.A. PATRICK SUPPES, Stanford University, California, U.S.A. JAN WOLEN´SKI, Jagiellonian University, Kraków, Poland
VOLUME 337
DYNAMIC EPISTEMIC LOGIC
by
Hans van Ditmarsch University of Otago New Zealand
Wiebe van der Hoek University of Liverpool United Kingdom
Barteld Kooi University of Groningen The Netherlands
A C.I.P. Catalogue record for this book is available from the Library of Congress.
ISBN 978-1-4020-6908-6 (PB) ISBN 978-1-4020-5838-7 (HB) ISBN 978-1-4020-5839-4 (e-book)
Published by Springer, P.O. Box 17, 3300 AA Dordrecht, The Netherlands. www.springer.com
Printed on acid-free paper
All Rights Reserved © 2008 Springer 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 1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Epistemic and Doxastic Logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Dynamic Epistemic Logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Information, Belief, and Knowledge . . . . . . . . . . . . . . . . . . . . . . . .
1 2 3 5
2
Epistemic Logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Basic System: S5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Language . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2 Semantics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.3 Axiomatisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Group Notions of Knowledge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Language . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.2 Semantics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.3 Axiomatisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Logics for Belief . . . . . . . . . . . . . . . . . .
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