Handbook of Spatial Logics
A spatial logic is a formal language interpreted over any class of structures featuring geometrical entities and relations, broadly construed. In the past decade, spatial logics have attracted much attention in response to developments in such diverse fie
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Handbook of Spatial Logics
HANDBOOK OF SPATIAL LOGICS
HANDBOOK OF SPATIAL LOGICS
Edited by
MARCO AIELLO University of Groningen
IAN PRATT-HARTMANN University of Manchester and
JOHAN VAN BENTHEM University of Amsterdam
A C.I.P. Catalogue record for this book is available from the Library of Congress.
ISBN 978-1-4020-5586-7 (HB) ISBN 978-1-4020-5587-4 (e-book)
Published by Springer, P.O. Box 17, 3300 AA Dordrecht, The Netherlands. www.springer.com
Cover Design by Lorenzo Rumori
Printed on acid-free paper
All Rights Reserved c 2007 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.
Preface
Space, with its manifold layers of structure, has been an inexhaustible source of intellectual fascination since Antiquity. The science that began with the empirical discoveries of the Egyptian ‘rope-stretchers’, and that has inspired many of the greatest developments in mathematics over the centuries, now comprises such topics as spatial databases, automated geometrical reasoning and digital image processing. In this long intellectual history, however, one relatively recent, yet crucial, event stands out: the rise of the logical stance in geometry. Fundamental to this development is the analysis of geometrical structures in relation to the formal languages used to describe them, and the recognition of the special mathematical challenges—and opportunities—which such an analysis presents. The interplay between logic and geometry is the subject of this book. By a spatial logic, we mean any formal language for describing geometrical entities and configurations, where ‘geometrical’ is understood in a broad sense. Unlike their well-studied temporal counterparts, spatial logics have been curiously neglected in the literature on mathematical logic, despite some early pioneering work by Tarski and others on the foundations of geometry and topology in the middle years of the previous century. Only in the last decade have spatial logics attracted renewed attention from logicians, partly as a response to work in such diverse fields as artificial intelligence, database theory, physics and philosophy. Today, there is a fast-growing body of literature on spatial logics, with motivations ranging from computational issues to the foundations of knowledge and information. But, for the newcomer to the field, this diversity of influences and approaches constitutes something of a mixed blessing: the field may be in a state of rapid development; but there is as yet no common research agenda, and no common vocabulary to allow ideas to be shared across disciplines. The aim of this book is to provide a resource which presents a view of the best current work in different communities
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