Computational Logic and Set Theory Applying Formalized Logic to Anal
As computer software becomes more complex, the question of how its correctness can be assured grows ever more critical. Formal logic embodied in computer programs is an important part of the answer to this problem.This must-read text presents the pioneeri
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Jacob T. Schwartz Domenico Cantone Eugenio G. Omodeo
Computational Logic and Set Theory Applying Formalized Logic to Analysis
Foreword by Martin Davis
Prof. Dr. Jacob T. Schwartz (January 9, 1930–March 2, 2009) New York University New York, NY USA Prof. Domenico Cantone Dept. of Mathematics & Computer Science University of Catania Viale Andrea Doria 6 95125 Catania Italy [email protected]
Prof. Eugenio G. Omodeo Dept. of Mathematics & Computer Science University of Trieste Via Valerio 12/1 34127 Trieste, Italy [email protected]
ISBN 978-0-85729-807-2 e-ISBN 978-0-85729-808-9 DOI 10.1007/978-0-85729-808-9 Springer London Dordrecht Heidelberg New York British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Control Number: 2011934034 © Springer-Verlag London Limited 2011 Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licenses issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publishers. The use of registered names, trademarks, etc., in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant laws and regulations and therefore free for general use. The publisher makes no representation, express or implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that may be made. Cover design: VTeX UAB, Lithuania Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Jacob Theodore “Jack” Schwartz (January 9, 1930–March 2, 2009), courtesy of Diana Robinson Schwartz
Foreword
Jack Schwartz, the principal, but alas posthumous, author of this book, turned his serious attention to computer science in the mid 1960s. At the time he had already been recognized as a brilliant young mathematician, and the two volumes of the magisterial Dunford–Schwartz Linear Operators already in print were widely admired. Jack saw that computers were going to have a revolutionary effect and that the expansions of their use would give rise to many fundamental problems, and he wanted to be part of that. He realized that as software became more complex the question of how its correctness could be ensured would become ever more critical. Moreover he saw formal logic embodied in computer programs as an important part of the answer. A substantial part of Jack’s research program in computer science derived from his appreciation of the possibility of expressing mathematical discourse in the language of set theory. In much the same way that the seven
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