Reasoning In Quantum Theory: Sharp And Unsharp Quantum Logics

REASONING IN QUANTUM THEORY TRENDS IN LOGIC Studia Logica Library VOLUME 22 Managing Editor Ryszard Wójcicki, Institute of Philosophy and Sociology, Polish Academy of Sciences, Warsaw, Poland Editors Vincent F. Hendricks, Department of Philosophy and Science Studies, Roskilde University, Denmark Daniele Mundici, Department of Mathematics “Ulisse Dini”, University of Florence, Italy Ewa Orłowska, National Institute of Telecommunications, Warsaw, Poland Krister Segerberg, Department of Philosophy, Uppsala University, Sweden 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 Ryszard Wójcicki The titles published in this series are listed at the end of this volume. REASONING IN QUANTUM THEORY Sharp and Unsharp Quantum Logics by M. DALLA CHIARA University of Florence, Italy R. GIUNTINI University of Cagliari, Italy and R. GREECHIE Louisiana Tech University, Ruston, U.S.A. SPRINGER-SCIENCE+BUSINESS MEDIA, B.V. A C.I.P. Catalogue record for this book is available from the Library of Congress. ISBN 978-90-481-6562-9 ISBN 978-94-017-0526-4 (eBook) DOI 10.1007/978-94-017-0526-4 Printed on acid-free paper All Rights Reserved © 2004 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 2004 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 List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxi PART I Mathematical and Physical Background . . . . . . . 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Chapter 1. 1.1. 1.2. 1.3. 1.4. 1.5. The mathematical scenario of quantum theory and Neumann’s axiomatization . . . . . . . . . . . . . . Algebraic structures . . . . . . . . . . . . . . . . . . . . The geometry of quantum theory . . . . . . . . . . . . . The axiomatization of orthodox QT . . . . . . . . . . . . The “logic” of the quantum events . . . .