Handbook of Quantum Logic and Quantum Structures

Quantum Logic

Edited by

  • Kurt Engesser, Kings College London, London, UK
  • Dov M. Gabbay, King's College London, UK
  • Daniel Lehmann, Hebrew University of Jerusalem, Israel

Quantum mechanics is said to be the most successful physical theory ever. It is, in fact, unique in its success when applied to concrete physical problems. On the other hand, however, it raises profound conceptual problems that are equally unprecedented. Quantum logic, the topic of this volume, can be described as an attempt to cast light on the puzzle of quantum mechanics from the point of view of logic. Since its inception in the famous 1936 paper by Birkhoff and von Neumann entitled, “The logic of quantum mechanics,” quantum logic has undergone an enormous development. Various schools of thought and approaches have emerged, and there are a variety of technical results. The chapters of this volume constitute a comprehensive presentation of the main schools, approaches and results in the field of quantum logic.
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Book information

  • Published: November 2008
  • Imprint: ELSEVIER
  • ISBN: 978-0-444-52869-8

Table of Contents

Foreword -DvurecenskiEditorial Preface -Engesser-Gabbay-Lehmann1.) The Birkho®-von Neumann Concept of Quantum Logic -Redei2.) Quantum Logic a Logic -Pavicic-MegillIs3.) Is Logic Empirical -Bacciagaluppi4.) Quantum Axiomatics -Aerts5.) Quantum Logic and Nonclassical Logics -Cattaneo-Dalla Chiara-Giuntini-Paoli6.) Soler's Theorem -Prestel7.) Operational Quantum Logic: A Survey and Analysis -Moore-Valckenborgh8.) Test Spaces -Wilce9.) Lehmann Nonmonotonicity and Holicity in Quantum Logic -Engesser-Gabbay-10.) Gentzen Methods in Quantum Logic -Nishimura11.) Extending Classical Logic for Reasoning about Quantum Systems - Chadha-Mateus-Sernadas-Sernadas12.) Quantum Logic and Categorical Logic -Abramsky-Coecke13.) Quantum Logic and Linear Logic -Abramsky-Coecke14.) Contexts in Quantum, Classical and Partition Logics -Svozil15.) A Quantum Logic of Down Below -Bruza-Widdows-Woods16.) A Completeness Theorem of Quantum Set Theory -Titani