Handbook of Quantum Logic and Quantum Structures: Quantum Logic

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.

Table of Contents:
Foreword -Dvurecenski Editorial Preface -Engesser-Gabbay-Lehmann 1.) The Birkho®-von Neumann Concept of Quantum Logic -Redei 2.) Quantum Logic a Logic -Pavicic-MegillIs 3.) Is Logic Empirical -Bacciagaluppi 4.) Quantum Axiomatics -Aerts 5.) Quantum Logic and Nonclassical Logics -Cattaneo-Dalla Chiara-Giuntini-Paoli 6.) Soler's Theorem -Prestel 7.) Operational Quantum Logic: A Survey and Analysis -Moore-Valckenborgh 8.) Test Spaces -Wilce 9.) Lehmann Nonmonotonicity and Holicity in Quantum Logic -Engesser-Gabbay- 10.) Gentzen Methods in Quantum Logic -Nishimura 11.) Extending Classical Logic for Reasoning about Quantum Systems - Chadha-Mateus-Sernadas-Sernadas 12.) Quantum Logic and Categorical Logic -Abramsky-Coecke 13.) Quantum Logic and Linear Logic -Abramsky-Coecke 14.) Contexts in Quantum, Classical and Partition Logics -Svozil 15.) A Quantum Logic of Down Below -Bruza-Widdows-Woods 16.) A Completeness Theorem of Quantum Set Theory -Titani