Engesser K., Gabbay D.M., Lehmann D. (eds.) Handbook of Quantum Logic and Quantum Structures: Quantum Logic

Elsevier, 2009. - 715 pp.
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.Foreword (by Anatolij Dvurecenskij).
Editorial Preface (by Kurt Engesser, Dov Gabbay and Daniel Lehmann).
The Birkhoff-von Neumann Concept of Quantum Logic (by Miklos Redei).
Is Quantum Logic a Logic (by Mladen Pavicic and Norman D. Megill).
Is Logic Empirical (by Guido Bacciagaluppi).
Quantum Axiomatics (by Diederik Aerts).
Quantum Logic and Nonclassical Logics (by Gianpiero Cattaneo, Maria Luisa Dalla Chiara, Roberto Giuntini and Francesco Paoli).
Gentzen Methods in Quantum Logic (by Hirokazu Nishimura).
Categorical Quantum Mechanics (by Samson Abramsky and Bob Coecke).
Extending Classical Logic for Reasoning about Quantum Systems (by Rohit Chadha, Paulo Mateus, Amicar Sernadas and Cristina Sernadas).
Soler's Theorem (by Alexander Prestel).
Operational Quantum Logic: A Survey and Analysis (by David J. Moore and Frank Valckenborgh).
Test Spaces (by Alexander Wilce).
Contexts in Quantum, Classical and Partition Logics (by Karl Svozil).
Nonmonotonicity and Holicity in Quantum Logic (by Kurt Engesser, Dov Gabbay and Daniel Lehmann).
A Quantum Logic of Down Below (by Peter D.Bruza, Dominic Widdows and John H.Woods).
A Completeness Theorem of Quantum Set Theory (by Satoko Titani).