Handbook of Quantum Logic and Quantum Structures: Quantum Logic

Front Cover
Kurt Engesser, Dov M. Gabbay, Daniel Lehmann
Elsevier, Jun 16, 2009 - Mathematics - 726 pages
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.

• Authored by eminent scholars in the field
• Material presented is of recent origin representing the frontier of the subject.
• Provides the most comprehensive and varied discussion of Quantum Mechanics available.
 

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Contents

Chapter 1 The Birkhoffvon Neumann Concept of Quantum Logic
1
Chapter 2 Is Quantum Logic a Logic?
23
Chapter 3 Is Logic Empirical?
49
Chapter 4 Quantum Axiomatics
79
Chapter 5 Quantum Logic and Nonclassical Logics
127
Chapter 6 Gentzen Methods in Quantum Logic
227
Chapter 7 Categorical Quantum Mechanics
261
Chapter 8 Extending Classical Logic for Reasoning about Quantum Systems
325
A Survey and Analysis
389
Chapter 11 Test Spaces
443
Chapter 12 Contexts in Quantum Classical and Partition Logic
551
Chapter 13 Nonmonotonicity and Holicity in Quantum Logic
587
Chapter 14 A Quantum Logic of Down Below
625
Chapter 15 A Completeness Theorem of Quantum Set Theory
661
Index
703
Copyright

Chapter 9 Solèrs Theorem
373

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About the author (2009)

Dov M. Gabbay is Augustus De Morgan Professor Emeritus of Logic at the Group of Logic, Language and Computation, Department of Computer Science, King's College London. He has authored over four hundred and fifty research papers and over thirty research monographs. He is editor of several international Journals, and many reference works and Handbooks of Logic.

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