Handbook of Quantum Logic and Quantum Structures: Quantum Structures

Front Cover
Kurt Engesser, Dov M. Gabbay, Daniel Lehmann
Elsevier, Aug 11, 2011 - Computers - 818 pages
Since its inception in the famous 1936 paper by Birkhoff and von Neumann entitled “The logic of quantum mechanics quantum logic, i.e. the logical investigation of quantum mechanics, has undergone an enormous development. Various schools of thought and approaches have emerged and there are a variety of technical results.

Quantum logic is a heterogeneous field of research ranging from investigations which may be termed logical in the traditional sense to studies focusing on structures which are on the border between algebra and logic. For the latter structures the term quantum structures is appropriate.

The chapters of this Handbook, which are authored by the most eminent scholars in the field, constitute a comprehensive presentation of the main schools, approaches and results in the field of quantum logic and quantum structures. Much of the material presented is of recent origin representing the frontier of the subject.

The present volume focuses on quantum structures. Among the structures studied extensively in this volume are, just to name a few, Hilbert lattices, D-posets, effect algebras MV algebras, partially ordered Abelian groups and those structures underlying quantum probability.

- Written by eminent scholars in the field of logic
- A comprehensive presentation of the theory, approaches and results in the field of quantum logic
- Volume focuses on quantum structures
 

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Contents

List of Authors
xi
Table of Contents
xv
Chapter 1 New Quantum Structures
1
Chapter 2 Quantum Structures and Fuzzy Set Theory
55
Chapter 3 Algebraic and Measuretheoretic Properties of Classes of Subspaces of an Inner Product Space
75
Chapter 4 Quantum Probability
121
Chapter 5 Quantum Logics as Underlying Structures of Generalized Probability Theory
147
Chapter 6 Quantum Logic and Partially Ordered Abelian Groups
215
Chapter 9 DPosets
367
Chapter 10 Wigners Theorem and its Generalizations
429
Chapter 11 Propositional Systems Hilbert Lattices and Generalized Hilbert Spaces
477
Chapter 12 Equations and Hilbert Lattices
525
Chapter 13 The Source of the Orthomodular Law
555
Chapter 14 Starting from the Convex Set of States
587
Chapter 15 Quantum Logic and Automata Theory
619
Chapter 16 Quantum Logic and Quantum Computation
755

Chapter 7 Quantum Structures and Operator Algebras
285
Chapter 8 Constructions of Quantum Structures
335

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Page xiii - Department of Computer Science and Technology Tsinghua University Beijing 100084, PR China...
Page 50 - Free sums of groups and their generalizations. An analysis of the associative law', Amer.
Page 790 - This volume contains the proceedings of the Workshop on Quantum Logic held in Erice (Sicily), December 2-9, 1979, at the Ettore Majorana Center for Scientific Culture.

About the author (2011)

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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