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Reasoning in Quantum Theory: Sharp and Unsharp Quantum Logics

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"Is quantum logic really logic?" This book argues for a positive answer to this question once and for all. There are many quantum logics and their structures are delightfully varied. The most radical aspect of quantum reasoning is reflected in unsharp quantum logics, a special heterodox branch of fuzzy thinking.
For the first time, the whole story of Quantum Logic is told; from its beginnings to the most recent logical investigations of various types of quantum phenomena, including quantum computation. Reasoning in Quantum Theory is designed for logicians, yet amenable to advanced graduate students and researchers of other disciplines.

Author(s): M. Dalla Chiara, R. Giuntini, R. Greechie (auth.)
Series: Trends in Logic 22
Edition: 1
Publisher: Springer Netherlands
Year: 2004

Language: English
Pages: 298
Tags: Order, Lattices, Ordered Algebraic Structures;Quantum Physics;Mathematical Logic and Foundations;Philosophy of Science

Front Matter....Pages i-xxi
Front Matter....Pages 1-8
The mathematical scenario of quantum theory and von Neumann’s axiomatization....Pages 9-40
Abstract axiomatic foundations of sharp QT....Pages 41-64
Back to Hilbert space....Pages 65-74
The emergence of fuzzy events in Hilbert space quantum theory....Pages 75-85
Effect algebras and quantum MV algebras....Pages 87-113
Abstract axiomatic foundations of unsharp quantum theory....Pages 115-135
To what extent is quantum ambiguity ambiguous?....Pages 137-145
Front Matter....Pages 147-154
Sharp quantum logics....Pages 155-169
Metalogical properties and anomalies of quantum logic....Pages 171-177
An axiomatization of OL and OQL....Pages 179-183
The metalogical intractability of orthomodularity....Pages 185-191
First-order quantum logics and quantum set theories....Pages 193-200
Partial classical logic, the Lindenbaum property and the hidden variable problem....Pages 201-216
Unsharp quantum logics....Pages 217-223
The Brouwer Zadeh logics....Pages 225-236
Partial quantum logics and Łukasiewicz’ quantum logic....Pages 237-247
Quantum computational logic....Pages 249-266
Conclusions....Pages 267-269
Back Matter....Pages 271-298