Chiara M.D., Giuntini R., Greechie R. Reasoning in Quantum Theory: Sharp and Unsharp Quantum Logics

Springer, 2004. — 319 p. — (Trends in Logic Studia Logica Library 22). — ISBN: 9048165628."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.Mathematical and Physical Background
The mathematical scenario of quantum theory and von Neumann’s axiomatization
Abstract axiomatic foundations of sharp QT
Back to Hilbert space
The emergence of fuzzy events in Hilbert space quantum theory
Effect algebras and quantum MV algebras
Abstract axiomatic foundations of unsharp quantum theory
To what extent is quantumambiguity ambiguous?
Quantum Logics as Logic
Sharp quantum logics
Metalogical properties and anomalies of quantum logic
An axiomatization of OL and OQL
The metalogical intractability of orthomodularity
First-order quantum logics and quantum set theories
Partial classical logic, the Lindenbaum property and the hidden variable problem
Unsharp quantum logics
The Brouwer Zadeh logics
Partial quantum logics and Lukasiewicz’ quantum logic
Quantum computational logic