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Pykacz J. Quantum Physics, Fuzzy Sets and Logic. Steps Towards a Many-Valued Interpretation of Quantum Mechanics

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Pykacz J. Quantum Physics, Fuzzy Sets and Logic. Steps Towards a Many-Valued Interpretation of Quantum Mechanics
Springer International Publishing, 2015 — 70p. — (SpringerBriefs in Physics) — ISBN: 978-3-319-19384-7 (eBook), 978-3-319-19383-0 (Softcover).
This Brief presents steps towards elaborating a new interpretation of quantum mechanics based on a specific version of Łukasiewicz infinite-valued logic. It begins with a short survey of main interpretations of quantum mechanics already proposed, as well as various models of many-valued logics and previous attempts to apply them for the description of quantum phenomena. The prospective many-valued interpretation of quantum mechanics is soundly based on a theorem concerning the isomorphic representation of Birkhoff-von Neumann quantum logic in the form of a special Łukasiewicz infinite-valued logic endowed with partially defined conjunctions and disjunctions.
Contents:
Introduction
A Brief Survey of Main Interpretations of Quantum Mechanics
A Brief Survey of Many-Valued Logics
Fuzzy Sets and Many-Valued Logics
Many-Valued Logics in Quantum Mechanics
Birkhoff-von Neumann Quantum Logic
B-vN Quantum Logic as as \(\infty \) -Valued Łukasiewicz Logic
Perspectives
The Many-Valued Interpretation of Quantum Mechanics
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