Quantum Physics, Fuzzy Sets and Logic [electronic resource] : Steps Towards a Many-Valued Interpretation of Quantum Mechanics / by Jarosław Pykacz.
Series: SpringerBriefs in PhysicsPublisher: Cham : Springer International Publishing : Imprint: Springer, 2015Description: VI, 70 p. online resourceContent type:- text
- computer
- online resource
- 9783319193847
- 530.12 23
- QC173.96-174.52

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 -- Birkhoff–von Neumann quantum logic as infinite-valued Łukasiewicz logic -- Perspectives -- The many-valued interpretation of quantum mechanics.
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.