Unification of Two Approaches to Quantum Logic: Every Birkhoff -von Neumann Quantum Logic is a Partial Infinite-Valued Łukasiewicz Logic

Studia Logica 95 (1-2):5 - 20 (2010)

In the paper it is shown that every physically sound Birkhoff - von Neumann quantum logic, i.e., an orthomodular partially ordered set with an ordering set of probability measures can be treated as partial infini te-valued Lukasiewicz logic, which unifies two competing approaches: the many-valued, and the two-valued but non-distributive, which have co-existed in the quantum logic theory since its very beginning
Keywords quantum logic  many-valued logic  Łukasiewicz logic
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DOI 10.1007/s11225-010-9252-8
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The Logic of Quantum Mechanics.Garrett Birkhoff & John von Neumann - 1937 - Journal of Symbolic Logic 2 (1):44-45.
Three-Valued Logic.Hilary Putnam - 1957 - Philosophical Studies 8 (5):73 - 80.

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