Abstract
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 infinite-valued Łukasiewicz 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.
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Pykacz, J. Unification of Two Approaches to Quantum Logic: Every Birkhoff – von Neumann Quantum Logic is a Partial Infinite-Valued Łukasiewicz Logic. Stud Logica 95, 5–20 (2010). https://doi.org/10.1007/s11225-010-9252-8
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DOI: https://doi.org/10.1007/s11225-010-9252-8