This may be of interest.
Brent
Quantum Logic as Classical Logic
Simon Kramer
(Submitted on 13 Jun 2014)
We propose a semantic representation of the standard quantum logic QL within the
classical, normal modal logic K via a lattice-embedding of orthomodular lattices into
Boolean algebras with one K-modal operator. Thus the classical logic K is a completion of
the quantum logic QL. In other words, we refute Birkhoff and von Neumann's classic thesis
that the logic (the formal character) of Quantum Mechanics would be non-classical as well
as Putnam's thesis that quantum logic (of his kind) would be the correct logic for
propositional inference in general. The propositional logic of Quantum Mechanics is modal
but classical, and the correct logic for propositional inference need not have an
extroverted quantum character. The normal necessity K-modality (the weakest of all normal
necessity modalities!) suffices to capture the subjectivity of observation in quantum
experiments, and this thanks to its failure to distribute over classical disjunction. (A
fortiori, all normal necessity modalities that do not distribute over classical
disjunction suffice.) The key to our result is the translation of quantum negation as
classical negation of observability.
Subjects: Quantum Physics (quant-ph); Logic in Computer Science (cs.LO); Mathematical
Physics (math-ph); Logic (math.LO); Quantum Algebra (math.QA)
Cite as: arXiv:1406.3526 [quant-ph]
(or arXiv:1406.3526v1 [quant-ph] for this version)
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