Substitution and truth in quantum logic

Philosophy of Science 49 (3):380-401 (1982)
Abstract
If p(x 1 ,...,x n ) and q(x 1 ,...,x n ) are two logically equivalent propositions then p(π (x 1 ),...,π (x n )) and q(π (x 1 ),...,π (x n )) are also logically equivalent where π is an arbitrary permutation of the elementary constituents x 1 ,...,x n . In Quantum Logic the invariance of logical equivalences breaks down. It is proved that the distribution rules of classical logic are in fact equivalent to the meta-linguistic rule of universal substitution and that the more restrictive structure of the substitution group of Quantum Logic prevents us from defining truth in a classical fashion. These observations lead to a more profound understanding of the Logic of Quantum Mechanics and of the role that symmetry principles play in that theory
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DOI 10.1086/289067
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Quantum Logic and the Classical Propositional Calculus.Othman Qasim Malhas - 1987 - Journal of Symbolic Logic 52 (3):834-841.
Generalizations of Kochen and Specker's Theorem and the Effectiveness of Gleason's Theorem.Ehud Hrushovski & Itamar Pitowsky - 2004 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 35 (2):177-194.

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