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Quantum logic
In quantum mechanics, quantum logic is a set of rules for reasoning about propositions that takes the principles of quantum theory into account. This research area and its name originated in a 1936 paper by Garrett Birkhoff and John von Neumann, who were attempting to reconcile the apparent inconsistency of classical logic with the facts concerning the measurement of complementary variables in quantum mechanics, such as position and momentum.
Quantum logic can be formulated either as a modified version of propositional logic or as a noncommutative and non-associative many-valued (MV) logic.〔http://arxiv.org/abs/quant-ph/0101028v2 Maria Luisa Dalla Chiara and Roberto Giuntini. 2008. ''Quantum Logic''., 102 pages PDF〕〔Dalla Chiara, M. L. and Giuntini, R.: 1994, Unsharp quantum logics, ''Foundations of Physics,'', 24, 1161–1177.〕〔http://planetphysics.org/encyclopedia/QuantumLMAlgebraicLogic.html I. C. Baianu. 2009. Quantum LMn Algebraic Logic.〕〔Georgescu, G. and C. Vraciu. 1970, On the characterization of centered Łukasiewicz algebras.,'' J. Algebra'', 16: 486–495.〕〔Georgescu, G. 2006, N-valued Logics and Łukasiewicz-Moisil Algebras, ''Axiomathes'', 16 (1–2): 123〕
Quantum logic has some properties that clearly distinguish it from classical logic, most notably, the failure of the distributive law of propositional logic:〔"Quantum logic" entry by Peter Forrest in the ''Routledge Encyclopedia of Philosophy'', Vol. 7 (1998), p. 882ff: "(logic ) differs from the standard sentential calculus ... The most notable difference is that the distributive laws fail, being replaced by a weaker law known as orthomodularity."〕
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