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Implicational quantum logic

Axiomathes 32 (2):473-483 (2022)

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  1. The philosophy of quantum mechanics.Max Jammer - 1974 - New York,: Wiley. Edited by Max Jammer.
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  • Louis Osgood Kattsoff. Modality and probability. The philosophical review, vol. 46 (1937), pp. 78–85.Garrett Birkhoff & John von Neumann - 1937 - Journal of Symbolic Logic 2 (1):44-44.
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  • Filters with infinitely many components.Abner Shimony - 1971 - Foundations of Physics 1 (4):325-328.
    With the use of a suitable assumption about the structure of the class of experimental filters, it is shown that the sequence of alternating replicas of two filters is their greatest lower bound, as Jauch suggests. A generalization of his suggestion yields the greatest lower bound of a denumerable set of filters. The criteria of admissibility of filters are briefly discussed.
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  • Quantum logic revisited.L. Román & B. Rumbos - 1991 - Foundations of Physics 21 (6):727-734.
    An adequate conjunction-implication pair is given for complete orthomodular lattices. The resulting conjunction is noncommutative in nature. We use the well-known lattice of closed subspaces of a Hilbert space, to give physical meaning to the given lattice operation.
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  • On the structure of quantum logic.P. D. Finch - 1969 - Journal of Symbolic Logic 34 (2):275-282.
    In the axiomatic development of the logic of nonrelativistic quantum mechanics it is not difficult to set down certain plausible axioms which ensure that the quantum logic of propositions has the structure of an orthomodular poset. This can be done in a number of ways, for example, as in Gunson [2], Mackey [4], Piron [5], Varadarajan [7] and Zierler [8], and we summarise one of these ways in §2 below.
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  • Implication connectives in orthomodular lattices.L. Herman, E. L. Marsden & R. Piziak - 1975 - Notre Dame Journal of Formal Logic 16 (3):305-328.
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  • The conditional in quantum logic.Gary M. Hardegree - 1974 - Synthese 29 (1-4):63 - 80.
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  • Sequential method in quantum logic.Hirokazu Nishimura - 1980 - Journal of Symbolic Logic 45 (2):339-352.
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  • The Logic of Quantum Mechanics.Garrett Birkhoff, John Von Neumann, The Annals & No Oct - 2008 - 37 (4):823–843.
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