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  1. Unified Interpretation of Quantum and Classical Logics.Kenji Tokuo - 2012 - Axiomathes (1):1-7.
    Quantum logic is only applicable to microscopic phenomena while classical logic is exclusively used for everyday reasoning, including mathematics. It is shown that both logics are unified in the framework of modal interpretation. This proposed method deals with classical propositions as latently modalized propositions in the sense that they exhibit manifest modalities to form quantum logic only when interacting with other classical subsystems.
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  • Quantum supports and modal logic.George Svetlichny - 1986 - Foundations of Physics 16 (12):1285-1295.
    LetA be a quasi-manual with finite operations. Associate to each E = {e 1 ,..., en} εA the set ΓE of modal formulas: □(e 1 ⋁ ··· ⋁ en), ◊ei → ∼□(e 1 ⋁ ··· ⋁ ei−1 ⋁ ei+1 ⋁ ··· ⋁ en), i=1,..., n. Set Γ A = ώ{ΓE|E εA}. We show that supports ofA are in one-to-one correspondence with certain Kripke models of Γ A where the supports are given by {x ε |A ‖ ◊ x is true}.
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  • Unified quantum logic.Mladen Pavičić - 1989 - Foundations of Physics 19 (8):999-1016.
    Unified quantum logic based on unified operations of implication is formulated as an axiomatic calculus. Soundness and completeness are demonstrated using standard algebraic techniques. An embedding of quantum logic into a new modal system is carried out and discussed.
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  • Modal‐type orthomodular logic.Graciela Domenech, Hector Freytes & Christian de Ronde - 2009 - Mathematical Logic Quarterly 55 (3):307-319.
    In this paper we enrich the orthomodular structure by adding a modal operator, following a physical motivation. A logical system is developed, obtaining algebraic completeness and completeness with respect to a Kripkestyle semantic founded on Baer*-semigroups as in [22].
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