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Imbedding of the quantum logic in the modal system of Brower

Herman Dishkant

Journal of Symbolic Logic 42 (3):321-328 (1977)

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Axiomatization of an Orthologic of Indeterminacy.Samuel C. Fletcher & David E. Taylor - forthcoming - Journal of Philosophical Logic:1-22.details Recently, we (Synthese, 199(5–6):13247–13281, 2021) proposed Kripke-like semantics for two quantum logics of interderminacy. These logics expand the vocabulary of standard Birkhoff-von Neumann propositional quantum logic with a pair of modal operators interpreted as “it is (in)determinate that”, allowing them to express in the object language statements such as “it is indeterminate that system S is spin-up in the x-direction”, as well as statements of any logical complexity involving ascriptions of (in)determinacy. We present an axiomatization of a logic closely related (...) Download Export citation Bookmark
(1 other version)The Orthologic of Epistemic Modals.Wesley H. Holliday & Matthew Mandelkern - 2024 - Journal of Philosophical Logic 53 (4):831-907.details Epistemic modals have peculiar logical features that are challenging to account for in a broadly classical framework. For instance, while a sentence of the form $$p\wedge \Diamond \lnot p$$ (‘p, but it might be that not p’) appears to be a contradiction, $$\Diamond \lnot p$$ does not entail $$\lnot p$$, which would follow in classical logic. Likewise, the classical laws of distributivity and disjunctive syllogism fail for epistemic modals. Existing attempts to account for these facts generally either under- or over-correct. (...) Download Export citation Bookmark 2 citations
Unified Interpretation of Quantum and Classical Logics.Kenji Tokuo - 2012 - Axiomathes (1):1-7.details 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. Download Export citation Bookmark
Modal‐type orthomodular logic.Graciela Domenech, Hector Freytes & Christian de Ronde - 2009 - Mathematical Logic Quarterly 55 (3):307-319.details 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]. Download Export citation Bookmark 6 citations
Quantum supports and modal logic.George Svetlichny - 1986 - Foundations of Physics 16 (12):1285-1295.details 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}. Download Export citation Bookmark 2 citations
Unified quantum logic.Mladen Pavičić - 1989 - Foundations of Physics 19 (8):999-1016.details 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. Download Export citation Bookmark

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