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  1. Implicational quantum logic.Kenji Tokuo - 2022 - Axiomathes 32 (2):473-483.
    A non-classical subsystem of orthomodular quantum logic is proposed. This system employs two basic operations: the Sasaki hook as implication and the _and-then_ operation as conjunction. These operations successfully satisfy modus ponens and the deduction theorem. In other words, they form an adjunction in terms of category theory. Two types of semantics are presented for this logic: one algebraic and one physical. The algebraic semantics deals with orthomodular lattices, as in traditional quantum logic. The physical semantics is given as a (...)
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  • Bohrification of operator algebras and quantum logic.Chris Heunen, Nicolaas P. Landsman & Bas Spitters - 2012 - Synthese 186 (3):719 - 752.
    Following Birkhoff and von Neumann, quantum logic has traditionally been based on the lattice of closed linear subspaces of some Hubert space, or, more generally, on the lattice of projections in a von Neumann algebra A. Unfortunately, the logical interpretation of these lattices is impaired by their nondistributivity and by various other problems. We show that a possible resolution of these difficulties, suggested by the ideas of Bohr, emerges if instead of single projections one considers elementary propositions to be families (...)
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  • Book review. [REVIEW]Chris Heunen - 2014 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 48 (2):99-100.
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  • The mathematical foundations of quantum mechanics.David A. Edwards - 1979 - Synthese 42 (1):1 - 70.
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  • The probability structure of quantum-mechanical systems.Zoltan Domotor - 1974 - Synthese 29 (1-4):155 - 185.
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  • An extension of the Łukasiewicz logic to the modal logic of quantum mechanics.Herman Dishkant - 1978 - Studia Logica 37 (2):149-155.
    An attempt is made to include the axioms of Mackey for probabilities of experiments in quantum mechanics into the calculus x0 of ukasiewicz. The obtained calculusQ contains an additional modal signQ and four modal rules of inference. The propositionQx is read x is confirmed. The most specific rule of inference may be read: for comparable observations implication is equivalent to confirmation of material implication.The semantic truth ofQ is established by the interpretation with the help of physical objects obeying to the (...)
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  • Partial Boolean algebras in a broader sense.Janusz Czelakowski - 1979 - Studia Logica 38 (1):1 - 16.
    The article deals with compatible families of Boolean algebras. We define the notion of a partial Boolean algebra in a broader sense (PBA(bs)) and then we show that there is a mutual correspondence between PBA(bs) and compatible families of Boolean algebras (Theorem (1.8)). We examine in detail the interdependence between PBA(bs) and the following classes: partial Boolean algebras in the sense of Kochen and Specker (§ 2), ortholattices (§ 3, § 5), and orthomodular posets (§ 4), respectively.
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  • Is logic empirical?Guido Bacciagaluppi - unknown
    The philosophical debate about quantum logic between the late 1960s and the early 1980s was generated mainly by Putnam's claims that quantum mechanics empirically motivates introducing a new form of logic, that such an empirically founded quantum logic is the `true' logic, and that adopting quantum logic would resolve all the paradoxes of quantum mechanics. Most of that debate focussed on the latter claim, reaching the conclusion that it was mistaken. This chapter will attempt to clarify the possible misunderstandings surrounding (...)
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  • Non-Boolean descriptions for mind-matter problems.Hans Primas - 2007 - Mind and Matter 5 (1):7-44.
    A framework for the mind-matter problem in a holistic universe which has no parts is outlined. The conceptual structure of modern quantum theory suggests to use complementary Boolean descriptions as elements for a more comprehensive non-Boolean description of a world without an a priori mind-matter distinction. Such a description in terms of a locally Boolean but globally non-Boolean structure makes allowance for the fact that Boolean descriptions play a privileged role in science. If we accept the insight that there are (...)
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