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  1.  11
    Fungibility in Quantum Sets.Kenji Tokuo - 2019 - Axiomathes 29 (3):297-310.
    It can be intuitively understood that sets and their elements in mathematics reflect the atomistic way of thinking in physics: Sets correspond to physical properties, and their elements correspond to particles that have these properties. At the same time, quantum statistics and quantum field theory strongly support the view that quantum particles are not individuals. Some of the problems faced in modern physics may be caused by such discrepancy between set theory and physical theory. The question then arises: Is it (...)
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  2.  36
    Extended Quantum Logic.Kenji Tokuo - 2003 - Journal of Philosophical Logic 32 (5):549-563.
    The concept of quantum logic is extended so that it covers a more general set of propositions that involve non-trivial probabilities. This structure is shown to be embedded into a multi-modal framework, which has desirable logical properties such as an axiomatization, the finite model property and decidability.
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  3.  48
    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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  4.  8
    Linearity and Negation.Kenji Tokuo - 2012 - Journal of Applied Non-Classical Logics 22 (1-2):43-51.
    The logical structure derived from the algebra of generalised projection operators on a module is investigated. With the assumption of the operators being linear, the associated logic becomes Boolean, while without the assumption, the logic does not admit negation: the concept of linearity of projection operators on a module corresponds to that of negation in Boolean logic. The logic of nonlinear operators is formalised and its soundness and completeness results are proved.
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