1. Kenji Tokuo (2012). Linearity and Negation. 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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  2. Kenji Tokuo (2012). Unified Interpretation of Quantum and Classical Logics. 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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  3. Kenji Tokuo (2003). Extended Quantum Logic. 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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