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  1.  69
    LK, LJ, Dual Intuitionistic Logic, and Quantum Logic.Hiroshi Aoyama - 2004 - Notre Dame Journal of Formal Logic 45 (4):193-213.
    In this paper, we study the relationship among classical logic, intuitionistic logic, and quantum logic . These logics are related in an interesting way and are not far apart from each other, as is widely believed. The results in this paper show how they are related with each other through a dual intuitionistic logic . Our study is completely syntactical.
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  2.  41
    The Strong Completeness of a System Based on Kleene's Strong Three-Valued Logic.Hiroshi Aoyama - 1994 - Notre Dame Journal of Formal Logic 35 (3):355-368.
    The present work, which was inspired by Kripke and McCarthy, is about a non-classical predicate logic system containing a truth predicate symbol. In this system, each sentence A is referred to not by a Gödel number but by its quotation name 'A'.
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  3.  15
    The Semantic Completeness of a Global Intuitionistic Logic.Hiroshi Aoyama - 1998 - Mathematical Logic Quarterly 44 (2):167-175.
    In this paper we will study a formal system of intuitionistic modal predicate logic. The main result is its semantic completeness theorem with respect to algebraic structures. At the end of the paper we will also present a brief consideration of its syntactic relationships with some similar systems.
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  4.  37
    Systems of Quantum Logic.Satoko Titani, Heiji Kodera & Hiroshi Aoyama - 2013 - Studia Logica 101 (1):193-217.
    Logical implications are closely related to modal operators. Lattice-valued logic LL and quantum logic QL were formulated in Titani S (1999) Lattice Valued Set Theory. Arch Math Logic 38:395–421, Titani S (2009) A Completeness Theorem of Quantum Set Theory. In: Engesser K, Gabbay DM, Lehmann D (eds) Handbook of Quantum Logic and Quantum Structures: Quantum Logic. Elsevier Science Ltd., pp. 661–702, by introducing the basic implication → which represents the lattice order. In this paper, we fomulate a predicate orthologic provided (...)
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