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Mitsuhiro Okada

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  •  337
    A simple relationship between Buchholz's new system of ordinal notations and Takeuti's system of ordinal diagrams
    Journal of Symbolic Logic 52 (3): 577-581. 1987.
    Logic and Philosophy of LogicProof Theory
  •  253
    The finite model property for various fragments of intuitionistic linear logic
    with Kazushige Terui
    Journal of Symbolic Logic 64 (2): 790-802. 1999.
    Recently Lafont [6] showed the finite model property for the multiplicative additive fragment of linear logic (MALL) and for affine logic (LLW), i.e., linear logic with weakening. In this paper, we shall prove the finite model property for intuitionistic versions of those, i.e. intuitionistic MALL (which we call IMALL), and intuitionistic LLW (which we call ILLW). In addition, we shall show the finite model property for contractive linear logic (LLC), i.e., linear logic with contraction, and for…Read more
    Proof TheoryIntuitionistic Logic
  •  114
    A direct independence proof of Buchholz's Hydra Game on finite labeled trees
    with Masahiro Hamano
    Archive for Mathematical Logic 37 (2): 67-89. 1998.
    We shall give a direct proof of the independence result of a Buchholz style-Hydra Game on labeled finite trees. We shall show that Takeuti-Arai's cut-elimination procedure of $(\Pi^{1}_{1}-CA) + BI$ and of the iterated inductive definition systems can be directly expressed by the reduction rules of Buchholz's Hydra Game. As a direct corollary the independence result of the Hydra Game follows.
    Proof Theory
  •  107
    A weak intuitionistic propositional logic with purely constructive implication
    Studia Logica 46 (4). 1987.
    We introduce subsystems WLJ and SI of the intuitionistic propositional logic LJ, by weakening the intuitionistic implication. These systems are justifiable by purely constructive semantics. Then the intuitionistic implication with full strength is definable in the second order versions of these systems. We give a relationship between SI and a weak modal system WM. In Appendix the Kripke-type model theory for WM is given.
    Intuitionistic LogicProof Theory
  •  69
    Weak Logical Constants and Second Order Definability of the Full-Strength Logical Constants
    Annals of the Japan Association for Philosophy of Science 7 (4): 163-172. 1989.
    Science, Logic, and MathematicsLogical Expressions