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  1.  53
    The Finite Model Property for Various Fragments of Intuitionistic Linear Logic.Mitsuhiro Okada & Kazushige Terui - 1999 - Journal of Symbolic Logic 64 (2):790-802.
    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 its intuitionistic version (ILLC). (...)
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  2.  56
    A Diagrammatic Inference System with Euler Circles.Koji Mineshima, Mitsuhiro Okada & Ryo Takemura - 2012 - Journal of Logic, Language and Information 21 (3):365-391.
    Proof-theory has traditionally been developed based on linguistic (symbolic) representations of logical proofs. Recently, however, logical reasoning based on diagrammatic or graphical representations has been investigated by logicians. Euler diagrams were introduced in the eighteenth century. But it is quite recent (more precisely, in the 1990s) that logicians started to study them from a formal logical viewpoint. We propose a novel approach to the formalization of Euler diagrammatic reasoning, in which diagrams are defined not in terms of regions as in (...)
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  3.  42
    Syntactic Reduction in Husserl’s Early Phenomenology of Arithmetic.Mirja Hartimo & Mitsuhiro Okada - 2016 - Synthese 193 (3):937-969.
    The paper traces the development and the role of syntactic reduction in Edmund Husserl’s early writings on mathematics and logic, especially on arithmetic. The notion has its origin in Hermann Hankel’s principle of permanence that Husserl set out to clarify. In Husserl’s early texts the emphasis of the reductions was meant to guarantee the consistency of the extended algorithm. Around the turn of the century Husserl uses the same idea in his conception of definiteness of what he calls “mathematical manifolds.” (...)
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  4.  46
    A Generalized Syllogistic Inference System Based on Inclusion and Exclusion Relations.Koji Mineshima, Mitsuhiro Okada & Ryo Takemura - 2012 - Studia Logica 100 (4):753-785.
    We introduce a simple inference system based on two primitive relations between terms, namely, inclusion and exclusion relations. We present a normalization theorem, and then provide a characterization of the structure of normal proofs. Based on this, inferences in a syllogistic fragment of natural language are reconstructed within our system. We also show that our system can be embedded into a fragment of propositional minimal logic.
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  5.  34
    Wittgenstein et le lien entre la signification d’un énoncé mathématique et sa preuve.Mathieu Marion & Mitsuhiro Okada - 2012 - Philosophiques 39 (1):101-124.
    La thèse selon laquelle la signification d’un énoncé mathématique est donnée par sa preuve a été soutenue à la fois par Wittgenstein et par les intuitionnistes, à la suite de Heyting et de Dummett. Dans ce texte, nous nous attachons à clarifier le sens de cette thèse chez Wittgenstein, afin de montrer en quoi sa position se distingue de celle des intuitionnistes. Nous montrons par ailleurs que cette thèse prend sa source chez Wittgenstein dans sa réflexion, durant la période intermédiaire, (...)
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  6.  15
    The Finite Model Property for Various Fragments of Intuitionistic Linear Logic.Mitsuhiro Okada & Kazushige Terui - 1999 - Journal of Symbolic Logic 64 (2):790-802.
    Recently Lafont [6] showed the finite model property for the multiplicative additive fragment of linear logic and for affine logic, 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, and intuitionistic LLW. In addition, we shall show the finite model property for contractive linear logic, i.e., linear logic with contraction, and for its intuitionistic version. The finite model property for related substructural logics also follow by our (...)
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  7.  40
    A Direct Independence Proof of Buchholz's Hydra Game on Finite Labeled Trees.Masahiro Hamano & Mitsuhiro Okada - 1998 - Archive for Mathematical Logic 37 (2):67-89.
    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.
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  8.  7
    Some Remarks on a Difference Between Gentzen's Finitist and Heyting's Intuitionist Approaches Toward Intuitionistic Logic and Arithmetic.Mitsuhiro Okada - 2008 - Annals of the Japan Association for Philosophy of Science 16 (1-2):1-17.
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  9.  17
    Linear Logic and Intuitionistic Logic.Mitsuhiro Okada - 2004 - Revue Internationale de Philosophie 4:449-481.
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  10.  26
    Weak Logical Constants and Second Order Definability of the Full-Strength Logical Constants.Mitsuhiro Okada - 1989 - Annals of the Japan Association for Philosophy of Science 7 (4):163-172.
  11.  30
    A New Correctness Criterion for the Proof Nets of Non-Commutative Multiplicative Linear Logics.Misao Nagayama & Mitsuhiro Okada - 2001 - Journal of Symbolic Logic 66 (4):1524-1542.
    This paper presents a new correctness criterion for marked Danos-Reginer graphs (D-R graphs, for short) of Multiplicative Cyclic Linear Logic MCLL and Abrusci's non-commutative Linear Logic MNLL. As a corollary we obtain an affirmative answer to the open question whether a known quadratic-time algorithm for the correctness checking of proof nets for MCLL and MNLL can be improved to linear-time.
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  12.  17
    On a Theory of Weak Implications.Mitsuhiro Okada - 1988 - Journal of Symbolic Logic 53 (1):200-211.
  13.  4
    A Direct Independence Proof of Buchholz's Hydra Game on Finite Labeled Trees.Masahiro Hamano & Mitsuhiro Okada - 2001 - Bulletin of Symbolic Logic 7 (4):534-535.
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  14.  17
    A Relationship Among Gentzen's Proof‐Reduction, Kirby‐Paris' Hydra Game and Buchholz's Hydra Game.Masahiro Hamano & Mitsuhiro Okada - 1997 - Mathematical Logic Quarterly 43 (1):103-120.
    We first note that Gentzen's proof-reduction for his consistency proof of PA can be directly interpreted as moves of Kirby-Paris' Hydra Game, which implies a direct independence proof of the game . Buchholz's Hydra Game for labeled hydras is known to be much stronger than PA. However, we show that the one-dimensional version of Buchholz's Game can be exactly identified to Kirby-Paris' Game , by a simple and natural interpretation . Jervell proposed another type of a combinatorial game, by abstracting (...)
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  15. Following a Rule: Waismann's Variation.Mathieu Marion & Mitsuhiro Okada - 2018 - In Gabriele M. Mras, Paul Weingartner & Bernhard Ritter (eds.), Philosophy of Logic and Mathematics. Berlin, Boston: De Gruyter. pp. 359-373.
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  16.  1
    Following a Rule: Waismann’s Variation.Mathieu Marion & Mitsuhiro Okada - 2019 - In Gabriele M. Mras, Paul Weingartner & Bernhard Ritter (eds.), Philosophy of Logic and Mathematics: Proceedings of the 41st International Ludwig Wittgenstein Symposium. De Gruyter. pp. 359-374.
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  17.  13
    Wittgenstein on Equinumerosity and Surveyability.Mathieu Marion & Mitsuhiro Okada - 2014 - Grazer Philosophische Studien 89 (1):61-78.
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  18.  10
    A New Correctness Criterion For The Proof Nets Of Non-Commutative Multiplicative Linear Logics.Misao Nagayama & Mitsuhiro Okada - 2001 - Journal of Symbolic Logic 66 (4):1524-1542.
    This paper presents a new correctness criterion for marked Danos-Reginer graphs of Multiplicative Cyclic Linear Logic MCLL and Abrusci's non-commutative Linear Logic MNLL. As a corollary we obtain an affirmative answer to the open question whether a known quadratic-time algorithm for the correctness checking of proof nets for MCLL and MNLL can be improved to linear-time.
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  19. -特集テーマ「タイプ理論」について.Mitsuhiro Okada - 2021 - Kagaku Tetsugaku 53 (2):1.
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  20. A Simple Relationship Between Buchholz's New System of Ordinal Notations and Takeuti's System of Ordinal Diagrams.Mitsuhiro Okada - 1987 - Journal of Symbolic Logic 52 (3):577-581.
  21.  31
    A Weak Intuitionistic Propositional Logic with Purely Constructive Implication.Mitsuhiro Okada - 1987 - Studia Logica 46 (4):371 - 382.
    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.
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  22.  64
    Remarks on Logic for Process Descriptions in Ontological Reasoning: A Drug Interaction Ontology Case Study.Mitsuhiro Okada, Barry Smith & Yutaro Sugimoto - 2008 - In InterOntology. Proceedings of the First Interdisciplinary Ontology Meeting, Tokyo, Japan, 26-27 February 2008. Tokyo: Keio University Press. pp. 127-138.
    We present some ideas on logical process descriptions, using relations from the DIO (Drug Interaction Ontology) as examples and explaining how these relations can be naturally decomposed in terms of more basic structured logical process descriptions using terms from linear logic. In our view, the process descriptions are able to clarify the usual relational descriptions of DIO. In particular, we discuss the use of logical process descriptions in proving linear logical theorems. Among the types of reasoning supported by DIO one (...)
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  23. Wittgenstein's Uniqueness Rule as an Elimination Rule of Inductive Types:帰納型消去規則としてのウィトゲンシュタインの一意性規則.Mitsuhiro Okada - 2021 - Kagaku Tetsugaku 53 (2):95-114.
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  24.  18
    Genetic Factors of Individual Differences in Decision Making in Economic Behavior: A Japanese Twin Study Using the Allais Problem.Chizuru Shikishima, Kai Hiraishi, Shinji Yamagata, Juko Ando & Mitsuhiro Okada - 2015 - Frontiers in Psychology 6.
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