21 found
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  1.  8
    A Modified Subformula Property for the Modal Logic S4.2.Mitio Takano - 2019 - Bulletin of the Section of Logic 48 (1).
    The modal logic S4.2 is S4 with the additional axiom ◊□A ⊃ □◊A. In this article, the sequent calculus GS4.2 for this logic is presented, and by imposing an appropriate restriction on the application of the cut-rule, it is shown that, every GS4.2-provable sequent S has a GS4.2-proof such that every formula occurring in it is either a subformula of some formula in S, or the formula □¬□B or ¬□B, where □B occurs in the scope of some occurrence of □ (...)
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  2.  37
    A Semantical Investigation Into Leśniewski's Axiom of His Ontology.Mitio Takano - 1985 - Studia Logica 44 (1):71 - 77.
    A structure A for the language L, which is the first-order language (without equality) whose only nonlogical symbol is the binary predicate symbol , is called a quasi -struoture iff (a) the universe A of A consists of sets and (b) a b is true in A ([p) a = {p } & p b] for every a and b in A, where a(b) is the name of a (b). A quasi -structure A is called an -structure iff (c) {p (...)
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  3.  23
    A Modified Subformula Property for the Modal Logics K5 and K5D.Mitio Takano - 2001 - Bulletin of the Section of Logic 30 (2):115-123.
  4.  22
    Ordered Sets R and Q as Bases of Kripke Models.Mitio Takano - 1987 - Studia Logica 46 (2):137 - 148.
    Those formulas which are valid in every Kripke model having constant domain whose base is the ordered set R of real numbers (or, the ordered set Q of rational numbers) are characterized syntactically.
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  5.  23
    Embeddings Between the Elementary Ontology with an Atom and the Monadic Second-Order Predicate Logic.Mitio Takano - 1987 - Studia Logica 46 (3):247 - 253.
    Let EOA be the elementary ontology augmented by an additional axiom S (S S), and let LS be the monadic second-order predicate logic. We show that the mapping which was introduced by V. A. Smirnov is an embedding of EOA into LS. We also give an embedding of LS into EOA.
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  6.  9
    Gentzenization of Trilattice Logics.Mitio Takano - 2016 - Studia Logica 104 (5):917-929.
    Sequent calculi for trilattice logics, including those that are determined by the truth entailment, the falsity entailment and their intersection, are given. This partly answers the problems in Shramko-Wansing.
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  7. Dedicated for the Memory of the Late Professor S. Maehara.Mitio Takano - forthcoming - Annals of the Japan Association for Philosophy of Science.
  8.  13
    Strong Completeness of Lattice-Valued Logic.Mitio Takano - 2002 - Archive for Mathematical Logic 41 (5):497-505.
    Strong completeness of S. Titani's system for lattice valued logic is shown by means of Dedekind cuts.
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  9. Intermediate Predicate Logics Determined by Ordinals.Pierluigi Minari, Mitio Takano & Hiroakira Ono - 1990 - Journal of Symbolic Logic 55 (3):1099-1124.
    For each ordinal $\alpha > 0, L(\alpha)$ is the intermediate predicate logic characterized by the class of all Kripke frames with the poset α and with constant domain. This paper will be devoted to a study of logics of the form L(α). It will be shown that for each uncountable ordinal of the form α + η with a finite or a countable $\eta (> 0)$ , there exists a countable ordinal of the form β + η such that L(α (...)
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  10. Completeness of a Cut-Free Calculus with Equality and Function Constants.Mitio Takano - 1985 - Archive for Mathematical Logic 25 (1):37-41.
     
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  11.  29
    Subformula Property in Many-Valued Modal Logics.Mitio Takano - 1994 - Journal of Symbolic Logic 59 (4):1263-1273.
  12.  29
    Syntactical Proof of Translation and Separation Theorems on Subsystems of Elementary Ontology.Mitio Takano - 1991 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 37 (9-12):129-138.
  13.  8
    Valid Sequents in Many-Valued Logics.Mitio Takano - 1980 - Annals of the Japan Association for Philosophy of Science 5 (5):245-260.
  14.  2
    New Modification of the Subformula Property for a Modal Logic.Mitio Takano - 2020 - Bulletin of the Section of Logic 49 (3):255-268.
    A modified subformula property for the modal logic KD with the additionalaxiom □ ◊ ⊃ □ ◊ A ∨ □ ◊B is shown. A new modification of the notion of subformula is proposed for this purpose. This modification forms a natural extension of our former one on which modified subformula property for the modal logics K5, K5D and S4.2 has been shown. The finite model property as well as decidability for the logic follows from this.
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  15.  24
    Cut-Elimination in the Intuitionistic Many-Valued Logic Based on a Partial Order.Mitio Takano - 1988 - Annals of the Japan Association for Philosophy of Science 7 (3):117-123.
  16.  2
    Axiomatization of a Basic Logic of Logical Bilattices.Mitio Takano - 2016 - Bulletin of the Section of Logic 45 (2).
    A sequential axiomatization is given for the 16-valued logic that has been proposed by Shramko-Wansing as a candidate for the basic logic of logical bilattices.
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  17.  15
    Cut-Free Systems for Three-Valued Modal Logics.Mitio Takano - 1992 - Notre Dame Journal of Formal Logic 33 (3):359-368.
  18.  9
    Syntactical Proof of Translation and Separation Theorems on Subsystems of Elementary Ontology.Mitio Takano - 1991 - Mathematical Logic Quarterly 37 (9‐12):129-138.
  19.  11
    An Interpolation Theorem in Many-Valued Logic.Masazumi Hanazawa & Mitio Takano - 1986 - Journal of Symbolic Logic 51 (2):448-452.
  20.  2
    A Sequent Calculus for the Lesniewskian Modal Logic.Mitio Takano - 1994 - Annals of the Japan Association for Philosophy of Science 8 (4):191-201.
  21.  4
    Extending the Family of Intuitionistic Many-Valued Logics Introduced by Rousseau.Mitio Takano - 1986 - Annals of the Japan Association for Philosophy of Science 7 (1):47-56.