7 found
  1.  42
    Kripke Completeness of Some Intermediate Predicate Logics with the Axiom of Constant Domain and a Variant of Canonical Formulas.Tatsuya Shimura - 1993 - Studia Logica 52 (1):23 - 40.
    For each intermediate propositional logicJ, J * denotes the least predicate extension ofJ. By the method of canonical models, the strongly Kripke completeness ofJ *+D(=x(p(x)q)xp(x)q) is shown in some cases including:1. J is tabular, 2. J is a subframe logic. A variant of Zakharyashchev's canonical formulas for intermediate logics is introduced to prove the second case.
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  2.  27
    Cut‐Elimination Theorem for the Logic of Constant Domains.Ryo Kashima & Tatsuya Shimura - 1994 - Mathematical Logic Quarterly 40 (2):153-172.
    The logic CD is an intermediate logic which exactly corresponds to the Kripke models with constant domains. It is known that the logic CD has a Gentzen-type formulation called LD and rules are replaced by the corresponding intuitionistic rules) and that the cut-elimination theorem does not hold for LD. In this paper we present a modification of LD and prove the cut-elimination theorem for it. Moreover we prove a “weak” version of cut-elimination theorem for LD, saying that all “cuts” except (...)
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  3.  32
    Kripke Incompleteness of Predicate Extensions of the Modal Logics Axiomatized by a Canonical Formula for a Frame with a Nontrivial Cluster.Tatsuya Shimura - 2000 - Studia Logica 65 (2):237-247.
    We generalize the incompleteness proof of the modal predicate logic Q-S4+ p p + BF described in Hughes-Cresswell [6]. As a corollary, we show that, for every subframe logic Lcontaining S4, Kripke completeness of Q-L+ BF implies the finite embedding property of L.
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  4.  27
    On the Strength of PA with a Non-Principal Ultrafilter Quantifier.Tatsuya Shimura - 1991 - Annals of the Japan Association for Philosophy of Science 8 (1):17-21.
  5.  22
    Kripke Incompleteness of Predicate Extentions of Gabbay-de Jongh's Logic of the Finite Binary Trees.Tatsuya Shimura - 2002 - Bulletin of the Section of Logic 31 (2):111-118.
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  6.  22
    Kripke Completeness of Predicate Extensions of Cofinal Subframe Logics.Tatsuya Shimura - 2001 - Bulletin of the Section of Logic 30 (2):107-114.
  7.  28
    Some Superintuitionistic Logics as the Logical Fragments of Equational Theories.Tatsuya Shimura & Nobu-Yuki Suzuki - 1993 - Bulletin of the Section of Logic 22:106-112.