7 found
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  1.  23
    Kripke Incomplete Logics Containing KTB.Yutaka Miyazaki - 2007 - Studia Logica 85 (3):303-317.
    It is shown that there is a Kripke incomplete logic in NExt(KTB ⊕ □2 p → □3 p). Furthermore, it is also shown that there exists a continuum of Kripke incomplete logics in NExt(KTB ⊕ □5 p → □6 p).
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  2.  28
    Some Properties of Orthologics.Yutaka Miyazaki - 2005 - Studia Logica 80 (1):75-93.
    In this paper, we present three main results on orthologics. Firstly, we give a sufficient condition for an orthologic to have variable separation property and show that the orthomodular logic has this property. Secondly, we show that the class of modular orthologics has an infinite descending chain. Finally we show that there exists a continuum of orthologics.
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  3.  14
    Kripke-Style Semantics of Orthomodular Logics.Yutaka Miyazaki - 2001 - Mathematical Logic Quarterly 47 (3):341-362.
    We present here a Kripke-style semantics for propositional orthomodular logics that is based on the representation theorem for orthomodular lattices by D.J. Foulis , in which a sort of semigroups is employed. This semantics can characterize the logics above the orthomodular logic by some elementary conditions.
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  4.  34
    A Splitting Logic in NExt(KTB).Yutaka Miyazaki - 2007 - Studia Logica 85 (3):381 - 394.
    It is shown that the normal modal logic of two reflexive points jointed with a symmetric binary relation splits the lattice of normal extensions of the logic KTB. By this fact, it is easily seen that there exists the third largest logic in the class of all normal extensions of KTB.
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  5.  16
    Normal Forms for Modal Logics Kb and Ktb.Yutaka Miyazaki - 2007 - Bulletin of the Section of Logic 36 (3/4):183-193.
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  6.  7
    Normal Modal Logics Determined by Aligned Clusters.Zofia Kostrzycka & Yutaka Miyazaki - 2017 - Studia Logica 105 (1):1-11.
    We consider the family of logics from NExt which are determined by linear frames with reflexive and symmetric relation of accessibility. The condition of linearity in such frames was first defined in the paper [9]. We prove that the cardinality of the logics under consideration is uncountably infinite.
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  7.  7
    A Splitting Logic in NExt.Yutaka Miyazaki - 2007 - Studia Logica 85 (3):381-394.
    It is shown that the normal modal logic of two reflexive points jointed with a symmetric binary relation splits the lattice of normal extensions of the logic KTB. By this fact, it is easily seen that there exists the third largest logic in the class of all normal extensions of KTB.
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