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  1.  33
    A Sahlqvist Theorem for Relevant Modal Logics.Takahiro Seki - 2003 - Studia Logica 73 (3):383-411.
    Kripke-completeness of every classical modal logic with Sahlqvist formulas is one of the basic general results on completeness of classical modal logics. This paper shows a Sahlqvist theorem for modal logic over the relevant logic Bin terms of Routley- Meyer semantics. It is shown that usual Sahlqvist theorem for classical modal logics can be obtained as a special case of our theorem.
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  2.  22
    Some Metacomplete Relevant Modal Logics.Takahiro Seki - 2013 - Studia Logica 101 (5):1115-1141.
    A logic is called metacomplete if formulas that are true in a certain preferred interpretation of that logic are theorems in its metalogic. In the area of relevant logics, metacompleteness is used to prove primeness, consistency, the admissibility of γ and so on. This paper discusses metacompleteness and its applications to a wider class of modal logics based on contractionless relevant logics and their neighbours using Slaney’s metavaluational technique.
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  3.  12
    The Γ-Admissibility of Relevant Modal Logics I — The Method of Normal Models.Takahiro Seki - 2011 - Studia Logica 97 (2):199-231.
  4.  25
    Halldén Completeness for Relevant Modal Logics.Takahiro Seki - 2015 - Notre Dame Journal of Formal Logic 56 (2):333-350.
    Halldén completeness closely resembles the relevance property. To prove Halldén completeness in terms of Kripke-style semantics, the van Benthem–Humberstone theorem is often used. In relevant modal logics, the Halldén completeness of Meyer–Fuhrmann logics has been obtained using the van Benthem–Humberstone theorem. However, there remain a number of Halldén-incomplete relevant modal logics. This paper discusses the Halldén completeness of a wider class of relevant modal logics, namely, those with some Sahlqvist axioms.
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  5.  34
    General Frames for Relevant Modal Logics.Takahiro Seki - 2003 - Notre Dame Journal of Formal Logic 44 (2):93-109.
    General frames are often used in classical modal logic. Since they are duals of modal algebras, completeness follows automatically as with algebras but the intuitiveness of Kripke frames is also retained. This paper develops basics of general frames for relevant modal logics by showing that they share many important properties with general frames for classical modal logic.
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  6.  19
    An Algebraic Proof of the Admissibility of Γ in Relevant Modal Logics.Takahiro Seki - 2012 - Studia Logica 100 (6):1149-1174.
    The admissibility of Ackermann's rule γ is one of the most important problems in relevant logics. The admissibility of γ was first proved by an algebraic method. However, the development of Routley-Meyer semantics and metavaluational techniques makes it possible to prove the admissibility of γ using the method of normal models or the method using metavaluations, and the use of such methods is preferred. This paper discusses an algebraic proof of the admissibility of γ in relevant modal logics based on (...)
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  7.  27
    Some Remarks on Maehara's Method.Takahiro Seki - 2001 - Bulletin of the Section of Logic 30 (3):147-154.
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  8.  34
    Metacompleteness of Substructural Logics.Takahiro Seki - 2012 - Studia Logica 100 (6):1175-1199.
    Metacompleteness is used to prove properties such as the disjunction property and the existence property in the area of relevant logics. On the other hand, the disjunction property of several basic propositional substructural logics over FL has been proved using the cut elimination theorem of sequent calculi and algebraic characterization. The present paper shows that Meyer’s metavaluational technique and Slaney’s metavaluational technique can be applied to basic predicate intuitionistic substructural logics and basic predicate involutive substructural logics, respectively. As a corollary (...)
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  9.  13
    The Γ-Admissibility of Relevant Modal Logics I — The Method of Normal Models.Takahiro Seki - 2011 - Studia Logica 97 (2):199-231.
    The admissibility of Ackermann's rule? is one of the most important problems in relevant logic. While the?-admissibility of normal modal logics based on the relevant logic R has been previously discussed, the case for weaker relevant modal logics has not yet been considered. The method of normal models has often been used to prove the?-admissibility. This paper discusses which relevant modal logics admit? from the viewpoint of the method of normal models.
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