9 found
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  1.  10
    Kripke Completeness of Strictly Positive Modal Logics Over Meet-Semilattices with Operators.Stanislav Kikot, Agi Kurucz, Yoshihito Tanaka, Frank Wolter & Michael Zakharyaschev - 2019 - Journal of Symbolic Logic 84 (2):533-588.
    Our concern is the completeness problem for spi-logics, that is, sets of implications between strictly positive formulas built from propositional variables, conjunction and modal diamond operators. Originated in logic, algebra and computer science, spi-logics have two natural semantics: meet-semilattices with monotone operators providing Birkhoff-style calculi and first-order relational structures (aka Kripke frames) often used as the intended structures in applications. Here we lay foundations for a completeness theory that aims to answer the question whether the two semantics define the same (...)
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  2.  20
    Kripke Completeness of Infinitary Predicate Multimodal Logics.Yoshihito Tanaka - 1999 - Notre Dame Journal of Formal Logic 40 (3):326-340.
    Kripke completeness of some infinitary predicate modal logics is presented. More precisely, we prove that if a normal modal logic above is -persistent and universal, the infinitary and predicate extension of with BF and BF is Kripke complete, where BF and BF denote the formulas pi pi and x x, respectively. The results include the completeness of extensions of standard modal logics such as , and its extensions by the schemata T, B, 4, 5, D, and their combinations. The proof (...)
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  3.  68
    A Map of Common Knowledge Logics.Mamoru Kaneko, Takashi Nagashima, Nobu-Yuki Suzuki & Yoshihito Tanaka - 2002 - Studia Logica 71 (1):57-86.
    In order to capture the concept of common knowledge, various extensions of multi-modal epistemic logics, such as fixed-point ones and infinitary ones, have been proposed. Although we have now a good list of such proposed extensions, the relationships among them are still unclear. The purpose of this paper is to draw a map showing the relationships among them. In the propositional case, these extensions turn out to be all Kripke complete and can be comparable in a meaningful manner. F. Wolter (...)
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  4. Rasiowa-Sokorski Lemma and Kripke Completeness of Predicate and Infinitary Modal Logics.Yoshihito Tanaka & Hiroakira Ono - 2000 - In Michael Zakharyaschev, Krister Segerberg, Maarten de Rijke & Heinrich Wansing (eds.), Advances in Modal Logic, Volume 2. CSLI Publications. pp. 419-437.
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  5.  1
    An Extension of Jónsson‐Tarski Representation and Model Existence in Predicate Non‐Normal Modal Logics.Yoshihito Tanaka - 2022 - Mathematical Logic Quarterly 68 (2):189-201.
  6.  28
    An Infinitary Extension of Jankov’s Theorem.Yoshihito Tanaka - 2007 - Studia Logica 86 (1):111 - 131.
    It is known that for any subdirectly irreducible finite Heyting algebra A and any Heyting algebra B, A is embeddable into a quotient algebra of B, if and only if Jankov’s formula χ A for A is refuted in B. In this paper, we present an infinitary extension of the above theorem given by Jankov. More precisely, for any cardinal number κ, we present Jankov’s theorem for homomorphisms preserving infinite meets and joins, a class of subdirectly irreducible complete κ-Heyting algebras (...)
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  7.  6
    An Infinitary Extension of Jankov’s Theorem.Yoshihito Tanaka - 2007 - Studia Logica 86 (1):111-131.
    It is known that for any subdirectly irreducible finite Heyting algebra A and any Heyting algebra, B, A is embeddable into a quotient algebra of B, if and only if Jankov's formula ${\rm{\chi A}}$ A for A is refuted in B. In this paper, we present an infinitary extension of the above theorem given by Jankov. More precisely, for any cardinal number ${\rm{\kappa }}$, we present Jankov's theorem for homomorphisms preserving infinite meets and joins, a class of subdirectly irreducible complete (...)
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  8.  18
    Model Existence in Non-Compact Modal Logic.Yoshihito Tanaka - 2001 - Studia Logica 67 (1):61-73.
    Predicate modal logics based on Kwith non-compact extra axioms are discussed and a sufficient condition for the model existence theorem is presented. We deal with various axioms in a general way by an algebraic method, instead of discussing concrete non-compact axioms one by one.
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  9.  9
    Cut-Elimination Theorems of Some Infinitary Modal Logics.Yoshihito Tanaka - 2001 - Mathematical Logic Quarterly 47 (3):327-340.
    In this article, a cut-free system TLMω1 for infinitary propositional modal logic is proposed which is complete with respect to the class of all Kripke frames.The system TLMω1 is a kind of Gentzen style sequent calculus, but a sequent of TLMω1 is defined as a finite tree of sequents in a standard sense. We prove the cut-elimination theorem for TLMω1 via its Kripke completeness.
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