17 found
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  1.  1
    A Sahlqvist Theorem for Distributive Modal Logic.Mai Gehrke, Hideo Nagahashi & Yde Venema - 2004 - Annals of Pure and Applied Logic 131 (1):65-102.
    In this paper we consider distributive modal logic, a setting in which we may add modalities, such as classical types of modalities as well as weak forms of negation, to the fragment of classical propositional logic given by conjunction, disjunction, true, and false. For these logics we define both algebraic semantics, in the form of distributive modal algebras, and relational semantics, in the form of ordered Kripke structures. The main contributions of this paper lie in extending the notion of Sahlqvist (...)
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  2.  35
    Canonical Extensions and Relational Completeness of Some Substructural Logics.J. Michael Dunn, Mai Gehrke & Alessandra Palmigiano - 2005 - Journal of Symbolic Logic 70 (3):713 - 740.
    In this paper we introduce canonical extensions of partially ordered sets and monotone maps and a corresponding discrete duality. We then use these to give a uniform treatment of completeness of relational semantics for various substructural logics with implication as the residual(s) of fusion.
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  3.  38
    Generalized Kripke Frames.Mai Gehrke - 2006 - Studia Logica 84 (2):241-275.
    Algebraic work [9] shows that the deep theory of possible world semantics is available in the more general setting of substructural logics, at least in an algebraic guise. The question is whether it is also available in a relational form.This article seeks to set the stage for answering this question. Guided by the algebraic theory, but purely relationally we introduce a new type of frames. These structures generalize Kripke structures but are two-sorted, containing both worlds and co-worlds. These latter points (...)
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  4.  29
    Euclidean Hierarchy in Modal Logic.van Benthem Johan, Bezhanishvili Guram & Gehrke Mai - 2003 - Studia Logica 75 (3):327-344.
    For a Euclidean space , let L n denote the modal logic of chequered subsets of . For every n 1, we characterize L n using the more familiar Kripke semantics, thus implying that each L n is a tabular logic over the well-known modal system Grz of Grzegorczyk. We show that the logics L n form a decreasing chain converging to the logic L of chequered subsets of . As a result, we obtain that L is also a logic (...)
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  5.  3
    Completeness of S4 with Respect to the Real Line: Revisited.Guram Bezhanishvili & Mai Gehrke - 2004 - Annals of Pure and Applied Logic 131 (1):287-301.
    We prove that S4 is complete with respect to Boolean combinations of countable unions of convex subsets of the real line, thus strengthening a 1944 result of McKinsey and Tarski 45 141). We also prove that the same result holds for the bimodal system S4+S5+C, which is a strengthening of a 1999 result of Shehtman 369).
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  6.  6
    Canonical Extensions for Congruential Logics with the Deduction Theorem.Mai Gehrke, Ramon Jansana & Alessandra Palmigiano - 2010 - Annals of Pure and Applied Logic 161 (12):1502-1519.
    We introduce a new and general notion of canonical extension for algebras in the algebraic counterpart of any finitary and congruential logic . This definition is logic-based rather than purely order-theoretic and is in general different from the definition of canonical extensions for monotone poset expansions, but the two definitions agree whenever the algebras in are based on lattices. As a case study on logics purely based on implication, we prove that the varieties of Hilbert and Tarski algebras are canonical (...)
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  7.  16
    Some Nonstandard Methods Applied to Distributive Lattices.Mai Gehrke, Matt Insall & Klaus Kaiser - 1990 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 36 (2):123-131.
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  8.  16
    The Order Structure of Stone Spaces and theTD-Separation Axiom.Mai Gehrke - 1991 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 37 (1):5-15.
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  9.  15
    On the Maximality of Some Conormal Extensions of a Lattice.Mai Gehrke & Klaus Kaiser - 1987 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 33 (1):13-18.
  10.  9
    Euclidean Hierarchy in Modal Logic.Johan van Benthem1 Guram Bezhanishvili & Mai Gehrke - 2003 - Studia Logica 75:327-344.
  11. Some Nonstandard Methods Applied to Distributive Lattices.Mai Gehrke, Matt Insall & Klaus Kaiser - 1990 - Mathematical Logic Quarterly 36 (2):123-131.
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  12.  4
    The Order Structure of Stone Spaces and the TD‐Separation Axiom.Mai Gehrke - 1991 - Mathematical Logic Quarterly 37 (1):5-15.
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  13.  1
    Indian Institute of Technology, Kanpur January 14–26, 2008.Ramon Jansana, Mai Gehrke, Alessandra Palmigiano, Mihir K. Chakraborty, Didier Dubois, Eric Pacuit, Rohit Parikh & Prakash Panangaden - 2008 - Bulletin of Symbolic Logic 14 (4).
  14. Relational Semantics for Full Linear Logic.Dion Coumans, Mai Gehrke & Lorijn van Rooijen - 2014 - Journal of Applied Logic 12 (1):50-66.
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  15. Canonical Extensions and Relational Completeness of Some Substructural Logics.J. Dunn, Mai Gehrke & Alessandra Palmigiano - 2005 - Journal of Symbolic Logic 70 (3):713-740.
    In this paper we introduce canonical extensions of partially ordered sets and monotone maps and a corresponding discrete duality. We then use these to give a uniform treatment of completeness of relational semantics for various substructural logics with implication as the residual of fusion.
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  16. On the Maximality of Some Conormal Extensions of a Lattice.Mai Gehrke & Klaus Kaiser - 1987 - Mathematical Logic Quarterly 33 (1):13-18.
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  17. Mr2027555 (2005a: 03039) 03b45 (03b35).Johan van Benthem, Guram Bezhanishvili & Mai Gehrke - 2003 - Studia Logica 75 (3):327-344.
     
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