34 found
Sort by:
Disambiguations:
Guram Bezhanishvili [30]G. Bezhanishvili [4]
  1. J. Van Benthem, G. Bezhanishvili, B. Ten Cate & D. Sarenac (forthcoming). Modal Logics for Products of Topologies. Studia Logica. To Appear.
    No categories
     
    My bibliography  
     
    Export citation  
  2. Guram Bezhanishvili & Joel Lucero-Bryan (forthcoming). Subspaces of Whose D-Logics Do Not Have the FMP. Archive for Mathematical Logic.
    No categories
    Direct download  
     
    My bibliography  
     
    Export citation  
  3. Marco Aiello, Guram Bezhanishvili, Isabelle Bloch & Valentin Goranko (2012). Logic for Physical Space. Synthese 186 (3):619-632.
    Since the early days of physics, space has called for means to represent, experiment, and reason about it. Apart from physicists, the concept of space has intrigued also philosophers, mathematicians and, more recently, computer scientists. This longstanding interest has left us with a plethora of mathematical tools developed to represent and work with space. Here we take a special look at this evolution by considering the perspective of Logic. From the initial axiomatic efforts of Euclid, we revisit the major milestones (...)
    No categories
    Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  4. Marco Aiello, Guram Bezhanishvili, Isabelle Bloch & Valentin Goranko (2012). Logic for Physical Space: From Antiquity to Present Days. Synthese 186 (3):619 - 632.
    Since the early days of physics, space has called for means to represent, experiment, and reason about it. Apart from physicists, the concept of space has intrigued also philosophers, mathematicians and, more recently, computer scientists. This longstanding interest has left us with a plethora of mathematical tools developed to represent and work with space. Here we take a special look at this evolution by considering the perspective of Logic. From the initial axiomatic efforts of Euclid, we revisit the major milestones (...)
    No categories
    Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  5. Lev Beklemishev, Guram Bezhanishvili, Daniele Mundici & Yde Venema (2012). Foreword. Studia Logica 100 (1-2):1-7.
    Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  6. Guram Bezhanishvili & Nick Bezhanishvili (2012). Canonical Formulas for Wk4. Review of Symbolic Logic 5 (4):731-762.
    We generalize the theory of canonical formulas for K4, the logic of transitive frames, to wK4, the logic of weakly transitive frames. Our main result establishes that each logic over wK4 is axiomatizable by canonical formulas, thus generalizing Zakharyaschev’s theorem for logics over K4. The key new ingredients include the concepts of transitive and strongly cofinal subframes of weakly transitive spaces. This yields, along with the standard notions of subframe and cofinal subframe logics, the new notions of transitive subframe and (...)
    No categories
    Direct download (7 more)  
     
    My bibliography  
     
    Export citation  
  7. Guram Bezhanishvili & Joel Lucero-Bryan (2012). More on D-Logics of Subspaces of the Rational Numbers. Notre Dame Journal of Formal Logic 53 (3):319-345.
    We prove that each countable rooted K4 -frame is a d-morphic image of a subspace of the space $\mathbb{Q}$ of rational numbers. From this we derive that each modal logic over K4 axiomatizable by variable-free formulas is the d-logic of a subspace of $\mathbb{Q}$ . It follows that subspaces of $\mathbb{Q}$ give rise to continuum many d-logics over K4 , continuum many of which are neither finitely axiomatizable nor decidable. In addition, we exhibit several families of modal logics finitely axiomatizable (...)
    Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  8. Guram Bezhanishvili & Joel Lucero-Bryan (2012). Subspaces of {Mathbb{Q}} Whose D-Logics Do Not Have the FMP. Archive for Mathematical Logic 51 (5-6):661-670.
    We show that subspaces of the space ${\mathbb{Q}}$ of rational numbers give rise to uncountably many d-logics over K4 without the finite model property.
    No categories
    Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  9. Guram Bezhanishvili & Nick Bezhanishvili (2011). An Algebraic Approach to Canonical Formulas: Modal Case. Studia Logica 99 (1-3):93-125.
    We introduce relativized modal algebra homomorphisms and show that the category of modal algebras and relativized modal algebra homomorphisms is dually equivalent to the category of modal spaces and partial continuous p-morphisms, thus extending the standard duality between the category of modal algebras and modal algebra homomorphisms and the category of modal spaces and continuous p-morphisms. In the transitive case, this yields an algebraic characterization of Zakharyaschev’s subreductions, cofinal subreductions, dense subreductions, and the closed domain condition. As a consequence, we (...)
    Direct download (7 more)  
     
    My bibliography  
     
    Export citation  
  10. Guram Bezhanishvili & David Gabelaia (2011). Connected Modal Logics. Archive for Mathematical Logic 50 (3-4):287-317.
    We introduce the concept of a connected logic (over S4) and show that each connected logic with the finite model property is the logic of a subalgebra of the closure algebra of all subsets of the real line R, thus generalizing the McKinsey-Tarski theorem. As a consequence, we obtain that each intermediate logic with the finite model property is the logic of a subalgebra of the Heyting algebra of all open subsets of R.
    No categories
    Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  11. Guram Bezhanishvili & Ramon Jansana (2011). Priestley Style Duality for Distributive Meet-Semilattices. Studia Logica 98 (1-2):83-122.
    We generalize Priestley duality for distributive lattices to a duality for distributive meet-semilattices. On the one hand, our generalized Priestley spaces are easier to work with than Celani’s DS-spaces, and are similar to Hansoul’s Priestley structures. On the other hand, our generalized Priestley morphisms are similar to Celani’s meet-relations and are more general than Hansoul’s morphisms. As a result, our duality extends Hansoul’s duality and is an improvement of Celani’s duality.
    Direct download (7 more)  
     
    My bibliography  
     
    Export citation  
  12. Guram Bezhanishvili, Leo Esakia & David Gabelaia (2010). The Modal Logic of Stone Spaces: Diamond as Derivative. Review of Symbolic Logic 3 (1):26-40.
    We show that if we interpret modal diamond as the derived set operator of a topological space, then the modal logic of Stone spaces is K4 and the modal logic of weakly scattered Stone spaces is K4G. As a corollary, we obtain that K4 is also the modal logic of compact Hausdorff spaces and K4G is the modal logic of weakly scattered compact Hausdorff spaces.
    Direct download (8 more)  
     
    My bibliography  
     
    Export citation  
  13. Guram Bezhanishvili, Silvio Ghilardi & Mamuka Jibladze (2010). An Algebraic Approach to Subframe Logics. Modal Case. Notre Dame Journal of Formal Logic 52 (2):187-202.
    We prove that if a modal formula is refuted on a wK4-algebra ( B ,□), then it is refuted on a finite wK4-algebra which is isomorphic to a subalgebra of a relativization of ( B ,□). As an immediate consequence, we obtain that each subframe and cofinal subframe logic over wK4 has the finite model property. On the one hand, this provides a purely algebraic proof of the results of Fine and Zakharyaschev for K4 . On the other hand, it (...)
    Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  14. Guram Bezhanishvili & Patrick J. Morandi (2010). Scattered and Hereditarily Irresolvable Spaces in Modal Logic. Archive for Mathematical Logic 49 (3):343-365.
    When we interpret modal ◊ as the limit point operator of a topological space, the Gödel-Löb modal system GL defines the class Scat of scattered spaces. We give a partition of Scat into α-slices S α , where α ranges over all ordinals. This provides topological completeness and definability results for extensions of GL. In particular, we axiomatize the modal logic of each ordinal α, thus obtaining a simple proof of the Abashidze–Blass theorem. On the other hand, when we interpret (...)
    No categories
    Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  15. Guram Bezhanishvili (2009). The Universal Modality, the Center of a Heyting Algebra, and the Blok–Esakia Theorem. Annals of Pure and Applied Logic 161 (3):253-267.
    Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  16. Guram Bezhanishvili & Nick Bezhanishvili (2009). An Algebraic Approach to Canonical Formulas: Intuitionistic Case. Review of Symbolic Logic 2 (3):517-549.
    We introduce partial Esakia morphisms, well partial Esakia morphisms, and strong partial Esakia morphisms between Esakia spaces and show that they provide the dual description of (, , 0) homomorphisms, and ( , s subreductions, cofinal subreductions, dense subreductions, and the closed domain condition. As a consequence, we obtain a new simplified proof (which is algebraic in nature) of Zakharyaschev’s theorem that each intermediate logic can be axiomatized by canonical formulas.
    Direct download (8 more)  
     
    My bibliography  
     
    Export citation  
  17. Guram Bezhanishvili & John Harding (2009). The Modal Logic of {Beta(Mathbb{N})}. Archive for Mathematical Logic 48 (3-4):231-242.
    Let ${\beta(\mathbb{N})}$ denote the Stone–Čech compactification of the set ${\mathbb{N}}$ of natural numbers (with the discrete topology), and let ${\mathbb{N}^\ast}$ denote the remainder ${\beta(\mathbb{N})-\mathbb{N}}$ . We show that, interpreting modal diamond as the closure in a topological space, the modal logic of ${\mathbb{N}^\ast}$ is S4 and that the modal logic of ${\beta(\mathbb{N})}$ is S4.1.2.
    No categories
    Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  18. Guram Bezhanishvili, Nick Bezhanishvili & Dick de Jongh (2008). The Kuznetsov-Gerčiu and Rieger-Nishimura Logics. Logic and Logical Philosophy 17 (1-2):73-110.
    We give a systematic method of constructing extensions of the Kuznetsov-Gerčiu logic KG without the finite model property (fmp for short), and show that there are continuum many such. We also introduce a new technique of gluing of cyclic intuitionistic descriptive frames and give a new simple proof of Gerčiu’s result [9, 8] that all extensions of the Rieger-Nishimura logic RN have the fmp. Moreover, we show that each extension of RN has the poly-size model property, thus improving on [9]. (...)
    Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  19. Guram Bezhanishvili & Silvio Ghilardi (2007). An Algebraic Approach to Subframe Logics. Intuitionistic Case. Annals of Pure and Applied Logic 147 (1):84-100.
    Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  20. J. Van Benthem, G. Bezhanishvili, B. Ten Cate & D. Sarenac (2006). Multimodal Logics of Products of Topologies. Studia Logica 84 (3):369 - 392.
    We introduce the horizontal and vertical topologies on the product of topological spaces, and study their relationship with the standard product topology. We show that the modal logic of products of topological spaces with horizontal and vertical topologies is the fusion ${\bf S4}\oplus {\bf S4}$ . We axiomatize the modal logic of products of spaces with horizontal, vertical, and standard product topologies. We prove that both of these logics are complete for the product of rational numbers ${\Bbb Q}\times {\Bbb Q}$ (...)
    Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  21. J. van Benthem, G. Bezhanishvili, B. ten Cate & D. Sarenac (2006). Multimo Dal Logics of Products of Topologies. Studia Logica 84 (3).
    We introduce the horizontal and vertical topologies on the product of topological spaces, and study their relationship with the standard product topology. We show that the modal logic of products of topological spaces with horizontal and vertical topologies is the fusion S4 ⊕ S4. We axiomatize the modal logic of products of spaces with horizontal, vertical, and standard product topologies.We prove that both of these logics are complete for the product of rational numbers ℚ × ℚ with the appropriate topologies.
    Direct download  
     
    My bibliography  
     
    Export citation  
  22. J. van Benthem, G. Bezhanishvili, B. ten Cate & D. Sarenac (2006). Mr2290114 (2007i: 03026) 03b45. Studia Logica 84 (3):369-392.
    No categories
     
    My bibliography  
     
    Export citation  
  23. Johan van Benthem, Guram Bezhanishvili, Balder Ten Cate & Darko Sarenac (2006). Modal Logics for Product Topologies. Studia Logica 84 (3):375-99.
    No categories
     
    My bibliography  
     
    Export citation  
  24. Johan van Benthem, Guram Bezhanishvili, Balder ten Cate & Darko Sarenac (2006). Multimo Dal Logics of Products of Topologies. Studia Logica 84 (3):369-392.
    Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  25. Guram Bezhanishvili, Leo Esakia & David Gabelaia (2005). Some Results on Modal Axiomatization and Definability for Topological Spaces. Studia Logica 81 (3):325 - 355.
    We consider two topological interpretations of the modal diamond—as the closure operator (C-semantics) and as the derived set operator (d-semantics). We call the logics arising from these interpretations C-logics and d-logics, respectively. We axiomatize a number of subclasses of the class of nodec spaces with respect to both semantics, and characterize exactly which of these classes are modally definable. It is demonstrated that the d-semantics is more expressive than the C-semantics. In particular, we show that the d-logics of the six (...)
    Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  26. Guram Bezhanishvili & Mai Gehrke (2005). Completeness of S4 with Respect to the Real Line: Revisited. Annals of Pure and Applied Logic 131 (1):287-301.
    Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  27. Johan Van Benthem, Guram Bezhanishvili & Mai Gehrke (2003). Euclidean Hierarchy in Modal Logic. Studia Logica 75 (3):327 - 344.
    For a Euclidean space ${\Bbb R}^{n}$ , let $L_{n}$ denote the modal logic of chequered subsets of ${\Bbb R}^{n}$ . 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 $L_{\infty}$ of chequered subsets of ${\Bbb R}^{\infty}$ . As a result, we obtain that $L_{\infty}$ is (...)
    Direct download (2 more)  
     
    My bibliography  
     
    Export citation  
  28. Johan van Benthem, Guram Bezhanishvili & Mai Gehrke (2003). Euclidean Hierarchy in Modal Logic. 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 (...)
    Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  29. Johan van Benthem, Guram Bezhanishvili & Mai Gehrke (2003). Mr2027555 (2005a: 03039) 03b45 (03b35). Studia Logica 75 (3):327-344.
     
    My bibliography  
     
    Export citation  
  30. Guram Bezhanishvili (2001). Glivenko Type Theorems for Intuitionistic Modal Logics. Studia Logica 67 (1):89-109.
    In this article we deal with Glivenko type theorems for intuitionistic modal logics over Prior's MIPC. We examine the problems which appear in proving Glivenko type theorems when passing from the intuitionistic propositional logic Intto MIPC. As a result we obtain two different versions of Glivenko's theorem for logics over MIPC. Since MIPCcan be thought of as a one-variable fragment of the intuitionistic predicate logic Q-Int, one of the versions of Glivenko's theorem for logics over MIPCis closely related to that (...)
    Direct download (7 more)  
     
    My bibliography  
     
    Export citation  
  31. Guram Bezhanishvili (2001). Review: Marcus Kracht, Tools and Techniques in Modal Logic. [REVIEW] Bulletin of Symbolic Logic 7 (2):278-279.
    Direct download (2 more)  
     
    My bibliography  
     
    Export citation  
  32. Guram Bezhanishvili (2000). Varieties of Monadic Heyting Algebras. Part III. Studia Logica 64 (2):215-256.
    This paper is the concluding part of [1] and [2], and it investigates the inner structure of the lattice (MHA) of all varieties of monadic Heyting algebras. For every n , we introduce and investigate varieties of depth n and cluster n, and present two partitions of (MHA), into varieties of depth n, and into varieties of cluster n. We pay a special attention to the lower part of (MHA) and investigate finite and critical varieties of monadic Heyting algebras in (...)
    Direct download (8 more)  
     
    My bibliography  
     
    Export citation  
  33. Guram Bezhanishvili (1999). Varieties of Monadic Heyting Algebras Part II: Duality Theory. Studia Logica 62 (1):21-48.
    In this paper we continue the investigation of monadic Heyting algebras which we started in [2]. Here we present the representation theorem for monadic Heyting algebras and develop the duality theory for them. As a result we obtain an adequate topological semantics for intuitionistic modal logics over MIPC along with a Kripke-type semantics for them. It is also shown the importance and the effectiveness of the duality theory for further investigation of monadic Heyting algebras and logics over MIPC.
    Direct download (7 more)  
     
    My bibliography  
     
    Export citation  
  34. Guram Bezhanishvili (1998). Varieties of Monadic Heyting Algebras. Part I. Studia Logica 61 (3):367-402.
    This paper deals with the varieties of monadic Heyting algebras, algebraic models of intuitionistic modal logic MIPC. We investigate semisimple, locally finite, finitely approximated and splitting varieties of monadic Heyting algebras as well as varieties with the disjunction and the existence properties. The investigation of monadic Heyting algebras clarifies the correspondence between intuitionistic modal logics over MIPC and superintuitionistic predicate logics and provides us with the solutions of several problems raised by Ono [35].
    Direct download (8 more)  
     
    My bibliography  
     
    Export citation