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  1. Johan Benthem, Nick Bezhanishvili & Ian Hodkinson (2012). Sahlqvist Correspondence for Modal Mu-Calculus. Studia Logica 100 (1-2):31-60.
    We define analogues of modal Sahlqvist formulas for the modal mu-calculus, and prove a correspondence theorem for them.
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  2. 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 (...)
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  3. Nick Bezhanishvili & Dick de Jongh (2012). Extendible Formulas in Two Variables in Intuitionistic Logic. Studia Logica 100 (1-2):61-89.
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  4. Nick Bezhanishvili & Dick Jongh (2012). Extendible Formulas in Two Variables in Intuitionistic Logic. Studia Logica 100 (1-2):61-89.
    We give alternative characterizations of exact, extendible and projective formulas in intuitionistic propositional calculus IPC in terms of n -universal models. From these characterizations we derive a new syntactic description of all extendible formulas of IPC in two variables. For the formulas in two variables we also give an alternative proof of Ghilardi’s theorem that every extendible formula is projective.
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  5. Johan van Benthem, Nick Bezhanishvili & Ian Hodkinson (2012). Sahlqvist Correspondence for Modal Mu-Calculus. Studia Logica 100 (1):31-60.
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  6. 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 (...)
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  7. 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.
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  8. 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]. (...)
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  9. Nick Bezhanishvili (2008). Frame Based Formulas for Intermediate Logics. Studia Logica 90 (2):139 - 159.
    In this paper we define the notion of frame based formulas. We show that the well-known examples of formulas arising from a finite frame, such as the Jankov-de Jongh formulas, subframe formulas and cofinal subframe formulas, are all particular cases of the frame based formulas. We give a criterion for an intermediate logic to be axiomatizable by frame based formulas and use this criterion to obtain a simple proof that every locally tabular intermediate logic is axiomatizable by Jankov-de Jongh formulas. (...)
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  10. Nick Bezhanishvili & Ian Hodkinson (2004). All Normal Extensions of S5-Squared Are Finitely Axiomatizable. Studia Logica 78 (3):443 - 457.
    We prove that every normal extension of the bi-modal system S52 is finitely axiomatizable and that every proper normal extension has NP-complete satisfiability problem.
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  11. Nick Bezhanishvili & Maarten Marx (2003). All Proper Normal Extensions of S5-Square Have the Polynomial Size Model Property. Studia Logica 73 (3):367 - 382.
    We show that every proper normal extension of the bi-modal system S5 2 has the poly-size model property. In fact, to every proper normal extension L of S5 2 corresponds a natural number b(L) - the bound of L. For every L, there exists a polynomial P(·) of degree b(L) + 1 such that every L-consistent formula is satisfiable on an L-frame whose universe is bounded by P(||), where || denotes the number of subformulas of . It is shown that (...)
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