1.  48
    Temporalising Tableaux.Roman Kontchakov, Carsten Lutz, Frank Wolter & Michael Zakharyaschev - 2004 - Studia Logica 76 (1):91 - 134.
    As a remedy for the bad computational behaviour of first-order temporal logic (FOTL), it has recently been proposed to restrict the application of temporal operators to formulas with at most one free variable thereby obtaining so-called monodic fragments of FOTL. In this paper, we are concerned with constructing tableau algorithms for monodic fragments based on decidable fragments of first-order logic like the two-variable fragment or the guarded fragment. We present a general framework that shows how existing decision procedures for first-order (...)
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  2.  25
    Undecidability of First-Order Intuitionistic and Modal Logics with Two Variables.Roman Kontchakov, Agi Kurucz & Michael Zakharyaschev - 2005 - Bulletin of Symbolic Logic 11 (3):428-438.
    We prove that the two-variable fragment of first-order intuitionistic logic is undecidable, even without constants and equality. We also show that the two-variable fragment of a quantified modal logic L with expanding first-order domains is undecidable whenever there is a Kripke frame for L with a point having infinitely many successors (such are, in particular, the first-order extensions of practically all standard modal logics like K, K4, GL, S4, S5, K4.1, S4.2, GL.3, etc.). For many quantified modal logics, including those (...)
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    Topology, Connectedness, and Modal Logic.Roman Kontchakov, Ian Pratt-Hartmann, Frank Wolter & Michael Zakharyaschev - 2008 - In Carlos Areces & Robert Goldblatt (eds.), Advances in Modal Logic, Volume 7. CSLI Publications. pp. 151-176.
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