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The Range of Modal Logic: An essay in memory of George Gargov

Johan van Benthem

Journal of Applied Non-Classical Logics 9 (2-3):407-442 (1999)

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Mereological Bimodal Logics.Li Dazhu & Yanjing Wang - 2022 - Review of Symbolic Logic 15 (4):823-858.details In this paper, using a propositional modal language extended with the window modality, we capture the first-order properties of various mereological theories. In this setting,$\Box \varphi $readsall the parts(of the current object)are$\varphi $, interpreted on the models with awhole-partbinary relation under various constraints. We show that all the usual mereological theories can be captured by modal formulas in our language via frame correspondence. We also correct a mistake in the existing completeness proof for a basic system of mereology by providing (...) Download Export citation Bookmark 1 citation
Guards, Bounds, and generalized semantics.Johan van Benthem - 2005 - Journal of Logic, Language and Information 14 (3):263-279.details Some initial motivations for the Guarded Fragment still seem of interest in carrying its program further. First, we stress the equivalence between two perspectives: (a) satisfiability on standard models for guarded first-order formulas, and (b) satisfiability on general assignment models for arbitrary first-order formulas. In particular, we give a new straightforward reduction from the former notion to the latter. We also show how a perspective shift to general assignment models provides a new look at the fixed-point extension LFP(FO) of first-order (...) Download Export citation Bookmark 5 citations
Some characterization and preservation theorems in modal logic.Tin Perkov - 2012 - Annals of Pure and Applied Logic 163 (12):1928-1939.details A class of Kripke models is modally definable if there is a set of modal formulas such that the class consists exactly of models on which every formula from that set is globally true. In this paper, a class is also considered definable if there is a set of formulas such that it consists exactly of models in which every formula from that set is satisfiable. The notion of modal definability is then generalized by combining these two. For thus obtained (...) Download Export citation Bookmark 2 citations

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