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Kripke completeness of strictly positive modal logics over meet-semilattices with operators

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Kikot, Stanislav, Kurucz, Agi, Tanaka, Yoshihito, Wolter, Frank and Zakharyaschev, Michael (2019) Kripke completeness of strictly positive modal logics over meet-semilattices with operators. Journal of Symbolic Logic, 84 (02). pp. 533-588. ISSN 0022-4812

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Abstract

Our concern is the completeness problem for spi-logics, that is, sets of implications between strictly positive formulas built from propositional variables, conjunction and modal diamond operators. Originated in logic, algebra and computer science, spi-logics have two natural semantics: meet-semilattices with monotone operators providing Birkhoff-style calculi and first-order relational structures (aka Kripke frames) often used as the intended structures in applications. Here we lay foundations for a completeness theory that aims to answer the question whether the two semantics define the same consequence relations for a given spi-logic.

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