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

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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Official URL: http://dx.doi.org/10.1017/jsl.2019.22

Abstract / Description

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.

Item Type: Article
Uncontrolled Keywords: semilattices with operators; modal logic; Kripke completeness
Subjects: 500 Natural Sciences and Mathematics > 510 Mathematics
Department: School of Computing and Digital Media
Depositing User: Stanislav Kikot
Date Deposited: 21 May 2020 08:45
Last Modified: 21 May 2020 08:45
URI: http://repository.londonmet.ac.uk/id/eprint/5803

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