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

Kikot, Stanislav and Kurucz, A. and Tanaka, Y. and Wolter, F. and Zakharyaschev, Michael (2019) Kripke completeness of strictly positive modal logics over meet-semilattices with operators. Journal of Symbolic Logic 84 (2), pp. 533-588. ISSN 0022-4812.

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Abstract

Our concern is the completeness problem for spi-logics, that is, sets of im- plications between strictly positive formulas built from propositional variables, conjunc- tion and modal diamond operators. Originated in logic, algebra and computer science, spi-logics have two natural semantics: meet-semilattices with monotone operators provid- ing 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 complete- ness theory that aims to answer the question whether the two semantics define the same consequence relations for a given spi-logic.

Metadata

Item Type: Article
School: Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences
Depositing User: Michael Zakhariyashchev
Date Deposited: 03 Apr 2019 14:49
Last Modified: 30 Jul 2025 22:10
URI: https://eprints.bbk.ac.uk/id/eprint/26985

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