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 (2). pp. 533-588.

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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.

Item Type:	Article
Uncontrolled Keywords:	semilattices with operators, modal logic, Kripke completeness
Depositing User:	Symplectic Admin
Date Deposited:	24 Apr 2019 08:45
Last Modified:	19 Jan 2023 00:53
DOI:	10.1017/jsl.2019.22
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3038157