Modal multilattice logics with Tarski, Kuratowski, and Halmos operators

Oleg Grigoriev; Yaroslav Petrukhin

doi:10.12775/LLP.2021.003

Authors

Oleg Grigoriev Lomonosov Moscow State University, Department of Logic, Faculty of Philosophy
Yaroslav Petrukhin Lodz University, Department of Logic, Institute of Philosophy

DOI:

https://doi.org/10.12775/LLP.2021.003

Keywords

multilattice logic, modal logic, sequent calculus, algebraic completeness, neighbourhood semantics, embedding theorem

Abstract

In this paper, we consider modal multilattices with Tarski, Kuratowski, and Halmos closure and interior operators as well as the corresponding logics which are multilattice versions of the modal logics MNT4, S4, and S5, respectively. The former modal multilattice logic is a new one. The latter two modal multilattice logics have been already mentioned in the literature, but algebraic completeness results have not been established for them before. We present a multilattice version of MNT4 in a form of a sequent calculus and prove the algebraic and neighbourhood completeness theorems for it. We extend the algebraic completeness result for the multilattice versions of S4 and S5 as well.

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