Basic modal congruent and monotonic multilattice logics

Авторы: Grigoriev Oleg, Petrukhin Yaroslav
Журнал: Journal of Logic and Computation
Том: 33
Номер: 6
Год издания: 2023
Издательство: Oxford University Press
Местоположение издательства: United Kingdom
Первая страница: 1379
Последняя страница: 1398
DOI: 10.1093/logcom/exac028
Аннотация: In the paper, we introduce multilattice versions of the basic congruent and monotonic modal logics. In the case of congruent and monotonic ones, we also study their extensions by Gödel’s rule. We formulate these logics in the form of sequent calculi and prove syntactic embedding theorems (as a consequence, we obtain cut admissibility and decidability). Then we present them algebraically and semantically: via modal multilattices and via general and descriptive neighbourhood frames. We show the dual equivalency of the categories of modal multilattices and descriptive neighbourhood frames. Using Lindenbaum–Tarski algebras, we prove that the sequent calculi under consideration are sound and complete with respect to modal multilattices.
Добавил в систему: Петрухин Ярослав Игоревич

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