Many-valued modal logics, coalgebraically

Marta Bilkova (Charles University, Prague)

Marta Bilkova (Charles University) will present "Many-valued modal logics, coalgebraically" on March 17 at 11 in Old Quad G09.

Abstract: We apply methods of coalgebraic logic to investigate many-valued modal logics which we therefore consider as coalgebraic languages interpreted over set-coalgebras with genuinely many-valued valuations. In this talk, we concentrate on expressivity of modal languages based on modalities understood semantically as many-valued predicate liftings. We provide a sufficient condition for a language generated by a set of such modalities to be expressive for bisimilarity: the condition says that we can separate behaviours using the propositional language and modalities. The condition is a generalization of the usual separation condition on the set of predicate liftings, but now it also involves the algebra of truth values substantially. Thus, adapting results of Schroder concerning expressivity of boolean coalgebraic logics to many-valued setting, we generalize results of Metcalfe and Marti, concerning Hennessy-Milner property for many-valued modal logics based on box and diamond.