Expressivity of Many-Valued Modal Logics, Coalgebraically

Autoři: Mgr. Marta Bílková, Ph.D.
Matěj Dostál
Rok vydání: 2016
Typ publikace: Konferenční příspěvek (mezinárodní konf.)
Periodikum: Logic, Language, Information, and Computation
Projekty: Modelování vágních kvantifikátorů v matematické fuzzy logice
Neklasické výrokové a predikátové logiky: přístup založený na uspořádání
Bibliografická citace: BÍLKOVÁ, Marta, DOSTÁL, Matěj. Expressivity of Many-Valued Modal Logics, Coalgebraically. In: VÄÄNÄNEN, J., HIRVONEN, A., DE QUEIROZ, R., eds. Logic, Language, Information, and Computation. Berlin: Springer, 2016, S. 109-124. Lecture Notes in Computer Science, 9803. ISBN 978-3-662-52920-1. ISSN 0302-9743
Dostupné z: doi:10.1007/978-3-662-52921-8_8
DOI: 10.1007/978-3-662-52921-8_8
ID: 461966

Abstrakt

We apply methods developed to study coalgebraic logic to investigate expressivity of many-valued modal logics which we consider as coalgebraic languages interpreted over set-coalgebras with many-valued valuations. The languages are based on many-valued predicate liftings. We provide a characterization theorem for a language generated by a set of such modalities to be expressive for bisimilarity: in addition to the usual condition on the set of predicate liftings being separating, we indicate a sufficient and sometimes also necessary condition on the algebra of truth values which guarantees expressivity. 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.