Expressivity of Many-Valued Modal Logics, Coalgebraically

0461966 - ÚI 2017 RIV DE eng C - Konferenční příspěvek (zahraniční konf.)
Bílková, Marta - Dostál, Matěj
Expressivity of Many-Valued Modal Logics, Coalgebraically.
Logic, Language, Information, and Computation. Berlin: Springer, 2016 - (Väänänen, J.; Hirvonen, A.; de Queiroz, R.), s. 109-124. Lecture Notes in Computer Science, 9803. ISBN 978-3-662-52920-1. ISSN 0302-9743.
[WoLLIC 2016. International Workshop /23./. Puebla (MX), 16.08.2016-19.08.2016]
Grant CEP: GA ČR(CZ) GF15-34650L; GA ČR GA13-14654S
Institucionální podpora: RVO:67985807
Klíčová slova: coalgebra * coalgebraic logic * predicate lifting * modal logic * many-valued logic * expressivity * bisimulation * Hennessy-Milner property
Kód oboru RIV: BA - Obecná matematika

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.
Trvalý link: http://hdl.handle.net/11104/0261503