Expressivity of Many Valued Modal Logics, Coalgebraically
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 [16] concerning expressivity of boolean coalgebraic logics to many valued setting, we generalize results of Metcalfe and Marti [13] concerning Hennessy Milner property for many valued modal logics based on \Box and \diamondsuit
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