Coalgebraic logic
A starting point of the paper is the characterization theorem for infinitary modal logic stating that two points in Kripke models satisfy the same infinitary modal formulas iff they are bisimilar; moreover, every bisimulation type is determined by a single formula [\textit{J. Barwise} and \textit{L. S. Moss}, Vicious circles (CSLI Lect. Notes 60), CSLI, Stanford (1996; Zbl 0865.03002)]. Coalgebraic logics are generalizations of infinitary modal logics. Such a logic is determined by a functor on sets with some properties; formulas are interpreted in coalgebras of that functor. Coalgebraic logics generalize modal logics as well as various logics of transition systems [\textit{J. J. M. M. Rutten}, ``A calculus of transition systems: towards universal coalgebra'', in: A. Ponse, M. de Rijke, Y. Venema (eds.), Modal logic and process algebra: a bisimulation perspective, CSLI Lect. Notes 53, 231-256 (1995; Zbl 0943.68508)]. The paper introduces a semantics for coalgebraic logics and proves soundness for the `minimal F-logic' (completeness remains an open problem). Moreover, it proves characterization results and a representation theorem stating that every final F-coalgebra can be extracted from an F-algebra with a complete semilattice ordering.
scientific article; zbMATH DE number 1308102