Coalgebraic Semantics of Non-classical Logics
by
ALEXANDER KURZ
Department of Cumputer Science, University of Leicester, UK

Three aspects of coalgebras are the following. Coalgebras generalise relational structures, they give rise to bisimilarity and coinduction, and they dualise algebras. Coalgebras are a category theoretic notion: any functor F on a category C gives rise to F-coalgebras. The functor F acts as a parameter allowing to encode different structures such as Kripke frames, neighbourhood frames, Markov chains and deterministic automata. Topologised structures arise from choosing for C a category of topological spaces. Of particular interest is the case where C is dual to a category of algebras, which then naturally provides (the algebraic semantics of) a logic for F-coalgebras. We will survey recent developments and show that classic results such as the representation theorem of Jónsson and Tarski and the definability theorem of Goldblatt and Thomason work in the coalgebraic setting.

Date received: May 30, 2007