Coalgebraic Logic over Analytic Spaces

Abstract We study coalgebras for endofunctors on the category of an-alytic spaces. Prominent examples are stochastic relations and Markov transition system. Modal logics are interpreted in these coalgebras using predicate liftings, and local versions of the notions of logical equivalence, behavioral equivalence, and bisimilarity are introduced. We show that these notions of equivalence of states coincide for a wide class of func-tors and modal logics. These notions are related to the more traditional (global) notions for coalgebras on the category of analytic spaces.