Stochastic coalgebraic logic: Bisimilarity and behavioral equivalence

Bisimulations, behavioral equivalence and logical equivalence are investigated for stochastic T-coalgebras that interpret coalgebraic logic which is defined in terms of predicate liftings. We investigate the conditions for the functor under which these notions of equivalence are related by discussing congruences for the underlying stochastic relation. It is demonstrated that logics as diverse as continuous time stochastic logic and general modal logics can be usefully approached through coalgebraic methods.