The Hennessy–Milner equivalence for continuous time stochastic logic with mu-operator

A continuous stochastic logic with a μ-operator μCSL is defined, and an interpretation through stochastic relations is proposed. We investigate morphisms for models of μCSL, showing that the associated congruences can be used for an investigation of bisimilarity. The Hennessy–Milner equivalence for μCSL is discussed, and it is shown that models are equivalent iff they are bisimilar, using a general criterion for bisimilarity from the theory of stochastic relations.