A Unifying Framework for Model Checking Labeled Kripke Structures, Modal Transition Systems and Interval Transition Systems

We build on the established work on modal transition systems and probabilistic specifications to sketch a framework in which system description, abstraction, and finite-state model checking all have a uniform presentation across various levels of qualitative and quantitative views together with mediating abstraction and concretization maps. We prove safety results for abstractions within and across such views for the entire modal mu-calculus and show that such abstractions allow for some compositional reasoning with respect to a uniform family of process algebras a la CCS.

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