System Description, Abstraction, and Veriication: a Uniform Treatment of Quality and Quantity

We build on the established work on modal transition systems and probabilistic speci-cations to sketch a framework in which system descriptions, abstraction, and nite-state model checking all have a uniform presentation across various levels of qualitative and quantitative views together with mediating abstraction and concretization maps. We choose labeled Kripke structures, modal transition systems, and interval transition systems as such possible views and interpret the latter models in a modal and probabilistic way. We prove safety results for their abstractions within and across such views for the \forall fragment" of the modal mu-calculus and show that they allow for some compositional reasoning with respect to a process algebra a la CCS. Modal reenement is shown to be sound for model checks based on a variety of probabilistic semantics. The view based on interval transition systems can be seen to provide a foundation for model checking systems with descriptions of evidence by endowing intervals with predicates of guarantees, respectively possibilities.