A uniform approach to three-valued semantics for μ-calculus on abstractions of hybrid automata

In this paper, we consider the definition of a three-valued semantics for a μ-calculus on abstractions of hybrid automata. To this end, we first develop a framework that is general in the sense that it provides a preservation result for several possible semantics of the modal operators. In a second step, we instantiate our framework to two particular abstractions. To this end, a key issue is the consideration of both over- and underapproximated reachability, while classic simulation-based abstractions rely only on overapproximations, and therefore limit the preservation to the universal (μ-calculus') fragment. To specialize our general result, we consider (1) modal abstractions, where the notions of 'may' and 'must' transitions are extended from the purely discrete to the hybrid time framework, and (2) so-called discrete bounded bisimulation abstractions. © 2010 Springer-Verlag.