Strong preservation of temporal fixpoint-based operators by abstract interpretation

Standard abstract model checking relies on abstract Kripke structures which approximate the concrete model by gluing together indistinguishable states. Strong preservation for a specification language L, encodes the equivalence of concrete and abstract model checking of formulas in L. Abstract interpretation allows to design abstract models which are more general than abstract Kripke structures. In this paper we show how abstract interpretation-based models can be exploited in order to specify a general strongly preserving abstract model checking framework. This is shown in particular for specification languages including standard temporal operators which admit a characterization as least/greatest fix-points, as e.g. standard "Finally", "Globally", "Until" and "Release" modalities.