We show that the alternation hierarchy of the modal mu-calculus does not collapse, and that all modal fix-point properties can be expressed with only a few alternations.Expand

This monograph aims to provide a powerful general-purpose proof tech nique for the verification of systems, whether finite or infinite. It extends the idea of finite local model-checking, which was… Expand

We present a sound and complete tableau proof system for establishing whether a set of elements of an arbitrary transition system model has a property expressed in (a slight extension of) the modal mu-calculus.Expand

We consider modal analogues of Hintikka et al.'s 'independence-friendly first-order logic', and discuss their relationship to equivalences previously studied in concurrency theory.Expand

We provide a sound and complete tableau system for proving temporal properties of states (processes or markings) in arbitrary infinite transition system models.Expand