Temporal Logic with Recursion

We introduce extensions of the standard temporal logics CTL and LTL with a recursion operator that takes propositional arguments. Unlike other proposals for modal fixpoint logics of high expressive power, we obtain logics that retain some of the appealing pragmatic advantages of CTL and LTL, yet have expressive power beyond that of the modal μ-calculus or MSO. We advocate these logics by showing how the recursion operator can be used to express interesting non-regular properties. We also study decidability and complexity issues of the standard decision problems.