On temporal logic versus datalog

We provide a direct and modular translation from the temporal logics CTL, ETL, FCTL (CTL extended with the ability to express fairness) and the Modal μ-calculus to Monadic inf-Datalog with built-in predicates. We call it inf-Datalog because the semantics we provide is a little different from the conventional Datalog least fixed point semantics, in that some recursive rules (corresponding to least fixed points) are allowed to unfold only finitely many times, whereas others (corresponding to greatest fixed points) are allowed to unfold infinitely many times. We characterize the fragments of Monadic inf-Datalog that have the same expressive power as Modal Logic (resp. CTL, alternation-free Modal μ-calculus and Modal μ-calculus). Our translation is interesting because it is direct and succinct. Moreover the fragments of Monadic inf-Datalog that we have exhibited have very simple syntactic characterizations as subsets of what we call Modal inf-Datalog programs.