Probabilistic temporal logics via the modal mu-calculus

This paper presents a mu-calculus-based modal logic for describing properties of probabilistic labeled transition systems (PLTSs) and develops a model-checking algorithm for determining whether or not states in finite-state PLTSs satisfy formulas in the logic. The logic is based on the distinction between (probabilistic) "systems" and (non- probabilistic) "observations": using the modal mu-calculus, one may specify sets of observations, and the semantics of our logic then enable statements to be made about the measures of such sets at various system states. The logic may be used to encode a variety of probabilistic modal and temporal logics; in addition, the model-checking problem for it may be reduced to the calculation of solutions to systems of non-linear equations.