A Quantitative Characterization of Weighted Kripke Structures in Temporal Logic

Abstract

We extend the usual notion of Kripke structures with a weighted transition relation and generalize the classical Boolean interpretation of CTL to a map which assigns to states and temporal formulae a real-valued distance describing the degree of satisfaction. We describe a general approach to obtaining quantitative interpretations for a generic extension of the CTL syntax and show that, for one such interpretation, the logic is both adequate and expressive with respect to quantitative bisimulation.