We extend the usual notion of Kripke Structures with a weighted transition relation, and generalize the usual Boolean satisfaction relation 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.
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