A Stochastic Interpretation of Propositional Dynamic Logic: Expressivity

Abstract

AbstractWe propose a probabilistic interpretation of Propositional Dynamic Logic (PDL). We show that logical and behavioral equivalence are equivalent over general measurable spaces. Bisimilarity is also discussed and shown to be equivalent to logical and behavioral equivalence, provided the base spaces are Polish spaces. We adapt techniques from coalgebraic stochastic logic and point out some connections to Souslin’s operation \(\mathcal{A}\) from descriptive set theory.KeywordsModal LogicMeasurable SpacePolish SpaceEquivalent ModelProbabilistic InterpretationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.