A Stochastic Interpretation of Propositional Dynamic Logic: Expressivity

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We 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.