A Decidable Propositional Dynamic Logic with Explicit Probabilities

A propositional version of Feldman and Harel's Pr DL (1982, “14th ACM Sympos. on Theory of Computing,” pp. 181–195; J. Comput. System Sci. 28 , No. 2 (1984), 193–215) is defined, and shown to be decidable in double-exponential space. The logic allows propositional-level formulas involving probabilistic programs, and contains the full (quantified) real-number theory for dealing with probabilities. The decidability proof introduces a succession of abstractions of the notion of a model, from the full generality of measure theoretical models, down to the finite schematic models , which seem to be the most basic structures relating programs and probabilities.

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