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June 2012 A stochastic interpretation of propositional dynamic logic: expressivity
Ernst-Erich Doberkat
J. Symbolic Logic 77(2): 687-716 (June 2012). DOI: 10.2178/jsl/1333566646

Abstract

We propose a probabilistic interpretation of Propositional Dynamic Logic (PDL). We show that logical and behavioral equivalence are equivalent over general measurable spaces. This is done first for the fragment of straight line programs and then extended to cater for the nondeterministic nature of choice and iteration, expanded to PDL as a whole. 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 𝒜 from descriptive set theory. This leads to a discussion of complete stochastic Kripke models and model completion, which permits an adequate treatment of the test operator.

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Ernst-Erich Doberkat. "A stochastic interpretation of propositional dynamic logic: expressivity." J. Symbolic Logic 77 (2) 687 - 716, June 2012. https://doi.org/10.2178/jsl/1333566646

Information

Published: June 2012
First available in Project Euclid: 4 April 2012

zbMATH: 1252.03074
MathSciNet: MR2787246
Digital Object Identifier: 10.2178/jsl/1333566646

Rights: Copyright © 2012 Association for Symbolic Logic

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Vol.77 • No. 2 • June 2012
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