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A Logic of Probability with Decidable Model Checking *

A predicate logic of probability, close to the logics of probability of Halpern et al ., is introduced. Our main result concerns the following model-checking problem: deciding whether a given formula holds on the structure defined by a given finite probabilistic process. We show that this model-checking problem is decidable for a rather large subclass of formulas of a second-order monadic logic of probability. We discuss also the decidability of satisfiability and compare our logic of probability with the probabilistic temporal logic pCTL * . * Partially supported by French-Israeli Arc-en-ciel/Keshet project No. 30 and No. 15. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Logic And Computation Oxford University Press

A Logic of Probability with Decidable Model Checking *

Abstract

A predicate logic of probability, close to the logics of probability of Halpern et al ., is introduced. Our main result concerns the following model-checking problem: deciding whether a given formula holds on the structure defined by a given finite probabilistic process. We show that this model-checking problem is decidable for a rather large subclass of formulas of a second-order monadic logic of probability. We discuss also the decidability of satisfiability and compare our logic of probability with the probabilistic temporal logic pCTL * . * Partially supported by French-Israeli Arc-en-ciel/Keshet project No. 30 and No. 15.
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