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Journal of Logic and Computation Advance Access originally published online on July 26, 2006
Journal of Logic and Computation 2006 16(4):461-487; doi:10.1093/logcom/exl004
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© The Author, 2006. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Original Articles

A Logic of Probability with Decidable Model Checking*

Daniéle Beauquier

University Paris 12, France

Alexander Rabinovich

Tel-Aviv University, Israel E-mail: rabino{at}math.tau.ac.il

Anatol Slissenko

University Paris 12, France E-mail: slissenko{at}univ-paris12.fr

E-mail: beauquier{at}univ-paris12.fr

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*.

Keywords: Predicate logic of probability; model checking; decidability; finite Markov chain


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