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Journal of Logic and Computation Advance Access published online on July 26, 2006
Journal of Logic and Computation, 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
Received October 12, 2003

Original Papers

A Logic of Probability with Decidable Model Checking

Daniéle Beauquier 1 *, Alexander Rabinovich 2 *, and Anatol Slissenko 1 *

1 University Paris 12, France
2 Tel-Aviv University, Israel

* To whom correspondence should be addressed.
Daniéle Beauquier, E-mail: beauquier{at}univ-paris12.fr
Alexander Rabinovich, E-mail: rabino{at}math.tau.ac.il
Anatol Slissenko, E-mail: slissenko{at}univ-paris12.fr


  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*

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

Partially supported by French-Israeli Arc-en-ciel/Keshet project No. 30 and No. 15.


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