Postprint version. Published in International Conference on Logic Programming (ICLP’2004) Proceedings: St. Malo, France, September 1, 2004, pages 137-148.
NOTE: At the time of publication, the author Alex Dekhtyar was not yet affiliated with Cal Poly.
In this paper we consider a logic programming framework for rea-soning about imprecise probabilities. In particular, we propose a new semantics, for the Probabilistic Logic Programs (p-programs) of Ng and Subrahmanian. P-programs represent imprecision using probability intervals. Our semantics, based on the possible worlds semantics, considers all point probability distributions that satisfy a given p-program. In the paper, we provide the exact characterization of such models of a p-program. We show that the set of models of a p-program can-not, in general case, be described by single intervals associated with atoms of the program. We provide algorithms for efficient construction of this set of models and study their complexity.