Possible Worlds Semantics for Probabilistic Logic Programs

In this paper we consider a logic programming framework for reasoning about imprecise probabilities. In particular, we propose a new semantics, for the Probabilistic Logic Programs (p-programs) of Ng and Subrahmanian. Pprograms 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 cannot, 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.