Revisiting the semantics of interval probabilistic logic programs

Abstract. Two approaches to logic programming with probabilities emerged over time: bayesian reasoning and probabilistic satisfiability (PSAT). The attrac tiveness of the former is in tying the logic programming research to the body of work on Bayes networks. The second approach ties computationally reasoning about probabilities with linear programming, and allows for natural expression of imprecision in probabilities via the use of intervals. In this paper we construct precise semantics for one PSAT-based formalism for reasoning with inteval probabilities, probabilistic logic programs (p-programs), orignally considered by Ng and Subrahmanian. We show that the probability ranges of atoms and formulas in p-programs cannot be expressed as single in tervals. We construct the prescise description of the set of models of p-programs and study the computational complexity if this problem, as well as the problem of consistency of a p-program. We also study the conditions under which our seman tics coincides with the single-interval semantics originally proposed by Ng and Subrahmanian for p-programs. Our work sheds light on the complexity of con struction of reasoning formalisms for imprecise probabilities and suggests that interval probabilities alone are inadequate to support such reasoning.