Probabilistic Horn abduction is a simple framework to combine probabilistic and logical reasoning into a coherent practical framework. The numbers can be consistently interpreted probabilistically, and all of the rules can be interpreted logically. The relationship between probabilistic Horn abduction and logic programming is at two levels. At the rst level probabilistic Horn abduction is an extension of pure Prolog, that is useful for diagnosis and other evidential reasoning tasks. At another level, current logic programming implementation techniques can be used to e ciently implement probabilistic Horn abduction. This forms the basis of an \anytime" algorithm for estimating arbitrary conditional probabilities. The focus of this paper is on the implementation. Scholar, Canadian Institute for Advanced Research 1