Inference in Probabilistic Logic Programs Using Lifted Explanations

In this paper, we consider the problem of lifted inference in the context of Prism-like probabilistic logic programming languages. Traditional inference in such languages involves the construction of an explanation graph for the query that treats each instance of a random variable separately. For many programs and queries, we observe that explanations can be summarized into substantially more compact structures introduced in this paper, called "lifted explanation graph". In contrast to existing lifted inference techniques, our method for constructing lifted explanations naturally generalizes existing methods for constructing explanation graphs. To compute probability of query answers, we solve recurrences generated from the lifted graphs. We show examples where the use of our technique reduces the asymptotic complexity of inference