First-order Probabilistic Inference Revisited

Following ideas in Poole~\poole, which we correct, formalize and extend, this paper presents the first provable algorithm for reasoning with probabilistic first-order representations at the {\em lifted} level. Specifically, the algorithm automates the process of probabilistic reasoning about populations of individuals, their properties and the relations between them, without the need to ground the probabilistic knowledge base. The algorithm makes use of unification to guide an interleaving of variable ordering and first-order variable elimination. Importantly, our contribution includes the formalization of concepts necessary to reason about the algorithm's correctness and its correctness proof