Weighted First Order Model Counting with Directed Acyclic Graph Axioms

Weighted First Order Model Counting (WFOMC) is the task of computing the weighted sum of the models of a first-order logic sentence. Probabilistic inference problems in many statistical relational learning frameworks can be cast as a WFOMC problem. However, in general, WFOMC is known to be intractable (#P_1- complete). Hence, logical fragments that admit polynomial time WFOMC are of significant interest. Such fragments are called domain liftable. Recent works have identified the two-variable fragment of first-order logic, extended with counting quantifiers, to be domain liftable. In this paper, we extend this fragment with a Directed Acyclic Graph axiom, i.e., a relation is interpreted as a Directed Acyclic Graph.