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Weighted First Order Model Counting with Directed Acyclic Graph Axioms

20 February 2023
Sagar Malhotra
Luciano Serafini
ArXiv (abs)PDFHTML
Abstract

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.

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