Lifted Inference with Linear Order Axiom

We consider the task of weighted first-order model counting (WFOMC) used for probabilistic inference in area statistical relational learning. Given a formula φ, domain size n and pair weight functions, what is sum all models φ over n? It was shown that computing WFOMC any logical sentence with at most two variables can be done time polynomial n. However, it also #P1-complete once we add third variable, which inspired search extensions two-variable fragment would still permit running One such extension quantifiers. In this paper, prove adding linear order axiom (which forces one predicates to introduce ordering elements each φ) on top quantifiers permits computation size. present new dynamic programming-based algorithm compute n, thus proving our primary claim.