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.

翻译：加权一阶模型计数（Weighted First Order Model Counting, WFOMC）是计算一阶逻辑语句所有模型加权和的任务。许多统计关系学习框架中的概率推理问题可转化为WFOMC问题。然而，通常WFOMC被证明是难解的（#P_1-完全）。因此，允许多项式时间WFOMC的逻辑片段备受关注，此类片段被称为域可提升（domain liftable）的。近期研究已确定扩展了计数量词的两变量一阶逻辑片段是域可提升的。本文通过引入有向无环图（Directed Acyclic Graph, DAG）公理对该片段进行扩展，即允许将关系解释为有向无环图。