Pearl and Verma developed d-separation as a widely used graphical criterion to reason about the conditional independencies that are implied by the causal structure of a Bayesian network. As acyclic ground probabilistic logic programs correspond to Bayesian networks on their dependency graph, we can compute conditional independencies from d-separation in the latter. In the present paper, we generalize the reasoning above to the non-ground case. First, we abstract the notion of a probabilistic logic program away from external databases and probabilities to obtain so-called program structures. We then present a correct meta-interpreter that decides whether a certain conditional independence statement is implied by a program structure on a given external database. Finally, we give a fragment of program structures for which we obtain a completeness statement of our conditional independence oracle. We close with an experimental evaluation of our approach revealing that our meta-interpreter performs significantly faster than checking the definition of independence using exact inference in ProbLog 2.

翻译：Pearl与Verma提出的d-分隔准则，是分析贝叶斯网络因果结构所蕴含条件独立性关系的经典图论方法。鉴于无环基概率逻辑程序在依赖图上与贝叶斯网络同构，我们可通过后者的d-分隔准则计算条件独立性。本文将上述推理推广至非基情形。首先，通过剥离外部数据库与概率信息，将概率逻辑程序抽象为所谓的程序结构；继而提出一个正确的元解释器，用于判定给定外部数据库上程序结构是否蕴含特定条件独立性陈述；最后，针对一类程序结构给出条件独立性判定算法的完备性证明。实验评估表明，与通过ProbLog 2精确推理验证独立性定义的方法相比，本元解释器在效率上具有显著优势。