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.

通过将概率逻辑程序结构抽象化为程序结构，并给出一个正确的元解释器来决定给定外部数据库的程序结构是否意味着某个特定的条件独立性陈述，本研究将 Pearl 和 Verma 的有向分离理论推广到非 ground 情况，进而从 d-separation 中计算条件独立性，实验评估结果显示，比起在 ProbLog 2 中使用精确推理来检查独立性定义，我们的元解释器的性能明显更快。