# On the Independencies Hidden in the Structure of a Probabilistic Logic Program

arXiv: https://arxiv.org/abs/2308.15865 · HTML: https://mlsanity.com/paper/2308.15865/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 17 references that are in the map.
- First posted on arXiv 30 Aug 2023.

## Builds on (most cited first, 3 of 3)

- [Causal Networks: Semantics and Expressiveness](https://mlsanity.com/paper/1304.2379/) (2013)
- [Strong Completeness and Faithfulness in Bayesian Networks](https://mlsanity.com/paper/1302.4973/) (2013)
- [On the Logic of Causal Models](https://mlsanity.com/paper/1304.2355/) (2013)

## Built on by (most cited first, 2 of 2)

- [Efficient Counterfactual Reasoning in ProbLog via Single World Intervention Programs](https://mlsanity.com/paper/2603.20505/) (2026)
- [From probability to causality in probabilistic logic programming](https://mlsanity.com/paper/2608.07230/) (2026)

## Abstract (arXiv)

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.