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

• URL: http://arxiv.org/abs/2308.15865v1
• Date: Wed, 30 Aug 2023 08:55:55 GMT
• Title: On the Independencies Hidden in the Structure of a Probabilistic Logic Program
• Authors: Kilian R\"uckschlo{\ss} (Ludwig-Maximilians-Universit\"at M\"unchen), Felix Weitk\"amper (Ludwig-Maximilians-Universit\"at M\"unchen)
• Abstract summary: We compute conditional independencies from d-separation in acyclic ground logic programs. We present a correct meta-interpreter that decides whether a certain conditional independence statement is implied by a program structure.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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