From probability to causality in probabilistic logic programming

2026-08-07

AI Summary

This work addresses the ambiguity in interventional reasoning that arises when probabilistic logic programs, relying solely on probabilistic information, correspond to multiple causal orderings. To resolve this issue, the paper introduces— for the first time—causal symmetry constraints into the identifiability analysis of such programs. By establishing a formal connection between probabilistic logic programs and Bayesian networks, the authors derive necessary and sufficient conditions under which a probability distribution uniquely determines a causal structure. Leveraging symmetry priors inherent in relational structures, the proposed framework yields a set of verifiable criteria that guarantee the learned program admits a well-defined interventional semantics, thereby eliminating the indeterminacy caused by non-unique causal orderings.

Abstract

Probabilistic logic programming is a formalism of statistical relational artificial intelligence that supports causal queries, including interventions from outside the system. When the structure of a probabilistic logic program is learned from data, however, only probabilistic information is used, and a single probability distribution may be compatible with several causal orders. This leads to ambiguity in interventional reasoning, raising the question of when the causal order is uniquely determined by the distribution. Exploiting the relationship between acyclic probabilistic logic programs and Bayesian networks, we derive conditions under which the probabilistic information encoded in a program determines a unique causal order. We also incorporate constraints arising from relational structure by taking into account prescribed sets of causal symmetries induced by the underlying relational vocabulary. The result is a method for verifying when a learned probabilistic logic program supports well-defined intervention semantics.

Problem

• probabilistic logic programming
• causal order
• interventional reasoning
• Bayesian networks
• causal ambiguity

Innovation

• probabilistic logic programming
• causal order
• Bayesian networks
• intervention semantics
• causal symmetries