Problem

Probabilistic logic programming (PLP) is a powerful framework for statistical relational AI that can handle causal queries and interventions. However, a significant challenge arises when the structure of a PLP is learned from purely probabilistic data. In such scenarios, a single probability distribution can be consistent with multiple potential causal orders, leading to ambiguity in how interventions would affect the system. This "correlation is not causation" dilemma means that without knowing the true causal direction, it's impossible to reliably predict the outcomes of external actions, highlighting the need for methods to uniquely determine the causal order from probabilistic information.

Method

The authors address this problem by leveraging the established relationship between acyclic probabilistic logic programs and Bayesian networks. Their method transfers well-known techniques for causal structure discovery from Bayesian networks, particularly Meek's rules for orienting edges based on probabilistic independencies (d-separation and Markov equivalence), to the PLP domain. To account for the relational structure inherent in PLPs, the paper introduces the concept of "causal symmetries." These symmetries, derived from the relational vocabulary, impose additional constraints on the possible causal structures. New orientation rules are then developed to exploit these symmetries, enabling the identification of a unique causal order in more complex scenarios. This includes "predicate symmetry," which assumes consistent causal directions between predicate pairs, and the incorporation of "prescribed symmetries" as background knowledge.

Results

The research successfully establishes conditions under which the probabilistic information encoded in a PLP can determine a unique causal order. Specifically, if a PLP is faithfully Markov to its dependency graph and that graph is orientable, then its causal structure is uniquely determined. This implies that different PLPs encoding the same probability distribution will also lead to the same post-intervention distributions, validating their use for interventional reasoning. The introduction of causal symmetries, especially predicate symmetry, proves effective in orienting edges in the ground dependency graphs that would otherwise remain ambiguous. For instance, symmetric forks, where a common cause influences multiple effects with similar relational structures, can now be uniquely oriented. The proposed methods are implemented in Prolog as part of the PLP-BN tools, making them practically applicable for verifying the causal content of learned PLPs.

Implications

This work provides a critical foundation for ensuring that probabilistic logic programs learned from data can be reliably used for causal inference and interventional reasoning. By verifying when the causal order is uniquely determined, the paper enhances the trustworthiness and applicability of PLPs in domains requiring accurate predictions of action effects, such as developing autonomous agents or modeling complex systems. The integration of relational symmetries offers a powerful mechanism to overcome limitations of purely probabilistic causal discovery in structured data. Future research directions include adapting the framework to handle deterministic relationships common in PLPs, which can currently breach the faithfulness assumption, and further exploring the completeness and computational complexity of symmetry-aware edge orientation rules beyond the current scope.