How Rules Represent Causal Knowledge: Causal Modeling with Probabilistic Logic Programming

2026-07-23

AI Summary

This work extends Pearl’s causal theory from Bayesian networks to probabilistic logic programming, enabling causal reasoning over non-temporal, synchronous events and thereby overcoming the original framework’s restriction to acyclic structures. Grounded in a philosophical foundation that does not rely on temporal ordering, the study presents the first formal causal semantics for probabilistic logic programs that aligns with Pearl’s theory and provides a precise definition of intervention operations. In stratified ProbLog programs, this semantics coincides with that of P-log; however, in non-stratified settings, it reveals crucial differences, substantially enhancing the expressiveness of causal reasoning within probabilistic logic programming.

Abstract

Pearl famously argues that causal knowledge enables the prediction of intervention effects. By contrast, purely descriptive knowledge supports only conclusions drawn from observations. His theory of causality, however, is developed exclusively within Bayesian networks and causal models. Consequently, it is largely restricted to acyclic causal relationships, and transferring its ideas to other formalisms risks misinterpretation or inconsistency. This paper brings Pearl's approach to causality into probabilistic logic programming (PLP). To this end, such programs are aligned with philosophical foundations established in prior work that do not rely on temporal notions; that is, all relevant events are assumed to occur simultaneously. A formal causal semantics for these programs, together with a notion of intervention and an implementation, is proposed. It is shown that this semantics coincides with the P-log semantics for stratified ProbLog programs, while the two may differ in the non-stratified case and for other PLP formalisms.

Problem

• causal knowledge
• probabilistic logic programming
• causal modeling
• intervention
• Bayesian networks

Innovation

• causal semantics
• probabilistic logic programming
• intervention
• Pearl's causality
• non-temporal causality