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

This paper addresses the challenge of representing causal knowledge within probabilistic logic programming (PLP). While Judea Pearl’s influential theory of causality provides a robust framework for intervention-based reasoning, it is primarily restricted to acyclic Bayesian networks. The authors seek to extend these causal principles to PLP frameworks, such as ProbLog and LP_MLN, by grounding them in a logical theory of causality based on Aristotle’s Posterior Analytics. Unlike approaches that rely on temporal succession to determine causal order, this paper adopts a framework where all events are assumed to occur simultaneously, focusing instead on causal explanation and logical justification.

The authors define a formal causal semantics for PLP that incorporates a notion of intervention, enabling the prediction of effects in complex systems. A key contribution is the demonstration that for stratified ProbLog programs, this new semantics coincides with standard interpretations, providing a sound causal foundation. For non-stratified programs, the authors show that their approach offers a distinct, philosophically grounded alternative to existing semantics. They also provide an implementation of this framework, showing that it preserves key epistemological principles such as causal foundation and non-interference, which are essential for distinguishing between mere observation and active intervention.

By bridging the gap between probabilistic logic programming and philosophical causal theory, this work provides a more flexible and theoretically rigorous way to model causal relationships. It allows researchers to apply causal reasoning to cyclic and non-stratified programs where traditional Bayesian network approaches fail. This is particularly relevant for artificial intelligence applications where agents must distinguish between observing a correlation and intervening in a system to achieve a desired outcome.