Solution of Hempel's Statistical Ambiguity Problem and Causal AI

The paper revisits Hempel's statistical ambiguity problem, where different statistical laws can produce contradictory predictions. Building on Nancy Cartwright's account of causes that raise probabilities across background contexts, it introduces Causal Rules and a semantic probabilistic inference procedure that incrementally incorporates statistically relevant information. The resulting Maximally Specific Causal Relationships (MSCRs) are claimed to yield consistent predictions, formalized in Theorem 1. The paper positions this procedure as a possible foundation for probabilistic causal learning in Causal AI and Causal Machine Learning, while relating it to invariant feature learning, invariant causal prediction, and spurious association.