Causal AI Resolves Hempel's Statistical Ambiguity Problem.

Carl Hempel's statistical ambiguity problem, where contradictory predictions can arise from statistical laws, has been a persistent challenge in inductive-statistical inference. Previous attempts to solve this, such as Hempel's Requirement of Maximal Specificity (RMS), lacked a formal proof of solution. This research tackles the problem by leveraging Nancy Cartwright's definition of causes and introducing the concept of Causal Rules. The authors develop a semantic probabilistic inference procedure designed to incrementally refine these Causal Rules. This process integrates all statistically relevant information, leading to the identification of Maximally Specific Causal Relationships (MSCRs). A key contribution is the proof (Theorem 1) that predictions derived from these MSCRs are inherently consistent, thereby resolving Hempel's ambiguity problem. This new procedure offers a probabilistic causal learning system with significant implications for emerging fields like Causal AI and Causal Machine Learning, which focus on understanding cause-and-effect in complex systems.