This paper addresses Carl Hempel's longstanding problem of statistical ambiguity in inductive-statistical inference, where contradictory predictions arise from statistical laws. Hempel proposed the Requirement of Maximal Specificity (RMS) to avoid such predictions. An analysis of RMS refinements by Wesley Salmon, Alberto Coffa, and James Fetzer led to the definition of maximally specific statistical laws: "the lawlike premises of an adequate explanation must specify all and only those properties whose presence or absence made a difference to the occurrence of its explanandum-phenomenon." However, no proof existed for a solution to the statistical ambiguity problem based on this definition. We utilize Nancy Cartwright's definition of causes that raise probabilities across background contexts and introduce the concept of Causal Rules. We then define a special semantic probabilistic inference procedure that incrementally refines these causal rules by incorporating all statistically relevant information. This procedure yields Maximally Specific Causal Relationships (MSCRs), for which we prove (Theorem 1) that predictions derived from them are consistent. This resolves the statistical ambiguity problem. The semantic probabilistic inference procedure provides a probabilistic causal learning system, which may be used in new areas such as Causal AI and Causal Machine Learning. These fundamentally explore causal inference as a tool for understanding cause-and-effect relationships within complex systems. Several notions related to RMS, such as invariant feature learning, invariant causal prediction, and spurious association, remain under discussion.
Blogger's Review: This paper effectively resolves Hempel's statistical ambiguity issue by introducing causal rules and semantic probabilistic inference, highlighting the significance of causal reasoning in complex systems. This lays a solid foundation for the future development of Causal AI and Causal Machine Learning, offering new perspectives for understanding causal relationships.