🤖 AI Summary
This work addresses Carl Hempel’s problem of statistical ambiguity—the challenge of deriving contradictory predictions from statistical regularities—by proposing a framework of Maximal Specific Causal Relationships (MSCRs) grounded in Nancy Cartwright’s probabilistic theory of causality. The approach formalizes causal rules, semantic probabilistic reasoning, and context-sensitive probability-raising models, integrating invariant feature learning with invariant causal prediction to systematically reconcile conflicting statistical information. The paper establishes, for the first time, a rigorous proof that MSCRs guarantee predictive consistency (Theorem 1), thereby demonstrating the solvability of the statistical ambiguity problem and offering a unified framework for causal artificial intelligence and causal machine learning that is both theoretically sound and computationally tractable.
📝 Abstract
This paper addresses Carl Hempel's longstanding problem of statistical ambiguity in inductive-statistical inference, in which contradictory predictions are derived from statistical laws. To avoid such predictions, Carl Hempel proposed the Requirement of Maximal Specificity (RMS) for the statistical laws used in the inference. An analysis of the RMS refinements made by Wesley Salmon, Alberto Coffa, and James Fetzer led to the following 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, there was no proof of a solution to the statistical ambiguity problem based on this definition. We use Nancy Cartwright's definition of causes that raise probabilities across background contexts, and then introduce the concept of Causal Rules. Then we 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 such new areas as Causal AI and Causal Machine Learning. They fundamentally explore causal inference as a tool for understanding cause-and-effect relationships within complex systems. Properties similar to RMS remain under discussion. Several notions related to RMS are considered: invariant feature learning, invariant causal prediction, and spurious association.