On Logical Consistency of Probabilistic Predictions

S. O. Speranski

Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 11 (2011) no. 1, pp. 99-115

Résumé

In present paper the statistical ambiguity problem (SAP) is discussed; it was formulated by Carl Hempel and associated with explanations based on inductive-statistical argumentation. In order to eliminate SAP we introduce the formal requirement of maximal specificity (RMS) in terms of logic and probability, and also provide the corresponding prediction scheme. Note that the resultant collection of regularities satisfying RMS is closely related to the construction of semantic probabilistic prediction proposed in companion works of Evgenii Vityaev and the author. We prove that no contradictions may occur while using rms-rules in conjunction with statistically non-negligible sets of available data. In other words, probabilistic theories obtained (inductively) by means of MSR can be viewed as consistent deductive systems.

Détail

Keywords: inductive-statistical explanations and predictions, statistical ambiguity problem, requirement of maximal specificity, probabilistic theory, inductive logic, consistency.

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