A supraclassical probabilistic entailment relationстатьяИсследовательская статья
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Аннотация:The paper presents an original supraclassical nontrivial plausible entailment relation p≈ that employs Kolmogorov’s probability theory. Its crucial feature is the primitivenessof a conditional probability, which one calculates with the help of the method of truthtables for classical propositional logic. I study the properties of the entailment relation inquestion. In particular, I show that while being supraclassical, i. e., all classical entailmentsand valid formulas are p≈-valid, but not vice versa, it is not trivial and enjoys the sameform of inconsistency as classical entailment |= does. I specify the place of the proposedprobability entailment relation in certain classifications of nonclassical entailment relations.In particular, I use Douven’s analysis of some probabilistic entailment relations that containsdozens of properties that are crucial for any probabilistic entailment relation, as well asHlobil’s choosing your nonmonotonic logic: shopper’s guide, due to the fact that p≈ isnot monotonic, and Cobreros, Egré, Ripley, van Rooij’s entailment relations for tolerantreasoning. At last, I perform a comparative analysis of classical, the proposed, and someother entailment relations closely related to the latter: those introduced by Bocharov, Markin,Voishvillo, Degtyarev, Ivlev, where the last two entailment relations are based on the so-calledprinciple of reverse deduction, which is an intuitively acceptable way to connect classical andprobabilistic entailment relations.