Titlebook: Probabilistic Extensions of Various Logical Systems; Zoran Ognjanovi? Book 2020 Springer Nature Switzerland AG 2020 Probability Logic.Unce

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Probabilized Sequent Calculus and Natural Deduction System for Classical Logic,equent” . with the intended meaning that “the probability of truthfulness of . is into the interval [a;b]”, and in a similar way the notion of “probabilized formula” A[a;b]. The soundness and completeness theorems are proved for all of the presented systems with respect to defined models.

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Logics with Probability Operators, measure on sets of worlds. We provide an infinitary axiomatization which contains an infinitary rule with countable many premisses and one conclusion, related to the Archimedean property of real numbers. Other probability logics considered by the authors of this book are then presented, and an overview of related works of other authors is given.

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Some New Probability Operators,t iterations and nesting of probabilistic operators are not allowed. In other words, admissible statements are Boolean combinations of the atomic probabilistic assessments. Beside the presentation of complete axiomatizations, we shall also discuss the hierarchical structure of the introduced logics in terms of their expressiveness.

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