Three prepositional calculi of probability

Studia Logica 39 (1):49 - 61 (1980)
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Abstract

Attempts are made to transform the basis of elementary probability theory into the logical calculus.We obtain the propositional calculus NP by a naive approach. As rules of transformation, NP has rules of the classical propositional logic (for events), rules of the ukasiewicz logic 0 (for probabilities) and axioms of probability theory, in the form of rules of inference. We prove equivalence of NP with a fragmentary probability theory, in which one may only add and subtract probabilities.

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Axiomatization of infinite-valued logics.J. Barkley Rosser - 1960 - Logique Et Analyse 3 (1):137-153.

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