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Probability logic. (English) Zbl 0547.03018
The paper opens with a brief historical sketch of the many varied conceptions of the subject which have been considered. Confined to the propositional level, a logic is then presented in which the notion of probability replaces that of truth. Superficially a many-valued logic, it differs from what has heretofore been studied as many-valued logic in that there is a loosening of the connection between value-assigning functions (i.e. ”truth”-functions) and connectives - values associated with a formula are not determined by its linguistic structure but by its probability-related structure. The logic is given not syntactically but semantically in terms of ’logical consequence’, suitably defined. This notion has the unusual feature that its assertions concern formulas having a value in a set of values, rather than some special designated value or values. When such sets of values are subintervals of [0,1] there is a decision procedure for determining whether or not the consequence relation holds. Examples generalizing some simple inference schemes of two-valued logic are given.

03B48 Probability and inductive logic
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