PL-a probabilistic logic

Abstract

A description is given of a logic called PL, which uses probability estimates to express uncertainties (without adopting the conventional probability axioms). The author proposes a generalization of the logical interpretations of the connectives and quantifiers to this case. The notions of a formula, a structure, assignment, satisfaction, deduction, etc., are generalizations of the corresponding first-order ones. A method of assigning semantics to PL is proposed, and some of its properties are studied. The soundness and completeness of PL is studied. In particular, PL is shown to be compatible with the first-order predicate calculus.<>