Probabilistic Logic

Abstract

Because many artificial intelligence applications require the ability to deal with uncertain knowledge, it is important to seek appropriate generalizations of logic for that case. We present here a semantical generalization of logic in which the truth-values of sentences are probability values (between 0 and 1). Our generalization applies to any logical system for which the consistency of a finite set of sentences can be established. (Although we cannot always establish the consistency of a finite set of sentences of first-order logic, our method is usable in those cases in which we can.) The method described in the present paper combines logic with probability theory in such a way that probabilistic logical entailment reduces to ordinary logical entailment when the probabilities of all sentences are either 0 or 1.