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Publication Details

Probabilistic Logic

by Nilsson, Nils J.

Technical Note 321
Institution: AI Center, SRI International
Address: 333 Ravenswood Ave., Menlo Park, CA 94025
Feb 1984.

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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.

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