A Belief-Function Logic

Abstract

We present BFL, a hybrid logic for representing uncertain knowledge. BFL attaches a quantified notion of belief --- based on Dempster-Shafer's theory of belief functions --- to classical first-order logic. The language of BFL is composed of objects of the form F:[a, b], where F is a firstorder sentence, and a and b are numbers in the [0,1] interval (with ab). Intuitively, a measures the strength of our belief in the truth of F, and (1--b) that in its falseness. A number of properties of first-order logic nicely generalize to BFL; in return, BFL gives us a new perspective on some important points of Dempster-Shafer theory (e.g., the role of Dempster's combination rule). Introduction Logic plays a central role in the task of representing knowledge in artificial intelligence. Much of logical tradition is concerned with two-valued logics, i.e. logics in which we can only talk about propositions being completely true or completely false (possibly, according to a given believer). This contr...