*Alessandro Saffiotti*

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 first-order sentence, and Q and b are numbers in the [O,l] interval (with a>=b). Intuitively, a measures the strength of our belief in the truth of F, and (l-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).

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