A new approach to updating beliefs

We define a new notion of conditional belief, which plays the same role for Dempster­ Shafer belief functions as conditional probability does for probability functions. Our definition is dif­ ferent from the standard definition given by Demp­ ster, and avoids many of the well-known problems of that definition. Just as the conditional prob­ ability Pr(·IB) is a probability function which is the result of conditioning on B being true, so too our conditional belief function Bel( ·I B) is a belief function which is the result of conditioning on B being true. We define the conditional belief as the lower en'll elope (that is, the infimum) of a family of conditional probability functions, and provide a closed-form expression for it. We show by example the intuitive appeal of our definition, and compare it in detail to the more standard definition, showing why and how it differs.