Geometric conditioning of belief functions

In this paper we study the problem of conditioning a belief function b with respect to an event A by geometrically projecting such belief function onto the simplex associated with A in the simplex of all belief functions. Two different such simplices can be defined, as each belief function can be represented as the vector of its basic probability values or the vector of its belief values. We show here that defining geometric conditional b.f.s by minimizing Lp distances between b and the conditioning simplex in the mass space produces simple, elegant results with straightforward interpretations in terms of degrees of belief. This opens the way to a systematic exploration of geometric conditioning in the belief spacetoo, and the relationships of these results with classical approaches to the problem.