Fabio Cuzzolin To submit to Artificial Intelligence Journal, 2010 Abstract 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. In opposition, the same conditional b.f.s in the belief space often deliver pseudo belief functions with less natural interpretations. The question of weather classical approaches, first and foremost Dempster's conditioning, can be reduced to same form of distance minimization remains open: the generation of families of combination rules generated by (geometrical) conditioning appears to be the natural prosecution of the presented research. sp  Download PDF  Zipped Postscript BibTeX entry @article{cuzzolin10aij,    AUTHOR = "Fabio Cuzzolin",    TITLE = "Geometric conditional belief functions",   JOURNAL = "to submit to Artificial Intelligence",    YEAR = "2010"  }