When upper conditional probabilities are conditional possibility measures

Conditioning for (non-additive) uncertainty measures is still an open problem. These measures can arise through probabilistic inference procedures, as in the case of possibility measures, that can be seen as the upper envelope of the extensions of a probability when the corresponding algebras are weakly logically independent. The aim of this paper is to define a conditioning rule (B-conditioning) such that the upper envelope of the extensions of a full conditional probability on an algebra A is a full B-conditional possibility on another algebra A' under weak logical independence of A, A'.