Coherence conditions for generalized probability assessments

In this paper we consider qualitative and generalized numerical probability assessments on finite families of conditional events. We assume the existence of suitable subsets of the set of constituents. Then, we give some conditions for the coherence of qualitative assessments and for the generalized coherence of interval-valued probability assessments. In the qualitative case we find precise probabilities which represent the qualitative ordering. In the numerical case we verify the solvability of suitable linear systems used in the algorithm for the checking of generalized coherence.