Coherence conditions for generalized probability assessments

In this paper we consider numerical and qualitative probability assessments on finite families of conditional events. We assume the existence of suitable subsets of the set of constituents. We give two results on coherence and generalized coherence of numerical probability assessments. Then, we give some conditions for the coherence of qualitative probability assessments. In the numerical case we verify the solvability of suitable linear systems used for the checking of coherence, or generalized coherence, of numerical probability assessments. In the qualitative case we find precise probabilities which represent the qualitative orderings. We illustrate our results by examining some examples.