Coherent numerical and ordinal probabilistic assessments

Conditions of coherence are given for generalized assessments of probability on arbitrary sets of conditional events, that is assessments including also imprecise values (probability intervals) and ordinal evaluations (comparative probabilities). Such coherence conditions ensure, like the well known de Finetti coherence condition for numerical probabilities, the possibility of extending generalized assessments of probability and preserving coherence. The main results demonstrate that the introduced coherence conditions are necessary and sufficient for the existence of a de Finetti coherent probability, agreeing with the generalized probabilistic assessment