Non Additive Ordinal Relations Representable by Lower and Upper Probabilities

We characterize (in terms of necessary and sufficient conditions) binary relations representable by a lower probability. Such relations can be non-additive (as the relations representable by a probability) and also not "partially monotone" (as the relations representable by a belief function). Moreover we characterize relations representable by upper probabilities and those representable by plausibility. In fact the conditions characterizing these relations are not immedi~tely deducible by means of "dual" conditions given on the contrary events, like in the numerical case.