On the Conceptual Status of Belief Functions with Respect to Coherent Lower Probabilities

The interpretations of belief functins and their relationships with other uncertainty theories have been widely debated in the literature. Focusing on the interpretation of belief functions based on non-negative masses, in this paper we provide a contribution to this topic by addressing two questions concerning the relationships between belief functions and coherent lower probabilities. The answers we provide to both questions tend to exclude the existence of intuitively appreciable relationships between the two theories, under the above mentioned interpretation. While this may be regarded as a confirmation of the conceptual autonomy of belief functions, we also propose future research about an alternative characterization, based on the notion of independence.