Inferential processes leading to possibility and necessity

This paper deals with the upper and lower bounds of a class of uncertainty measures endowed with particular characteristics (decomposability, monotonicity, partial additivity and so on). We consider an initial partial assessment consistent with either probability or possibility or necessity, then we study the upper and lower envelopes of all possible extensions. By resorting to a notion of weak logical independence we get as lower or upper envelope a possibility or a necessity, respectively, starting either from a probability or from a possibility or from a necessity.