T-conditional possibilities: Coherence and inference

In this paper we refer to an axiomatic definition of T-conditional possibility, where T is any t-norm. We characterize a full T-conditional possibility in terms of a suitable set of unconditional possibilities. Starting from this characterization we are able to manage coherent conditional possibility assessments and their enlargements. To compare T-conditional possibility related to different t-norm T, we study binary relations locally representable by a T-conditional possibility.