Interval-Based Possibilistic Logic in a Coherent Setting

In probability theory the notion of coherence has been introduced by de Finetti in terms of bets and it reveals to be equivalent to the notion of consistence of a partial assessment with a finitely additive probability. An important feature of coherent assessments is their coherent extendibility: in general we obtain a class of coherent extensions, determining a lower and an upper envelope. A similar notion of coherence has been recently introduced for (T-conditional) possibility measures, where T is a t-norm. The extendibility of coherent possibility assessments reveals to be particularly suitable for studying interval-based possibilistic logic. Our aim is to compare the results implied by the coherent setting with those obtained in different approaches, in particular, that relying on classical T-based conditioning.