Credibilistic Independence of Two Propositions

In this paper the notion of (probabilistic) independence of two events defined classically in the theory of probability is extended in the theory of belief functions as the credibilistic independence of two propositions. This new notion of independence which is compatible with the probabilistic independence as soon as the belief function is Bayesian, is defined from Fagin-Halpern belief conditioning formulas drawn from Total Belief Theorem (TBT) when working in the framework of belief functions to model epistemic uncertainties. We give some illustrative examples of this notion at the end of the paper.