Credal nets under epistemic irrelevance

We present a new approach to credal nets, which are graphical models that generalise Bayesian nets to imprecise probability. Instead of applying the commonly used notion of strong independence, we replace it by the weaker notion of epistemic irrelevance. We show how assessments of epistemic irrelevance allow us to construct a global model out of given local uncertainty models and mention some useful properties. The main results and proofs are presented using the language of sets of desirable gambles, which provides a very general and expressive way of representing imprecise probability models.