We focus on credal nets, which are graphical models that generalise Bayesian
nets to imprecise probability. We replace the notion of strong independence
commonly used in credal nets with the weaker notion of epistemic irrelevance,
which is arguably more suited for a behavioural theory of probability. Focusing
on directed trees, we show how to combine the given local uncertainty models in
the nodes of the graph into a global model, and we use this to construct and
justify an exact message-passing algorithm that computes updated beliefs for a
variable in the tree.