We generalise Cozman’s concept of a credal network under epistemic irrelevance (2000) to the case where lower (and upper) probabilities are allowed to be zero. Our main definition is expressed in terms of coherent lower previsions and imposes epistemic irrelevance by means of strong coherence rather than element-wise Bayes’s rule. We also present a number of alternative representations for the resulting joint model, both in terms of lower previsions and credal sets, a notable example being an intuitive characterisation of the joint credal set by means of linear constraints. We end by applying our method to a simple case: the independent natural extension for two binary variables. This allows us to, for the first time, find analytical expressions for the extreme points of this special type of independent product
