Underlying Bayesian network modeling and causal discovery is Pearl's result that for every strictly positive distribution there exists a unique minimal undirected independency map (Imap) , and, for every total ordering of variables, a unique minimal I-map dag [Pearl, 1988]. Whilst strict positivity is sucient for uniqueness, we show that it is not necessary. We show that for the existence of a
... [Show full abstract] unique minimal I-map dag it is a necessary and sucient condition that there be no two variables which are equivalent. This allows modeling of a wider class of processes, including those with fully eective causal interventions. Our result is as simple as, but more general than, that of Pearl.