On deducing conditional independence from d-separation in causal graphs with feedback

Pearl and Dechter (1996) claimed that the d-separation criterion for condit ional independence in acyclic causal networks also applies to networks of d iscrete variables that have feedback cycles, provided that the variables of the system are uniquely determined by the random disturbances. I show by e xample that this is not true in general. Some condition stronger than uniqu eness is needed, such as the existence of a causal dynamics guaranteed to l ead to the unique solution.