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Pearl and Dechter (1996) claimed that the d-separation criterion forconditional independence in acyclic causal networks also applies to networks ofdiscrete variables that have feedback cycles, provided that the variables ofthe system are uniquely determined by the random disturbances. I show byexample that this is not true in general. Some condition stronger thanuniqueness is needed, such as the existence of a causal dynamics guaranteed tolead to the unique solution.

On Deducing Conditional Independence from d-Separation in Causal Graphs with Feedback (Research Note)