*The d-sepset: Interface b/w Subnets in a MSBN
Defi: Let Di=(Ni,Ei) (i=1,2) be two DAGs such that their union D is a DAG. I=N1?N2 is a d-sepset b/w D1 and D2 if for every x?I with its parents parn(x) in D, either parn(x)?N1 or parn(x) ?N2. D is said to be sectioned into {D1,D2}.
Theorem: Let a DAG D=(N,E) be sectioned into {D1,…,Dk} and Iij=Ni ?Nj be the d-sepset b/w Di and Dj. Then for each i, ? j Iij d-separates [Pearl88] Ni\ ?j Iij from N\Ni.
Semantics: If D represents the dependence relations among elements of N, then d-sepset ensures that variables in a subnet are independent of other variables given the d-sepsets of the subnet.