 MCd-separation uses the graphical notion of d-separation, introduced by Pearl (1988). Let \(X, Y \in \bV, \bZ \subseteq \bV \setminus \{X, Y\}\). As noted above, a path from X to Y is a sequence of variables \(\langle X = X_1 , \ldots ,X_k = Y\rangle\) such that for each \(X_i\), \(X_{i+1}\), there is either an arrow from \(X_i\) to \(X_{i+1}\) or an arrow from \(X_{i+1}\) to \(X_i\) in \(\bG\). A variable \(X_i , 1 \lt i \lt k\) is a collider on the path just in case there is an arrow from \(X_{i-1}\) to \(X_i\) and from \(X_{i+1}\) to \(X_i\). That is, \(X_i\) is a collider on a path just in case two arrows converge on \(X_i\) in the path. \(\bZ\) d-separates X and Y just in case every path \(\langle X = X_1 , \ldots ,X_k = Y\rangle\) from X to Y contains at least one variable \(X_i\) such that either: (i) \(X_i\) is a collider, and no descendant of \(X_i\) (including \(X_i\) itself) is in \(\bZ\); or (ii) \(X_i\) is not a collider, and \(X_i\) is in \(\bZ\). MCd-separation states that d-separation is sufficient for conditional independence.