Let us consider variables $A,B,C,D$ such that
- $A$ is conditionally independent of $B$ given $C$, i.e. $A \bot B|C$
- $A$ is conditionally dependent on $B$ given $D$, i.e. $A \not\bot B|D$
Are $A$ and $B$ conditionally independent of each other given $C,D$? Are they not? Can we conclude anything about their conditional independence?
That is, can we say anything about the following claim? $A \bot B|C,D$