 Pearl (2009: Chapter 3) develops an axiomatic system he calls the do-calculus for computing post-intervention probabilities that can be applied to systems with latent variables, where the causal structure on \(\bV\) is represented by an ADMG (including double-headed arrows) instead of a DAG. The axioms of this system are presented in  Supplement on the do-calculus.  One useful special case is given by the