 This treatment of interventions has been expanded in a number of directions. The ‘manipulation theorem’ (theorem 3.6 of SGS 2000) generalizes the formula to cover a much broader class of interventions, including ones that don’t break all the arrows into the variables that are intervened on. 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. 