 Given a deterministic causal model—a system of structural equations—the way to formally represent an intervention on an endogenous variable, \(V\), is straightforward: you remove the structural equation which has that variable on its left-hand-side, and leave all the other equations unchanged. You go on to treat \(V\) as if it were an exogenous variable, with the value or the probability distribution it was given through the intervention. Assuming the system of equations is acyclic, you can then work out the value of the other variables in the model, or the probability distribution over the values of the other variables in the model, as before.