Yeah, Judea Pearl's book is the definitive work. His formalism also has an aspect that you could say is similar to imagining an intervention in a counterfactual

Yeah, Judea Pearl's book is the definitive work. His formalism also has an aspect that you could say is similar to imagining an intervention in a counterfactual way, and computing its likelihood given the data. His paper "Why I'm only half Bayesian" lays out how he sees the epistemology of this.