On Open-Universe Causal Reasoning

We extend two kinds of causal models, structural equation models and simulation models, to infinite variable spaces. This enables a semantics of counterfactuals, calculus of intervention, and axiomatization of causal reasoning for rich, expressive generative models—including those in which a causal representation exists only implicitly—in an open-universe setting. Further, we show that under suitable restrictions the two kinds of models are equivalent, perhaps surprisingly since their conditional logics differ substantially in the general case. We give a series of complete axiomatizations in which the open-universe nature of the setting is seen to be essential.