Reasoning About Causal Models With Infinitely Many Variables

Generalized structural equations models (GSEMs) [Peters and Halpern 2021], are, as the name suggests, a generalization of structural equations models (SEMs). They can deal with (among other things) infinitely many variables with infinite ranges, which is critical for capturing dynamical systems. We provide a sound and complete axiomatization of causal reasoning in GSEMs that is an extension of the sound and complete axiomatization provided by Halpern [2000] for SEMs. Considering GSEMs helps clarify what properties Halpern's axioms capture.

Causal Modeling With Infinitely Many Variables

Structural-equations models (SEMs) are perhaps the most commonly used framework for modeling causality. However, as we show, naively extending this framework to infinitely many variables, which is necessary, for example, to model dynamical systems, runs into several problems. We introduce GSEMs (generalized SEMs), a flexible generalization of SEMs that directly specify the results of interventions, in which (1) systems of differential equations can be represented in a natural and intuitive manner, (2) certain natural situations, which cannot be represented by SEMs at all, can be represented easily, (3) the definition of actual causality in SEMs carries over essentially without change.