Reasoning About Causal Models With Infinitely Many Variables
This work addresses foundational issues in causal inference for dynamical systems, but it is incremental as it builds directly on existing axiomatizations.
The paper tackles the problem of causal reasoning in generalized structural equations models (GSEMs), which handle infinitely many variables, and provides a sound and complete axiomatization that extends prior work for structural equations models.
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.