# Reasoning About Causal Models With Infinitely Many Variables

arXiv: https://arxiv.org/abs/2112.11362 · HTML: https://mlsanity.com/paper/2112.11362/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 18 references that are in the map.
- First posted on arXiv 21 Dec 2021.

## Builds on (most cited first, 3 of 3)

- [Causal Consistency of Structural Equation Models](https://mlsanity.com/paper/1707.00819/) (2017)
- [Abstracting Causal Models](https://mlsanity.com/paper/1812.03789/) (2018)
- [Causal Modeling With Infinitely Many Variables](https://mlsanity.com/paper/2112.09171/) (2021)

## Built on by (most cited first, 7 of 7)

- [Causal Models with Constraints](https://mlsanity.com/paper/2301.06845/) (2023)
- [Nondeterministic Causal Models](https://mlsanity.com/paper/2405.14001/) (2024)
- [Counterfactuals Modulo Temporal Logics](https://mlsanity.com/paper/2306.08916/) (2023)
- [Do Not Marginalize Mechanisms, Rather Consolidate!](https://mlsanity.com/paper/2310.08377/) (2023)
- [Behaviour Explanation via Causal Analysis of Mental States: A Preliminary Report](https://mlsanity.com/paper/2205.07443/) (2022)
- [Temporal Causal Reasoning with (Non-Recursive) Structural Equation Models](https://mlsanity.com/paper/2501.10190/) (2025)
- [On the Semantics of Primary Cause in Hybrid Dynamic Domains](https://mlsanity.com/paper/2602.14994/) (2026)

## Abstract (arXiv)

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.