# On Open-Universe Causal Reasoning

arXiv: https://arxiv.org/abs/1907.02170 · HTML: https://mlsanity.com/paper/1907.02170/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jul 2019.

## Built on by (most cited first, 6 of 6)

- [How Causal Abstraction Underpins Computational Explanation](https://mlsanity.com/paper/2508.11214/) (2025)
- [A Topological Perspective on Causal Inference](https://mlsanity.com/paper/2107.08558/) (2021)
- [Causal Modeling With Infinitely Many Variables](https://mlsanity.com/paper/2112.09171/) (2021)
- [Punctuation and Predicates in Language Models](https://mlsanity.com/paper/2508.14067/) (2025)
- [Observing Interventions: A logic for thinking about experiments](https://mlsanity.com/paper/2111.12978/) (2021)
- [Causality in the human niche: lessons for machine learning](https://mlsanity.com/paper/2506.13803/) (2025)

## Abstract (arXiv)

We extend two kinds of causal models, structural equation models and simulation models, to infinite variable spaces. This enables a semantics for conditionals founded on a 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 as their axiomatizations 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.