# Axiomatization of Interventional Probability Distributions

arXiv: https://arxiv.org/abs/2305.04479 · HTML: https://mlsanity.com/paper/2305.04479/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 39 references that are in the map.
- First posted on arXiv 8 May 2023.

## Builds on (most cited first, 6 of 6)

- [Foundations of Structural Causal Models with Cycles and Latent Variables](https://mlsanity.com/paper/1611.06221/) (2016)
- [Causal Networks: Semantics and Expressiveness](https://mlsanity.com/paper/1304.2379/) (2013)
- [Compositional Abstraction Error and a Category of Causal Models](https://mlsanity.com/paper/2103.15758/) (2021)
- [Markov Properties for Graphical Models with Cycles and Latent Variables](https://mlsanity.com/paper/1710.08775/) (2017)
- [On the Intersection Property of Conditional Independence and its Application to Causal Discovery](https://mlsanity.com/paper/1403.0408/) (2014)
- [Conditions and Assumptions for Constraint-based Causal Structure Learning](https://mlsanity.com/paper/2103.13521/) (2021)

## Built on by (most cited first, 1 of 1)

- [What is causal about causal models and representations?](https://mlsanity.com/paper/2501.19335/) (2025)

## Abstract (arXiv)

Causal intervention is an essential tool in causal inference. It is axiomatized under the rules of do-calculus in the case of structure causal models. We provide simple axiomatizations for families of probability distributions to be different types of interventional distributions. Our axiomatizations neatly lead to a simple and clear theory of causality that has several advantages: it does not need to make use of any modeling assumptions such as those imposed by structural causal models; it only relies on interventions on single variables; it includes most cases with latent variables and causal cycles; and more importantly, it does not assume the existence of an underlying true causal graph as we do not take it as the primitive object--in fact, a causal graph is derived as a by-product of our theory. We show that, under our axiomatizations, the intervened distributions are Markovian to the defined intervened causal graphs, and an observed joint probability distribution is Markovian to the obtained causal graph; these results are consistent with the case of structural causal models, and as a result, the existing theory of causal inference applies. We also show that a large class of natural structural causal models satisfy the theory presented here. We note that the aim of this paper is axiomatization of interventional families, which is subtly different from "causal modeling."