# Markov categories, causal theories, and the do-calculus

arXiv: https://arxiv.org/abs/2204.04821 · HTML: https://mlsanity.com/paper/2204.04821/

## Key facts

- No citing papers in the map yet (data through 7 Oct 2026).
- Placed in Causal reasoning in LLMs, one of 17 directions in LLM reasoning.
- Builds on 2 of its 18 references that are in the map.
- First posted on arXiv 11 Apr 2022.

## Placed in

- LLM reasoning / [Causal reasoning in LLMs](https://mlsanity.com/lr/causal-reasoning-in-llms/)

## Builds on (most cited first, 2 of 2)

- [A synthetic approach to Markov kernels, conditional independence and theorems on sufficient statistics](https://mlsanity.com/paper/1908.07021/) (2019)
- [Causal Inference by String Diagram Surgery](https://mlsanity.com/paper/1811.08338/) (2018)

## Abstract (arXiv)

We give a category-theoretic treatment of causal models that formalizes the syntax for causal reasoning over a directed acyclic graph (DAG) by associating a free Markov category with the DAG in a canonical way. This framework enables us to define and study important concepts in causal reasoning from an abstract and "purely causal" point of view, such as causal independence/separation, causal conditionals, and decomposition of intervention effects. Our results regarding these concepts abstract away from the details of the commonly adopted causal models such as (recursive) structural equation models or causal Bayesian networks. They are therefore more widely applicable and in a way conceptually clearer. Our results are also intimately related to Judea Pearl's celebrated do-calculus, and yield a syntactic version of a core part of the calculus that is inherited in all causal models. In particular, it induces a simpler and specialized version of Pearl's do-calculus in the context of causal Bayesian networks, which we show is as strong as the full version.