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.

本文使用范畴论方法对因果模型进行了分类处理，从“纯因果”的角度定义了因果独立/分离、因果条件等重要概念，并产生了一个核心部分的语法版本的syntactic do-calculus在所有因果模型中继承。

Markov类别、因果理论和do-演算