Markov Categories, Causal Theories, and the Do-Calculus

Yimu Yin, Jiji Zhang

Research output: Contribution to journalJournal articlepeer-review


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.

Original languageEnglish
Pages (from-to)1-24
Number of pages24
JournalStudies in Logic
Issue number6
Publication statusPublished - Dec 2021


Dive into the research topics of 'Markov Categories, Causal Theories, and the Do-Calculus'. Together they form a unique fingerprint.

Cite this