# On the Logic of Causal Models

arXiv: https://arxiv.org/abs/1304.2355 · HTML: https://mlsanity.com/paper/1304.2355/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Mar 2013.

## Built on by (most cited first, 19 of 19)

- [Causal Deep Learning](https://mlsanity.com/paper/2303.02186/) (2023)
- [Causal Discovery with Fewer Conditional Independence Tests](https://mlsanity.com/paper/2406.01823/) (2024)
- [Learning Unknown Intervention Targets in Structural Causal Models from Heterogeneous Data](https://mlsanity.com/paper/2312.06091/) (2023)
- [Causality Pursuit from Heterogeneous Environments via Neural Adversarial Invariance Learning](https://mlsanity.com/paper/2405.04715/) (2024)
- [Identifying Causal Effects Under Functional Dependencies](https://mlsanity.com/paper/2403.04919/) (2024)
- [Unveiling the Structure of Do-Calculus Reasoning via Derivation Graphs](https://mlsanity.com/paper/2606.03719/) (2026)
- [On the Independencies Hidden in the Structure of a Probabilistic Logic Program](https://mlsanity.com/paper/2308.15865/) (2023)
- [Causal DAG Summarization (Full Version)](https://mlsanity.com/paper/2504.14937/) (2025)
- [Approximate Implication with d-Separation](https://mlsanity.com/paper/2105.14463/) (2021)
- [Navigating causal deep learning](https://mlsanity.com/paper/2212.00911/) (2022)
- [Causal Razors](https://mlsanity.com/paper/2302.10331/) (2023)
- [Separability, Contextuality, and the Quantum Frame Problem](https://mlsanity.com/paper/2304.10010/) (2023)
- [CAGE: Causality-Aware Shapley Value for Global Explanations](https://mlsanity.com/paper/2404.11208/) (2024)
- [Leveraging Causal Graphs for Blocking in Randomized Experiments](https://mlsanity.com/paper/2111.02306/) (2021)
- [Differentiable and Transportable Structure Learning](https://mlsanity.com/paper/2206.06354/) (2022)
- [CausalOps -- Towards an Industrial Lifecycle for Causal Probabilistic Graphical Models](https://mlsanity.com/paper/2308.01375/) (2023)
- [Classifying Causal Structures: Ascertaining when Classical Correlations are Constrained by Inequalities](https://mlsanity.com/paper/2308.02380/) (2023)
- [Approximate Implication for Probabilistic Graphical Models](https://mlsanity.com/paper/2310.13942/) (2023)
- [Membership Testing in Markov Equivalence Classes via Independence Query Oracles](https://mlsanity.com/paper/2403.05759/) (2024)

## Abstract (arXiv)

This paper explores the role of Directed Acyclic Graphs (DAGs) as a representation of conditional independence relationships. We show that DAGs offer polynomially sound and complete inference mechanisms for inferring conditional independence relationships from a given causal set of such relationships. As a consequence, d-separation, a graphical criterion for identifying independencies in a DAG, is shown to uncover more valid independencies then any other criterion. In addition, we employ the Armstrong property of conditional independence to show that the dependence relationships displayed by a DAG are inherently consistent, i.e. for every DAG D there exists some probability distribution P that embodies all the conditional independencies displayed in D and none other.