# Formalizing Statistical Causality via Modal Logic

arXiv: https://arxiv.org/abs/2210.16751 · HTML: https://mlsanity.com/paper/2210.16751/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 73 references that are in the map.
- First posted on arXiv 30 Oct 2022.

## Builds on (most cited first, 11 of 11)

- [Causal Networks: Semantics and Expressiveness](https://mlsanity.com/paper/1304.2379/) (2013)
- [Constraint-based Causal Discovery from Multiple Interventions over Overlapping Variable Sets](https://mlsanity.com/paper/1403.2150/) (2014)
- [A Modification of the Halpern-Pearl Definition of Causality](https://mlsanity.com/paper/1505.00162/) (2015)
- [Probabilistic Reasoning across the Causal Hierarchy](https://mlsanity.com/paper/2001.02889/) (2020)
- [Statistical Epistemic Logic](https://mlsanity.com/paper/1907.05995/) (2019)
- [Towards Logical Specification of Statistical Machine Learning](https://mlsanity.com/paper/1907.10327/) (2019)
- [An Epistemic Approach to the Formal Specification of Statistical Machine Learning](https://mlsanity.com/paper/2004.12734/) (2020)
- [Approximation and Dependence via Multiteam Semantics](https://mlsanity.com/paper/1510.09040/) (2015)
- [Probabilistic team semantics](https://mlsanity.com/paper/1803.02180/) (2018)
- [Thinking About Causation: A Causal Language with Epistemic Operators](https://mlsanity.com/paper/2010.16217/) (2020)
- [Sound and Relatively Complete Belief Hoare Logic for Statistical Hypothesis Testing Programs](https://mlsanity.com/paper/2208.07074/) (2022)

## Built on by (most cited first, 2 of 2)

- [StatWhy: Formal Verification Tool for Statistical Hypothesis Testing Programs](https://mlsanity.com/paper/2405.17492/) (2024)
- [Why3-py: A Tool for Formal Verification of Hypothesis Testing and Meta-Analysis in Python](https://mlsanity.com/paper/2607.03951/) (2026)

## Abstract (arXiv)

We propose a formal language for describing and explaining statistical causality. Concretely, we define Statistical Causality Language (StaCL) for expressing causal effects and specifying the requirements for causal inference. StaCL incorporates modal operators for interventions to express causal properties between probability distributions in different possible worlds in a Kripke model. We formalize axioms for probability distributions, interventions, and causal predicates using StaCL formulas. These axioms are expressive enough to derive the rules of Pearl's do-calculus. Finally, we demonstrate by examples that StaCL can be used to specify and explain the correctness of statistical causal inference.