# Towards Logical Specification of Statistical Machine Learning

arXiv: https://arxiv.org/abs/1907.10327 · HTML: https://mlsanity.com/paper/1907.10327/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jul 2019.

## Built on by (most cited first, 4 of 4)

- [Formalizing Statistical Causality via Modal Logic](https://mlsanity.com/paper/2210.16751/) (2022)
- [Toward A Logical Theory Of Fairness and Bias](https://mlsanity.com/paper/2306.13659/) (2023)
- [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 introduce a logical approach to formalizing statistical properties of machine learning. Specifically, we propose a formal model for statistical classification based on a Kripke model, and formalize various notions of classification performance, robustness, and fairness of classifiers by using epistemic logic. Then we show some relationships among properties of classifiers and those between classification performance and robustness, which suggests robustness-related properties that have not been formalized in the literature as far as we know. To formalize fairness properties, we define a notion of counterfactual knowledge and show techniques to formalize conditional indistinguishability by using counterfactual epistemic operators. As far as we know, this is the first work that uses logical formulas to express statistical properties of machine learning, and that provides epistemic (resp. counterfactually epistemic) views on robustness (resp. fairness) of classifiers.