# Statistical Epistemic Logic

arXiv: https://arxiv.org/abs/1907.05995 · HTML: https://mlsanity.com/paper/1907.05995/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Jul 2019.

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

- [Sound and Relatively Complete Belief Hoare Logic for Statistical Hypothesis Testing Programs](https://mlsanity.com/paper/2208.07074/) (2022)
- [Formalizing Statistical Causality via Modal Logic](https://mlsanity.com/paper/2210.16751/) (2022)
- [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 modal logic for describing statistical knowledge, which we call statistical epistemic logic. We propose a Kripke model dealing with probability distributions and stochastic assignments, and show a stochastic semantics for the logic. To our knowledge, this is the first semantics for modal logic that can express the statistical knowledge dependent on non-deterministic inputs and the statistical significance of observed results. By using statistical epistemic logic, we express a notion of statistical secrecy with a confidence level. We also show that this logic is useful to formalize statistical hypothesis testing and differential privacy in a simple and abstract manner.