Statistical Epistemic Logic

Abstract

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.

References in corpus (3)

• Hybrid Statistical Estimation of Mutual Information and its Application to Information Flow
• Towards Logical Specification of Statistical Machine Learning
• On the Anonymization of Differentially Private Location Obfuscation

Cited by in corpus (2)

• An Epistemic Approach to the Formal Specification of Statistical Machine Learning
• Formalizing Statistical Causality via Modal Logic