Statistical Epistemic Logic

DOI10.1007/978-3-030-31175-9_20arXiv1907.05995MaRDI QIDQ6322040

Yusuke Kawamoto

Publication date: 12 July 2019

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.

Mathematics Subject Classification ID

Foundations and philosophical topics in statistics (62A01) Logics of knowledge and belief (including belief change) (03B42) Privacy of data (68P27)

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