  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.
