Frequentist Probability Logic

In this paper, we present a logic \(\textbf{FPL}\) (Frequentist Probability Logic) to reason about probabilities with a relative frequency interpretation. We show that it is possible to interpret the language of \(\textbf{FPL}\) with the standard semantics for propositional logic. \(\textbf{FPL}\) can give a peculiar frequentist interpretation of a probability operator. We then give a proof system for the language, prove that the traditional theorems of probability hold, and prove soundness and completeness.