A probabilistic logic based on propositional intuitionistic logic

Abstract

We introduce a probabilistic extension of propositional intuitionistic logic. The logic allows making statements such as P≥sA, with the intended meaning "the probability of truthfulness of A is greater than or equal to s. We describe the corresponding class of models, which are Kripke models with a naturally arrising notion of probability, and give a sound and complete infinitary axiomatic system. We prove that the logic is decidable.