A probabilistic extension of intuitionistic logic
Zoran Marković, Zoran Ognjanović, Miodrag Rašković · Mathematical logic quarterly · 2003
Abstract We introduce a probabilistic extension of propositional intuitionistic logic. The logic allows making statements such as P≥sα, with the intended meaning “the probability of truthfulness of α is at least s”. We describe the corresponding class of models, which are Kripke models with a naturally arising notion of probability, and give a sound and complete infinitary axiomatic system. We prove that the logic is decidable.