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A probabilistic extension of intuitionistic logic. (English) Zbl 1022.03011
Summary: We introduce a probabilistic extension of propositional intuitionistic logic. The logic allows for making statements such as $$P_{\geq s} \alpha$$, with the intended meaning “the probability of truthfulness of $$\alpha$$ 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.

##### MSC:
 03B48 Probability and inductive logic 03B25 Decidability of theories and sets of sentences 68T37 Reasoning under uncertainty in the context of artificial intelligence
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