Intuitionistic Autoepistemic Logic

In this paper we propose intuitionistic logic as the minimal logic most suitable to define autoepistemic logic. We start from a formal analysis of the notion of consistency on an intuitionistic basis, via Gentzen’s sequent calculus. Then we show that the epistemic operator M interpreted as a consistency operator behaves coherently and is also an adequate interpretation of the intuitionistic consistency notion. Intuitionistic stable sets are introduced and given a semantics, on the basis of a bimodal structure, which is shown to be sound and complete. The results of the work are related to Gabbay’s μ-models. The relation between our formalization and other works on autoepistemic logic is also investigated.