Intuitionistic Autoepistemic Logic

In this paper we address the problem of combining a logic with nonmonotonic modal logic. In particular we study the intuitionistic case. We start from a formal analysis of the notion of intuitionistic consistency via the sequent calculus. The epistemic operator M is interpreted as the consistency operator of intuitionistic logic by introducing intuitionistic stable sets. On the basis of a bimodal structure we also provide a semantics for intuitionistic stable sets.     

A uniform tableau method for intuitionistic modal logics I

We present tableau systems and sequent calculi for the intuitionistic analoguesIK, ID, IT, IKB, IKDB, IB, IK4, IKD4, IS4, IKB4, IK5, IKD5, IK45, IKD45 andIS5 of the normal classical modal logics. We provide soundness and completeness theorems with respect to the models of intuitionistic logic enriched by a modal accessibility relation, as proposed by G. Fischer Servi. We then show the disjunction property forIK, ID, IT, IKB, IKDB, IB, IK4, IKD4, IS4, IKB4, IK5, IK45 andIS5. We also investigate the relationship of these logics with some other intuitionistic modal logics proposed in the literature.Work carried out in the framework of the agreement between the Italian PT Administration and the Fondazione Ugo Bordoni.Presented byDov Gabbay