Intuitionistic Epistemic Logic with Distributed Knowledge

Abstract

We develop intuitionistic epistemic logicswith distributed knowledge, which is more general thana logic proposed by (J¨ager & Marti 2016) in thata distributed knowledge operator is parameterized bya group of agents.Specifically, we present Hilbertsystems of intuitionistic K, KT, KD, K4, K4D, and S4 withdistributed knowledge. The semantic completeness ofthe logics with regard to suitable Kripke frames is shownby modifying the standard argument of the semanticcompleteness of classical distributed knowledge logicsvia the concept of pseudo-model.We also presentcut-free sequent calculi for the logics, based on which weestablish Craig interpolation theorem and decidability.