Abstract

MURAI, Ryo  and  SANO, Katsuhiko. Intuitionistic Epistemic Logic with Distributed Knowledge. Comp. y Sist. [online]. 2022, vol.26, n.2, pp.823-834.  Epub Mar 10, 2023. ISSN 2007-9737.  https://doi.org/10.13053/cys-26-2-4259.

We develop intuitionistic epistemic logics with distributed knowledge, which is more general than a logic proposed by (Jäger & Marti 2016) in that a distributed knowledge operator is parameterized by a group of agents. Specifically, we present Hilbert systems of intuitionistic K, KT, KD, K4, K4D, and S4 with distributed knowledge. The semantic completeness of the logics with regard to suitable Kripke frames is shown by modifying the standard argument of the semantic completeness of classical distributed knowledge logics via the concept of pseudo-model. We also present cut-free sequent calculi for the logics, based on which we establish Craig interpolation theorem and decidability.

Keywords : Intuitionistic logic; epistemic logic; distributed knowledge.

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