A canonical model construction for intuitionistic distributed knowledge

Intuitionistic epistemic logic is an active research field. However, so far no consensus has been reached what the correct form of intuitionistic epistemic logic is and more technical and conceptual work is needed to obtain a better understanding. This article tries to make a small technical contribution to this enterprise. Roughly speaking, a proposition is distributed knowledge among a group of agents if it follows from their combined knowledge. We are interested in formalizing intuitionistic distributed knowledge. Our focus is on two theories IDK and IDT, presented as Hilbert-style systems, and the proof of the completeness of these theories; their correctness is obvious. Intuitionistic distributed knowledge is semantically treated following the standard lines of intuitionistic modal logic. Motivated by an approach due to Fagin, Halpern, and Vardi, though significantly simplified for the treatment of IDK and IDT, we show completeness of these systems via a canonical model construction.