Varieties of Distributed Knowledge

Distributed knowledge is one of the better known group knowledge modalities. While its intuitive idea is relatively clear, there is ample room for interpretation of details. We investigate 12 definitions of distributed knowledge that differ from each other in the kinds of information sharing the agents can perform in order to achieve shared mutual knowledge of a proposition. We then show which kinds of distributed knowledge are equivalent, and which kinds imply each other, i.e., for any two variants $τ_1$ and $τ_2$ of distributed knowledge we show whether a proposition $ϕ$ being distributed knowledge under definition $τ_1$ implies that $ϕ$ is distributed knowledge under definition $τ_2$.