Varieties of Distributed Knowledge

TL;DR

This paper analyzes twelve different formal definitions of distributed knowledge, comparing their logical relationships and equivalences to clarify the concept's interpretative nuances in multi-agent systems.

Contribution

It provides a systematic comparison of twelve distributed knowledge definitions, establishing their logical implications and equivalences.

Findings

Identifies which distributed knowledge variants are equivalent.

Determines implications between different definitions.

Clarifies the interpretative scope of distributed knowledge.

Abstract

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 $\tau_1$ and $\tau_2$ of distributed knowledge we show whether a proposition $\phi$ being distributed knowledge under definition $\tau_1$ implies that $\phi$ is distributed knowledge under definition $\tau_2$.