Synergistic Knowledge

TL;DR

This work proposes the notion of synergistic knowledge, which makes it possible to model relationships between agents and the knowledge that the group would have, if the agents shared all their individual knowledge.

Abstract

In formal epistemology, group knowledge is often modelled as the knowledge that the group would have, if the agents shared all their individual knowledge. However, this interpretation does not account for relations between agents. In this work, we propose the notion of synergistic knowledge which makes it possible to model those relationships.

Figures (7)

• Figure 1: The two processes $P$ and $Q$ cannot distinguish between worlds $v_Pv_Q$ and $v_Qv_P$.
• Figure 2: Dining cryptographers model.
• Figure 3: The $\kappa$-model used in Example \ref{['example:no std dk']} does not satisfy standard group knowledge. Reflexive arrows are implicit.
• Figure 4: The $\delta$-model for Example \ref{['example:alg:T']}. Only arrows for maximal agent patterns are shown.
• Figure 5: An improper $\delta$-model. Only the maximal agent patterns are shown.

Theorems & Definitions (115)

• Definition 1: Simplex
• Definition 2: Complex
• Lemma 1
• proof
• Remark 1
• Definition 3: Indistinguishability
• Lemma 2
• proof
• Lemma 3
• proof