Multi-agent Topological Models for Evidence Diffusion
Teodor-Ștefan Zotescu

Abstract:
This thesis explores the effect of social structure on the beliefs and knowledge of agents who reason in an evidence-based manner. This is done by formally analysing the mechanisms of information flow in the networks formed by the agents. This thesis is a contribution to the formal foundation of the idea that a distinct Social Epistemology is needed to account for real-world doxastic and epistemic phenomena. The first part of the original contribution of this work is bridging the gap between multi-agent Topological Evidence Models (Partitional Models) and Threshold models for diffusion. The resulting framework, which we call Evidence Diffusion Models, allows for the formal analysis of multi-agent evidence-based reasoning in the context of a social network where evidence pieces are being communicated between agents via threshold-limited diffusion. The second part of the original contribution of this work is this formal analysis per se. We show that, in our setting, network structures are expressible and known both defeasibly and infallibly by the agents. We prove that defeasible knowledge and (defeasible) distributed knowledge are easily lost under the diffusion of pieces of evidence in a network, whereas distributed evidence is strongly robust. Further, we obtain so-called Cluster Theorems characterising the evidential and network conditions for evidence cascades to form, and for individuals and groups to obtain knowledge in the diffusion process. Finally, we prove results about four special networks — the Total network, the Star network, the Cycle, and the Wheel network — characterising their speed of evidence diffusion and epistemic reliability, and probe the generalisability of the results that were obtained by Zollman about the same networks, but whilst working in a different paradigm.