Exploiting Vagueness for Multi-Agent Consensus

TL;DR

This paper introduces a framework using Kleene's three-valued logic to model vagueness in multi-agent consensus, enabling agents to adopt borderline truth values to reduce inconsistency and achieve more precise shared beliefs.

Contribution

It presents a novel consensus model leveraging vagueness and intermediate truth values, demonstrating improved convergence and payoff-based belief refinement in multi-agent systems.

Findings

Agents converge to more precise shared beliefs.

Vagueness reduces inconsistency among agents.

Payoff-based selection improves belief quality.

Abstract

A framework for consensus modelling is introduced using Kleene's three valued logic as a means to express vagueness in agents' beliefs. Explicitly borderline cases are inherent to propositions involving vague concepts where sentences of a propositional language may be absolutely true, absolutely false or borderline. By exploiting these intermediate truth values, we can allow agents to adopt a more vague interpretation of underlying concepts in order to weaken their beliefs and reduce the levels of inconsistency, so as to achieve consensus. We consider a consensus combination operation which results in agents adopting the borderline truth value as a shared viewpoint if they are in direct conflict. Simulation experiments are presented which show that applying this operator to agents chosen at random (subject to a consistency threshold) from a population, with initially diverse opinions, results in convergence to a smaller set of more precise shared beliefs. Furthermore, if the choice of agents for combination is dependent on the payoff of their beliefs, this acting as a proxy for performance or usefulness, then the system converges to beliefs which, on average, have higher payoff.