BeliefFlow: A Framework for Logic-Based Belief Diffusion via Iterated Belief Change

Abstract

This paper presents BeliefFlow, a novel framework for representing how logical beliefs spread among interacting agents within a network. In a Belief Flow Network (BFN), agents communicate asynchronously. The agents' beliefs are represented using epistemic states, which encompass their current beliefs and conditional beliefs guiding future changes. When communication occurs between two connected agents, the receiving agent changes its epistemic state using an improvement operator, a well-known type of rational iterated belief change operator that generalizes belief revision operators. We show that BFNs satisfy appealing properties, leading to two significant outcomes. First, in any BFN with strong network connectivity, the beliefs of all agents converge towards a global consensus. Second, within any BFN, we show that it is possible to compute an optimal strategy for influencing the global beliefs. This strategy, which involves controlling the beliefs of a least number of agents through bribery, can be identified from the topology of the network and can be computed in polynomial time.