We investigate minimization-based approaches to iterated belief change in multi-agent systems. A network of agents is represented by an undirected graph, where propositional formulas are associated with vertices. Information is shared between vertices via a procedure where each vertex minimizes disagreement with other vertices in the graph. Each iterative approach takes into account the proximity between vertices, with the underlying assumption that information from nearby sources is given higher priority than information from more distant sources. We have identified two main approaches to iteration: in the first approach, a vertex takes into account the information at its immediate neighbours only, and information from more distant vertices is propagated via iteration; in the second approach, a vertex first takes into account information from distance-1 neighbours, then from distance-2 neighbours, and so on, in a prioritized fashion. There prove to be three distinct ways to define the second approach, so in total we have four types of iteration. We define these types formally, find relationships between them, and investigate their basic logical properties. We also implemented the approaches in a software system called Equibel.
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