On logics of group belief in structured coalitions

Abstract

In the study of group belief formation, groups of agents are often assumed to possess a topological structure. Here we investigate some ways in which this topological structure may provide the semantical basis for logics of group belief. We impose a partial order on a set of agents first to be able to express preferences of agents by their doxastic abilities, secondly to express the idea of a coalition (well formed group) and thirdly to give a natural semantics for the group belief operator. We define the group belief of a set of agents in two different ways and study their corresponding logics. We also study a logic where doxastic preference is expressed by a binary operator. We prove completeness and discuss correspondences between the logics.