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.
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Notes
- 1.
Topological structures in groups are also used to formalise group attitudes in Dunin-Keplicz and Verbrugge [3]. As they emphasise, this structure may be based on power or dependency relations that reflect different social commitments. [3] considers different group topologies but the approach is somewhat different from ours. The topologies are mainly used to model different forms of communication between agents in a group. A related, formal account of group beliefs is studied in [2] using a concept of (group) epistemic profile to model doxastic reasoning. However epistemic profiles are an additional feature, not derived from the group topological structure.
- 2.
See e.g. [3] and further references given there.
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Balbiani, P., Pearce, D., Uridia, L. (2016). On Logics of Group Belief in Structured Coalitions. In: Michael, L., Kakas, A. (eds) Logics in Artificial Intelligence. JELIA 2016. Lecture Notes in Computer Science(), vol 10021. Springer, Cham. https://doi.org/10.1007/978-3-319-48758-8_7
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