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The geometry of knowledge. (English) Zbl 1087.03011
Béziau, J.-Y. (ed.) et al., Aspects of universal logic. Selected papers from the international workshop on universal logic, Neuchâtel, Switzerland, October 6–8, 2003. Neuchâtel: Université de Neuchâtel, Centre de Recherches Sémiologiques. Travaux de Logique. Centre de Recherches Sémiologiques 17, 1-31 (2004).
Summary: The most widely used attractive logical account of knowledge uses standard epistemic models, i.e., graphs whose edges are indistinguishability relations for agents. In this paper, we discuss more general topological models for a multi-agent epistemic language, whose main uses so far have been in reasoning about space. We show that this more geometrical perspective affords greater powers of distinction in the study of common knowledge, defining new collective agents, and merging information for groups of agents.
For the entire collection see [Zbl 1077.03003].

03B42 Logics of knowledge and belief (including belief change)
68T27 Logic in artificial intelligence