Knowledge and simplicial complexes

van Ditmarsch, Hans and Goubault, Éric and Ledent, Jérémy and Rajsbaum, Sergio; (2022) Knowledge and simplicial complexes. In: Philosophy of Computing. Philosophical Studies Series, 143 . Springer, Cham, Switzerland, pp. 1-50. ISBN 9783030752675 (

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Simplicial complexes are a versatile and convenient paradigm on which to build all the tools and techniques of the logic of knowledge, on the assumption that initial epistemic models can be described in a distributed fashion. Thus, we can define: knowledge, belief, bisimulation, the group notions of mutual, distributed and common knowledge, and also dynamics in the shape of simplicial action models. We give a survey on how to interpret all such notions on simplicial complexes, building upon the foundations laid in Goubault et al. (Inf Comput 278:104597, 2021).