2020/02/20 by Hans van Ditmarsch, van Ditmarsch, Hans, Éric Goubault +5 · 2 citations
Computer Science · #Logic, Reasoning, and Knowledge #Advanced Algebra and Logic #Semantic Web and Ontologies
paper · doi:10.48550/arxiv.2002.08863
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 prior work by Goubault and others.