# Knowledge and simplicial complexes

arXiv: https://arxiv.org/abs/2002.08863 · HTML: https://mlsanity.com/paper/2002.08863/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Feb 2020.

## Built on by (most cited first, 2 of 2)

- [A Simplicial Model for KB4n: Epistemic Logic with Agents that May Die](https://mlsanity.com/paper/2108.10293/) (2021)
- [Simplicial Models for the Epistemic Logic of Faulty Agents](https://mlsanity.com/paper/2311.01351/) (2023)

## Abstract (arXiv)

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.