# Semi-simplicial Set Models for Distributed Knowledge

arXiv: https://arxiv.org/abs/2303.14976 · HTML: https://mlsanity.com/paper/2303.14976/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Mar 2023.

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

- [Simplicial Models for the Epistemic Logic of Faulty Agents](https://mlsanity.com/paper/2311.01351/) (2023)
- [Where Common Knowledge Cannot Be Formed, Common Belief Can -- Planning with Multi-Agent Belief Using Group Justified Perspectives](https://mlsanity.com/paper/2412.07981/) (2024)

## Abstract (arXiv)

In recent years, a new class of models for multi-agent epistemic logic has emerged, based on simplicial complexes. Since then, many variants of these simplicial models have been investigated, giving rise to different logics and axiomatizations. In this paper, we present a further generalization, where a group of agents may distinguish two worlds, even though each individual agent in the group is unable to distinguish them. For that purpose, we generalize beyond simplicial complexes and consider instead simplicial sets. By doing so, we define a new semantics for epistemic logic with distributed knowledge. As it turns out, these models are the geometric counterpart of a generalization of Kripke models, called "pseudo-models". We identify various interesting sub-classes of these models, encompassing all previously studied variants of simplicial models; and give a sound and complete axiomatization for each of them.