# A many-sorted epistemic logic for chromatic hypergraphs

arXiv: https://arxiv.org/abs/2308.00477 · HTML: https://mlsanity.com/paper/2308.00477/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Aug 2023.

## Built on by (most cited first, 1 of 1)

- [Simplicial Models for the Epistemic Logic of Faulty Agents](https://mlsanity.com/paper/2311.01351/) (2023)

## Abstract (arXiv)

We propose a many-sorted modal logic for reasoning about knowledge in multi-agent systems. Our logic introduces a clear distinction between participating agents and the environment. This allows to express local properties of agents and global properties of worlds in a uniform way, as well as to talk about the presence or absence of agents in a world. The logic subsumes the standard epistemic logic and is a conservative extension of it. The semantics is given in chromatic hypergraphs, a generalization of chromatic simplicial complexes, which were recently used to model knowledge in distributed systems. We show that the logic is sound and complete with respect to the intended semantics. We also show a further connection of chromatic hypergraphs with neighborhood frames.