# A Simplicial Complex Model for Dynamic Epistemic Logic to study Distributed Task Computability

arXiv: https://arxiv.org/abs/1809.03095 · HTML: https://mlsanity.com/paper/1809.03095/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Sep 2018.

## 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)

The usual epistemic model S5n for a multi-agent system is based on a Kripke frame, which is a graph whose edges are labeled with agents that do not distinguish between two states. We propose to uncover the higher dimensional information implicit in this structure, by considering a dual, simplicial complex model. We use dynamic epistemic logic (DEL) to study how an epistemic simplicial complex model changes after a set of agents communicate with each other. We concentrate on an action model that represents the so called immediate snapshot communication patterns of asynchronous agents, because it is central to distributed computability (but our setting works for other communication patterns). There are topological invariants preserved from the initial epistemic complex to the one after the action model is applied, which determine the knowledge that the agents gain after communication. Finally, we describe how a distributed task specification can be modeled as a DEL action model, and show that the topological invariants determine whether the task is solvable. We thus provide a bridge between DEL and the topological theory of distributed computability, which studies task solvability in a shared memory or message passing architecture.