# A Simplicial Model for KB4n: Epistemic Logic with Agents that May Die

arXiv: https://arxiv.org/abs/2108.10293 · HTML: https://mlsanity.com/paper/2108.10293/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 42 references that are in the map.
- First posted on arXiv 23 Aug 2021.

## Builds on (most cited first, 8 of 8)

- [Networks beyond pairwise interactions: structure and dynamics](https://mlsanity.com/paper/2006.01764/) (2020)
- [A Knowledge-Based Analysis of the Blockchain Protocol](https://mlsanity.com/paper/1707.08751/) (2017)
- [Wanted Dead or Alive : Epistemic logic for impure simplicial complexes](https://mlsanity.com/paper/2103.03032/) (2021)
- [A Simplicial Complex Model for Dynamic Epistemic Logic to study Distributed Task Computability](https://mlsanity.com/paper/1809.03095/) (2018)
- [Knowledge and simplicial complexes](https://mlsanity.com/paper/2002.08863/) (2020)
- [Logical Obstruction to Set Agreement Tasks for Superset-Closed Adversaries](https://mlsanity.com/paper/2011.13630/) (2020)
- [Unbeatable Set Consensus via Topological and Combinatorial Reasoning](https://mlsanity.com/paper/1605.07354/) (2016)
- [Logic and Topology for Knowledge, Knowability, and Belief - Extended Abstract](https://mlsanity.com/paper/1707.09978/) (2017)

## 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)
- [Changing agents and ascribing beliefs in dynamic epistemic logic](https://mlsanity.com/paper/2211.02452/) (2022)

## Abstract (arXiv)

The standard semantics of multi-agent epistemic logic S5 is based on Kripke models whose accessibility relations are reflexive, symmetric and transitive. This one dimensional structure contains implicit higher-dimensional information beyond pairwise interactions, that we formalized as pure simplicial models in a previous work (Information and Computation, 2021). Here we extend the theory to encompass simplicial models that are not necessarily pure. The corresponding class of Kripke models are those where the accessibility relation is symmetric and transitive, but might not be reflexive. Such models correspond to the epistemic logic KB4 . Impure simplicial models arise in situations where two possible worlds may not have the same set of agents. We illustrate it with distributed computing examples of synchronous systems where processes may crash.