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

TL;DR

This paper introduces a simplicial complex model for dynamic epistemic logic to analyze how communication affects knowledge in distributed systems, linking topological invariants to task solvability.

Contribution

It develops a novel simplicial complex framework for DEL, connecting topological invariants with distributed task solvability in asynchronous multi-agent systems.

Findings

Topological invariants determine agents' knowledge after communication.

The model links DEL with topological distributed computability theory.

Task solvability is characterized by invariants preserved under communication actions.

Abstract

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.