# Asynchronous Announcements

## TL;DR

This paper introduces a novel multi-agent epistemic logic for asynchronous announcements, capturing how agents receive and believe announcements over time, with a complete axiomatization and applications to distributed computing.

## Contribution

It develops the first complete axiomatization of asynchronous announcement logic, modeling asynchronous message reception and belief updates in multi-agent systems.

## Key findings

- Provides a reduction system for formulas in AA
- Models message exchange processes in distributed computing
- Demonstrates the logic's completeness and applicability

## Abstract

We propose a multi-agent epistemic logic of asynchronous announcements, where truthful announcements are publicly sent but individually received by agents, and in the order in which they were sent. Additional to epistemic modalities the logic contains dynamic modalities for making announcements and for receiving them. What an agent believes is a function of her initial uncertainty and of the announcements she has received. Beliefs need not be truthful, because announcements already made may not yet have been received. As announcements are true when sent, certain message sequences can be ruled out, just like inconsistent cuts in distributed computing. We provide a complete axiomatization for this \emph{asynchronous announcement logic} (AA). It is a reduction system that also demonstrates that any formula in $AA$ is equivalent to one without dynamic modalities, just as for public announcement logic. A detailed example modelling message exchanging processes in distributed computing in $AA$ closes our investigation.