Communication Modalities

TL;DR

This paper addresses the challenge that Byzantine faults render knowledge too strong for triggering actions and for reliable interpretation of messages. It proposes extending runs-and-systems with two modalities, $H_i$ (hope) and creed, yielding a KH logic (knowledge and hope) that can express the informational content of messages from potentially faulty senders and accommodate heterogeneous agent types. It defines $H_i \varphi$ as $(\mathit{correct}_i \to B_i \varphi)$ and introduces dual accessibility relations $\mathcal{K}_i$ and $\mathcal{H}_i$ on Kripke models, with results such as mutual hope $E^H_G \varphi$ proving $\varphi$ when $|G|\ge f+1$. This framework decouples faulty actions from knowledge, enabling reliable reasoning about learning from communication in Byzantine and heterogeneous multi-agent systems and guiding fault-tolerant protocol design.

Abstract

Epistemic analysis of distributed systems is one of the biggest successes among applications of logic in computer science. The reason for that is that agents' actions are necessarily guided by their knowledge. Thus, epistemic modal logic, with its knowledge and belief modalities (and group versions thereof), has played a vital role in establishing both impossibility results and necessary conditions for solvable distributed tasks. In distributed systems, knowledge is largely attained via communication. It has been standard in both distributed systems and dynamic epistemic logic to treat incoming messages as trustworthy, thus, creating difficulties in the epistemic analysis of byzantine distributed systems where faulty agents may lie. In this paper, we argue that handling such communication scenarios calls for additional modalities representing the informational content of messages that should not be taken at face value. We present two such modalities: hope for the case of fully byzantine agents and creed for non-uniform communication protocols in general.