A Logic for Repair and State Recovery in Byzantine Fault-tolerant Multi-agent Systems

TL;DR

This paper introduces an epistemic logic with dynamic modalities for modeling and analyzing repair and state recovery in Byzantine fault-tolerant multi-agent systems, supporting reasoning about agents' fault status and updates.

Contribution

It presents a novel logical framework with hope and dynamic modalities, complete axiomatizations, and demonstrates its utility in fault detection and recovery scenarios.

Findings

Logic supports modeling of fault detection, isolation, and recovery.

Complete axiomatizations enable formal reasoning about system updates.

Examples illustrate the logic's applicability to fault-tolerant distributed systems.

Abstract

We provide an epistemic logical language and semantics for the modeling and analysis of byzantine fault-tolerant multi-agent systems. This not only facilitates reasoning about the agents' fault status but also supports model updates for implementing repair and state recovery. For each agent, besides the standard knowledge modality our logic provides an additional modality called hope, which is capable of expressing that the agent is correct (not faulty), and also dynamic modalities enabling change of the agents' correctness status. These dynamic modalities are interpreted as model updates that come in three flavours: fully public, more private, or involving factual change. We provide complete axiomatizations for all these variants in the form of reduction systems: formulas with dynamic modalities are equivalent to formulas without. Therefore, they have the same expressivity as the logic of knowledge and hope. Multiple examples are provided to demonstrate the utility and flexibility of our logic for modeling a wide range of repair and state recovery techniques that have been implemented in the context of fault-detection, isolation, and recovery (FDIR) approaches in fault-tolerant distributed computing with byzantine agents.