Knowledge and common knowledge in a distributed environment

TLDR

Knowledge reasoning is fundamental to distributed systems, underpinning protocol design and viewed as the transformation of system state through communication. The paper proposes a general framework to formalize and reason about knowledge in distributed systems. The framework introduces weaker attainable variants of common knowledge and investigates their properties within distributed systems. The study demonstrates that group knowledge states aid protocol design, distinguishes distributed from common knowledge, shows common knowledge is unattainable in practice, and introduces attainable weaker variants.

Abstract

Reasoning about knowledge seems to play a fundamental role in distributed systems. Indeed, such reasoning is a central part of the informal intuitive arguments used in the design of distributed protocols. Communication in a distributed system can be viewed as the act of transforming the system's state of knowledge. This paper presents a general framework for formalizing and reasoning about knowledge in distributed systems. It is shown that states of knowledge of groups of processors are useful concepts for the design and analysis of distributed protocols. In particular, distributed knowledge corresponds to knowledge that is “distributed” among the members of the group, while common knowledge corresponds to a fact being “publicly known.” The relationship between common knowledge and a variety of desirable actions in a distributed system is illustrated. Furthermore, it is shown that, formally speaking, in practical systems common knowledge cannot be attained. A number of weaker variants of common knowledge that are attainable in many cases of interest are introduced and investigated.