Knowledge and common knowledge in a distributed environment

Abstract

We argue that the right way to understand distributed protocols is by considering how messages change the state of knowledge of a system. We present a hierarchy of knowledge states that a system may be in, and discuss how communication can move the system's state of knowledge of a fact up the hierarchy. Of special interest is the notion of common knowledge. Common knowledge is an essential state of knowledge for reaching agreements and coordinating action. We show that in practical distributed systems, common knowledge is not attainable. We introduce various relaxations of common knowledge that are attainable in many cases of interest. We describe in what sense these notions are appropriate, and discuss their relationship to each other. We conclude with a discussion of the role of knowledge in distributed systems.

Optimized distributed implementation of multiparty interactions with Restriction

“…The formalization of different kinds of knowledge and related logic, called epistemic logic, have been intensively studied [22,29,30]. In rough sets theory [40], objects are defined through a set of attributes.…”

Cognitive Systems Platforms using Open Source

“…In the first case agents communicate through a digital channel, capable for semantic messages exchange. Due to information exchange, agents build different types of common knowledge [28]. This common knowledge in fact underlies collective intelligence.…”

Coordination, timing and common knowledge

“…3 This paradox, together with a formal analysis of knowledge and common knowledge about timing, appears in Section 8 of Halpern and Moses (1990). A more entertaining cheating spouse version of this paradox appears in the Stanford Ph.D. thesis, Moses (1986), of Yoram Moses.…”

“…An important exception is Dasgupta, Steiner, and Stewart (2012) who study how relaxing the need for perfect synchronicity in action choices weakens the nature of the approximate common knowledge of timing required for coordination. This connection between higher order knowledge and timing has been extensively studied in the computer science literature; see Halpern and Moses (1990), chapter 8 of Fagin, Halpern, Moses, and Vardi (1995) and references therein. Recent work in the computer science literature, Ben-Zvi and and Gonczarowski and Moses (2013), like Dasgupta, Steiner, and Stewart (2012), examines how changing the degree of synchronicity of coordination required changes the higher order knowledge requirements.…”