Resolving Asynchronous Distributed Knowledge

2026-06-30

AI Summary

This work proposes a history-based epistemic logic for distributed systems that operate asynchronously without a global clock and where agents cannot observe information exchanges among non-participating parties. The logic defines truth relative to both global states and agents’ local observation histories, incorporating partial observability and introducing novel asynchronous modal operators. It provides the first formal characterization of the dynamic evolution of distributed knowledge in asynchronous settings. By moving beyond traditional assumptions of synchrony and global awareness, the study demonstrates the failure of several standard synchronous knowledge axioms under asynchrony and establishes a more expressive and practical foundation for reasoning about knowledge in distributed computation.

Abstract

There are by now various epistemic modal logics with intersection modalities for distributed knowledge and intersection update modalities for dynamic phenomena like agents sharing (all their) information, agents receiving information from other agents, and full information protocols. One of those is the logic of Resolving Distributed Knowledge, by Agotnes and Wang. It has distributed knowledge modalities for arbitrary subsets of the set of all agents and it also has so-called resolution modalities for arbitrary subsets of agents sharing their knowledge. In that logic, the agents not involved in the knowledge sharing are aware of the agents sharing knowledge, agents are memory-less, and the kind of dynamics represents synchronous updates, where there is common awareness of the global clock. In contrast, in this contribution we present a logic for Resolving Asynchronous Distributed Knowledge. It is an asynchronous generalization of the synchronous logic of resolving distributed knowledge. The logical semantics is history-based: truth is not only with respect to a given world in a model, but also with respect to a given history of prior resolutions, of which each individual agent can only observe a part. In particular, an agent is unaware of resolutions for groups of agents not including her. As is to be expected, this comes with many technical complications, for example concerning the axiomatization. The synchronous axioms relating resolution to distributed knowledge are now invalid. The modelling advantages of such an asynchronous novel logic, for distributed computing and similar areas, are however substantial and a major asset.

Problem

• asynchronous
• distributed knowledge
• epistemic logic
• resolution modality
• history-based semantics

Innovation

• asynchronous distributed knowledge
• resolution modality
• history-based semantics
• epistemic logic
• distributed computing