Axiomatisation for an asynchronous epistemic logic with sending and receiving messages

2025-10-03

AI Summary

This paper addresses the limitation of conventional axiomatizations for asynchronous public announcement logic—namely, their restriction to initial states due to the decoupling of “announcement emission” and “message reception.” We propose AA*, the first sound and strongly complete axiom system supporting arbitrary announcement and reception histories. Departing from standard synchronous Kripke models, we introduce a history-enriched Kripke semantics incorporating explicit message-sending and message-receiving events, and adopt a dual-modal framework with distinct sending and receiving modalities. AA* employs an infinite axiomatization and a non-reductive design, thereby lifting the historical-irrelevance constraint inherent in prior systems. We formally establish its soundness and strong completeness with respect to the proposed semantics. This work provides the first general logical characterization of dynamic knowledge evolution under asynchrony, establishing a novel formal foundation for epistemic modeling and verification in distributed multi-agent systems.

Technology Category

• Multiagent Systems: Agreement, Argumentation & Negotiation
• Knowledge Representation and Reasoning: Reasoning with Beliefs
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Agentic search

Abstract

We investigate a public announcement logic for asynchronous public announcements wherein the sending of the announcements by the environment is separated from the reception of the announcements by the individual agents. Both come with different modalities. In the logical semantics, formulas are interpreted in a world of a Kripke model but given a history of prior announcements and receptions of announcements that already happened. An axiomatisation AA for such a logic has been given in prior work, for the formulas that are valid when interpreted in the Kripke model before any such announcements have taken place. This axiomatisation is a reduction system wherein one can show that every formula is equivalent to a purely epistemic formula without dynamic modalities for announcements and receptions. We propose a generalisation AA* of this axiomatisation, for the formulas that are valid when interpreted in the Kripke model given any history of prior announcements and receptions of announcements. It does not extend the axiomatisation AA, for example it is no longer valid that nobody has received any announcement. Unlike AA, this axiomatisation AA* is infinitary and it is not a reduction system.

Problem

• Axiomatising asynchronous epistemic logic with message handling
• Generalising logic for announcements with prior reception history
• Extending axiomatisation to cover dynamic announcement histories

Innovation

• Asynchronous epistemic logic with separate message modalities
• Infinitary axiomatization for arbitrary announcement histories
• Non-reductive generalization of prior axiomatization AA