Agent-time Epistemics and Coordination

TL;DR

This paper extends epistemic logic by incorporating time into knowledge operators, enabling a more expressive framework to analyze how agents coordinate and share knowledge over time.

Contribution

It introduces a generalized epistemic formalism with time-indexed knowledge operators, exploring the relationship between temporal structures and knowledge states.

Findings

Nested knowledge relates to event ordering even when not temporally aligned.

Generalized common knowledge corresponds to tight coordination, not just simultaneity.

Decoupling epistemic necessity from temporal necessity broadens understanding of agent coordination.

Abstract

A minor change to the standard epistemic logical language, replacing $K_{i}$ with $K_{\node{i,t}}$ where $t$ is a time instance, gives rise to a generalized and more expressive form of knowledge and common knowledge operators. We investigate the communication structures that are necessary for such generalized epistemic states to arise, and the inter-agent coordination tasks that require such knowledge. Previous work has established a relation between linear event ordering and nested knowledge, and between simultaneous event occurrences and common knowledge. In the new, extended, formalism, epistemic necessity is decoupled from temporal necessity. Nested knowledge and event ordering are shown to be related even when the nesting order does not match the temporal order of occurrence. The generalized form of common knowledge does {\em not} correspond to simultaneity. Rather, it corresponds to a notion of tight coordination, of which simultaneity is an instance.