Logics of Temporal-Epistemic Actions

TL;DR

This paper introduces Dynamic Epistemic Temporal Logic, extending action models to temporal Kripke models, enabling reasoning about how actions influence both knowledge and the flow of time in multi-agent systems.

Contribution

It develops a novel framework for temporal action models that modify temporal structures and agents' beliefs, extending atemporal Dynamic Epistemic Logic to temporal contexts.

Findings

Defined temporal action models for multi-agent systems

Proved preservation of epistemic-temporal properties under actions

Provided axiomatizations for theories of temporal action models

Abstract

We present Dynamic Epistemic Temporal Logic, a framework for reasoning about operations on multi-agent Kripke models that contain a designated temporal relation. These operations are natural extensions of the well-known "action models" from Dynamic Epistemic Logic. Our "temporal action models" may be used to define a number of informational actions that can modify the "objective" temporal structure of a model along with the agents' basic and higher-order knowledge and beliefs about this structure, including their beliefs about the time. In essence, this approach provides one way to extend the domain of action model-style operations from atemporal Kripke models to temporal Kripke models in a manner that allows actions to control the flow of time. We present a number of examples to illustrate the subtleties involved in interpreting the effects of our extended action models on temporal Kripke models. We also study preservation of important epistemic-temporal properties of temporal Kripke models under temporal action model-induced operations, provide complete axiomatizations for two theories of temporal action models, and connect our approach with previous work on time in Dynamic Epistemic Logic.