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 (DEL). 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 DEL.

Highlights

  • Anyone who has been late to an appointment or missed a deadline is aware that it is often difficult to keep track of time

  • We have presented Dynamic Epistemic Temporal Logic (DETL), a general framework for reasoning about transformations on Kripke models with a designated timekeeping relation

  • Our “temporal” action models are a generalization of the atemporal action models familiar from Dynamic Epistemic Logic

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Summary

Introduction

Anyone who has been late to an appointment or missed a deadline is aware that it is often difficult to keep track of time This basic difficulty is the motivation for this paper, which presents a framework called Dynamic Epistemic Temporal Logic that allows us to reason about epistemic agents’ changing beliefs about time, from one point in time to the next. The determination of independent criteria that capture the models of a certain framework (e.g., Epistemic Temporal Logic) that are representable within our setting remains an open problem Some such criteria are known for DEL itself (van Benthem et al 2009) and we speculate that many features of this work might be put to use for the analysis of our own framework.

Dynamic epistemic temporal logic
Examples
Explicit and implicit representations of time
Agents mistaken about time
Proof system and completeness
Preservation results
Connections with previous work
Proof system for RDETL
Translation of LYDEL into LDETL
Connecting the theories of YDEL and RDETL
Conclusion
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