Logics of temporal-epistemic actions

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...

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Bibliographic Details
Published in:Synthese (Dordrecht) 2016-03, Vol.193 (3), p.813-849
Main Authors: Renne, Bryan, Sack, Joshua, Yap, Audrey
Format: Article
Language:English
Subjects:
Asynchronous
Beliefs
Coordinate systems
Dynamic epistemic logic
Education
Epistemology
Logic
Logical theorems
Metaphysics
Model theory
Philosophy
Philosophy of Language
Philosophy of Science
Reason
Reasoning
Resultants
Semantics
Temporal logic
Time
Uniqueness
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Summary: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.
ISSN:0039-7857
1573-0964
DOI:10.1007/s11229-015-0773-6