Logics of temporal-epistemic actions

• 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
• ISSN: 0039-7857; 1573-0964
• DOI: 10.1007/s11229-015-0773-6

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.