Temporal languages for epistemic programs

Abstract
This paper adds temporal logic to public announcement logic (PAL) and dynamic epistemic logic (DEL). By adding a previous-time operator to PAL, we express in the language statements concerning the muddy children puzzle and sum and product. We also express a true statement that an agent’s beliefs about another agent’s knowledge flipped twice, and use a sound proof system to prove this statement. Adding a next-time operator to PAL, we provide formulas that express that belief revision does not take place in PAL. We also discuss relationships between announcements and the new knowledge agents thus acquire; such relationships are related to learning and to Fitch’s paradox. We also show how inverse programs and hybrid logic each can be used to help determine whether or not an arbitrary structure represents the play of a game. We then add a past-time operator to DEL, and discuss the importance of adding yet another component to the language in order to prove completeness.
Keywords Dynamic epistemic logic  Epistemic logic  Games  Modal logic  Public announcement logic  Temporal logic
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DOI 10.1007/s10849-007-9054-1
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References found in this work BETA
Logics of Public Communications.Jan Plaza - 2007 - Synthese 158 (2):165 - 179.
Fitch's Paradox of Knowability.Berit Brogaard & Joe Salerno - 2010 - The Stanford Encyclopedia of Philosophy.
Hybrid Languages.Patrick Blackburn & Jerry Seligman - 1995 - Journal of Logic, Language and Information 4 (3):251-272.
What One May Come to Know.J. van Benthem - 2004 - Analysis 64 (2):95-105.

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Citations of this work BETA
Merging Frameworks for Interaction.van Benthem Johan, Gerbrandy Jelle, Hoshi Tomohiro & Pacuit Eric - 2009 - Journal of Philosophical Logic 38 (5):491-526.
Logic for Update Products and Steps Into the Past.Joshua Sack - 2010 - Annals of Pure and Applied Logic 161 (12):1431-1461.

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