Temporal languages for epistemic programs

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
Berit Brogaard & Joe Salerno, Fitch's Paradox of Knowability. The Stanford Encyclopedia of Philosophy.
Patrick Blackburn & Jerry Seligman (1995). Hybrid Languages. Journal of Logic, Language and Information 4 (3):251-272.

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Citations of this work BETA
Joshua Sack (2010). Logic for Update Products and Steps Into the Past. Annals of Pure and Applied Logic 161 (12):1431-1461.

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