Quantifying over Boolean announcements

Various extensions of public announcement logic have been proposed with quantification over announcements. The best-known extension is called arbitrary public announcement logic, APAL. It contains a primitive language construct Box phi intuitively expressing that "after every public announcemen...

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Bibliographic Details
Published in:	Logical methods in computer science Vol. 18, Issue 1; no. 1
Main Authors:	van Ditmarsch, Hans, French, Tim
Format:	Journal Article
Language:	English
Published:	Logical Methods in Computer Science Association 01.01.2022 Logical Methods in Computer Science e.V
Subjects:	Computer Science computer science - computational complexity computer science - logic in computer science
ISSN:	1860-5974, 1860-5974
Online Access:	Get full text
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Summary:	Various extensions of public announcement logic have been proposed with quantification over announcements. The best-known extension is called arbitrary public announcement logic, APAL. It contains a primitive language construct Box phi intuitively expressing that "after every public announcement of a formula, formula phi is true". The logic APAL is undecidable and it has an infinitary axiomatization. Now consider restricting the APAL quantification to public announcements of Boolean formulas only, such that Box phi intuitively expresses that "after every public announcement of a Boolean formula, formula phi is true". This logic can therefore called Boolean arbitrary public announcement logic, BAPAL. The logic BAPAL is the subject of this work. Unlike APAL it has a finitary axiomatization. Also, BAPAL is not at least as expressive as APAL. A further claim that BAPAL is decidable is deferred to a companion paper.
ISSN:	1860-5974 1860-5974
DOI:	10.46298/lmcs-18(1:20)2022