Hans van Ditmarsch ; Tim French - Quantifying over Boolean announcements

lmcs:4147 - Logical Methods in Computer Science, January 21, 2022, Volume 18, Issue 1 - https://doi.org/10.46298/lmcs-18(1:20)2022
Quantifying over Boolean announcements

Authors: Hans van Ditmarsch ; Tim French ORCID-iD

    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.

    Volume: Volume 18, Issue 1
    Published on: January 21, 2022
    Accepted on: December 20, 2021
    Submitted on: December 15, 2017
    Keywords: Computer Science - Logic in Computer Science,Computer Science - Computational Complexity


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