TY - JOUR

T1 - Quantifying over Boolean announcements

AU - Van Ditmarsch, Hans

AU - French, Tim

PY - 2022/1/21

Y1 - 2022/1/21

N2 - 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 ☐φ intuitively expressing that “after every public announcement of a formula, formula φ 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 ☐φ intuitively expresses that “after every public announcement of a Boolean formula, formula φ is true”. This logic can therefore be 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.

AB - 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 ☐φ intuitively expressing that “after every public announcement of a formula, formula φ 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 ☐φ intuitively expresses that “after every public announcement of a Boolean formula, formula φ is true”. This logic can therefore be 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.

UR - http://www.scopus.com/inward/record.url?scp=85123514837&partnerID=8YFLogxK

U2 - 10.46298/LMCS-18(1:20)2022

DO - 10.46298/LMCS-18(1:20)2022

M3 - Article

AN - SCOPUS:85123514837

VL - 18

JO - Logical Methods in Computer Science

JF - Logical Methods in Computer Science

SN - 1860-5974

IS - 1

ER -