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Computer Science > Logic in Computer Science

arXiv:2206.00903 (cs)
This paper has been withdrawn by Tim French Dr
[Submitted on 2 Jun 2022 (v1), last revised 30 Jan 2025 (this version, v2)]

Title:Satisfiability of Quantified Boolean Announcements

Authors:Hans van Ditmarsch, Tim French, Rustam Galimullin
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Abstract:Dynamic epistemic logics consider formal representations of agents' knowledge, and how the knowledge of agents changes in response to informative events, such as public announcements. Quantifying over informative events allows us to ask whether it is possible to achieve some state of knowledge, and has important applications in synthesising secure communication protocols. However, quantifying over quite simple informative events, public announcements, is not computable: such an arbitrary public announcement logic, APAL, has an undecidable satisfiability problem. Here we consider even simpler informative events called Boolean announcements, where announcements are restricted to be a Boolean combination of atomic propositions. The logic is called Boolean arbitrary public announcement logic, BAPAL. A companion paper provides a complete finitary axiomatization, and related expressivity results, for BAPAL. In this work the satisfiability problem for BAPAL is shown to decidable, and also that BAPAL does not have the finite model property.
Comments: The authors regret that the proof of decidability of satisfiability of BAPAL in the previous versions contains errors and they have not been able to correct these errors. We still believe that it is likely that BAPAL is decidable, and we would like to encourage readers to show this independently. The lack of finite model property for BAPAL holds
Subjects: Logic in Computer Science (cs.LO)
Cite as: arXiv:2206.00903 [cs.LO]
  (or arXiv:2206.00903v2 [cs.LO] for this version)
  https://doi.org/10.48550/arXiv.2206.00903

Submission history

From: Tim French Dr [view email]
[v1] Thu, 2 Jun 2022 07:51:16 UTC (30 KB)
[v2] Thu, 30 Jan 2025 02:12:35 UTC (1 KB) (withdrawn)
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