Problem
Research questions and friction points this paper is trying to address.
Dynamic Epistemic Logic
Boolean Announcement
Secure Communication
Satisfiability of Quantified Boolean Announcements
🤖 AI Summary
This paper investigates the satisfiability problem for Boolean Arbitrary Public Announcement Logic (BAPAL). Addressing the challenge that BAPAL lacks the finite model property and its extension, Arbitrary Public Announcement Logic (APAL), is known to be undecidable, we establish, for the first time, that BAPAL satisfiability is decidable and prove its strong completeness. Methodologically, we integrate dynamic epistemic semantics with novel model-theoretic analysis, canonical model construction, and type-elimination techniques—overcoming the failure of standard finite-model methods. Our results fill a fundamental gap in the computational landscape of BAPAL and, more significantly, provide the first computationally grounded logical foundation for the automated synthesis of knowledge-updating secure communication protocols. This advances the applicability of dynamic epistemic logic in formal security verification, substantially extending its theoretical and practical scope.
📝 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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Boolean Arbitrary Public Announcement Logic
Decidability
Simplified APAL
🔎 Similar Papers
No similar papers found.
