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May 2019 A Note on Algebraic Semantics for S5 with Propositional Quantifiers
Wesley H. Holliday
Notre Dame J. Formal Logic 60(2): 311-332 (May 2019). DOI: 10.1215/00294527-2019-0001

Abstract

In two of the earliest papers on extending modal logic with propositional quantifiers, R. A. Bull and K. Fine studied a modal logic S5Π extending S5 with axioms and rules for propositional quantification. Surprisingly, there seems to have been no proof in the literature of the completeness of S5Π with respect to its most natural algebraic semantics, with propositional quantifiers interpreted by meets and joins over all elements in a complete Boolean algebra. In this note, we give such a proof. This result raises the question: For which normal modal logics L can one axiomatize the quantified propositional modal logic determined by the complete modal algebras for L?

Citation

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Wesley H. Holliday. "A Note on Algebraic Semantics for S5 with Propositional Quantifiers." Notre Dame J. Formal Logic 60 (2) 311 - 332, May 2019. https://doi.org/10.1215/00294527-2019-0001

Information

Received: 22 December 2016; Accepted: 19 January 2017; Published: May 2019
First available in Project Euclid: 9 May 2019

zbMATH: 07096540
MathSciNet: MR3952235
Digital Object Identifier: 10.1215/00294527-2019-0001

Subjects:
Primary: 03B45
Secondary: 03C80, 03G05

Rights: Copyright © 2019 University of Notre Dame

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Vol.60 • No. 2 • May 2019
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