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• W2593187777 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?" @default.
• W2593187777 created "2017-03-16" @default.
• W2593187777 creator A5088813725 @default.
• W2593187777 date "2019-05-01" @default.
• W2593187777 modified "2023-09-26" @default.
• W2593187777 title "A Note on Algebraic Semantics for S5 with Propositional Quantifiers" @default.
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• W2593187777 doi "https://doi.org/10.1215/00294527-2019-0001" @default.
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