Notre Dame Journal of Formal Logic 60 (2):311-332 (2019)

Wesley H. Holliday
University of California, Berkeley
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
Keywords modal logic  propositional quantifiers  algebraic semantics  monadic algebras  MacNeille completion
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DOI 10.1215/00294527-2019-0001
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References found in this work BETA

A Completeness Theorem in Modal Logic.Saul A. Kripke - 1959 - Journal of Symbolic Logic 24 (1):1-14.
Propositional Quantifiers in Modal Logic.Kit Fine - 1970 - Theoria 36 (3):336-346.
Propositional Quantification in Bimodal S5.Peter Fritz - 2020 - Erkenntnis 85 (2):455-465.
Extensions of the Lewis System S5.Schiller Joe Scroggs - 1951 - Journal of Symbolic Logic 16 (2):112-120.

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Citations of this work BETA

Logic Talk.Alexander W. Kocurek - 2021 - Synthese 199 (5-6):13661-13688.
Propositional Quantification in Bimodal S5.Peter Fritz - 2020 - Erkenntnis 85 (2):455-465.
On the Logic of Belief and Propositional Quantification.Yifeng Ding - 2021 - Journal of Philosophical Logic 50 (5):1143-1198.

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