Fritz P. Propositional Quantifiers

Cambridge: Cambridge University Press, 2024. — 118 p.Propositional quantifiers are quantifiers binding proposition letters, understood as variables. This Element introduces propositional quantifiers and explains why they are especially interesting in the context of propositional modal logics. It surveys the main results on propositionally quantified modal logics which have been obtained in the literature, presents a number of open questions, and provides examples of applications of such logics to philosophical problems.Propositional Quantifiers
Introduction
Why Propositional Quantifiers?
Redundancy
Fragments of Higher-Order Logic
Outlook
Historical Overview
Relational Frames
Propositionally Quantified Modal Languages
Modal Logics Based on Classical Logic
Relational Frames and Normality
The Barcan Formula and Atomicity
S5 and the Reduction of Possible Worlds
Axiomatizability
Completeness Results
Model Theory
Beyond Relational Frames
Neighborhood Frames
Complete Boolean Algebras
Pointed Frames, and Matrices
Incomplete Boolean Algebras
General Frames
Variable Propositional Domains
Substitutional Quantifiers
Conclusion
List of Abbreviations
References
Acknowledgments