Propositional Quantifiers

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. Cover Title Page Imprints Page Propositional Quantifiers Contents 1 Propositional Quantifiers 1.1 Introduction 1.2 Why Propositional Quantifiers? 1.3 Redundancy 1.4 Fragments of Higher-Order Logic 1.5 Outlook 1.6 Historical Overview 2 Relational Frames 2.1 Propositionally Quantified Modal Languages 2.2 Modal Logics Based on Classical Logic 2.3 Relational Frames and Normality 2.4 The Barcan Formula and Atomicity 2.5 S5 and the Reduction of Possible Worlds 2.6 Axiomatizability 2.7 Completeness Results 2.8 Model Theory 3 Beyond Relational Frames 3.1 Neighborhood Frames 3.2 Complete Boolean Algebras 3.3 Pointed Frames, and Matrices 3.4 Incomplete Boolean Algebras 3.5 General Frames 3.6 Variable Propositional Domains 3.7 Substitutional Quantifiers 4 Conclusion List of Abbreviations References Acknowledgments