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Modal Logic and Classical Logic

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The present work is a rewritten version of van Benthem's dissertation ``Modal Correspondence Theory'' (University of Amsterdam, 1976) and a supplementary report called ``Modal Logic as Second-Order Logic'' (University of Amsterdam, 1977).

Author(s): Johan van Benthem
Series: Indices. Monographs in Philosophical Logic and Formal Linguistics, volume 3
Publisher: Bibliopolis
Year: 1983

Language: English
Pages: 217

Part 1. A Short Survey of Propositional Modal Logic

I. Historical Background
II. Possible Worlds Semantics
III. Definability
IV. Modal Algebras
V. Axiomatic Theories
VI. Completeness

Part 2. First-Order Definability of Modal Formulas

VII. Local and Global First-Order Definability
VIII. A Model-Theoretic Characterization of First-Order Definability
IX. The Method of Substitutions
X. Disproving First-Order Definability
XI. Relative First-Order Definability
XII. Modal Predicate Logic
XIII. Preservation Classes of Modal Formulas

Part 3. Modal Definability

XIV. Modally Definable Elementary Classes of Frames
XV. Preservation Results for First-Order Formulas
Appendix: Tense Logic
XVI. Modally Definable Classes of Frames
Appendix: Higher-Order Correspondence

Part 4. Higher-Order Definability

XVII. Universal Second-Order Sentences
XVIII. Second-Order Logic
XIX. The Theory of Finite Types

Bibliography