Modal Logic and Classical Logic

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). 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 Johan Van Benthem. Revision Of Author's Thesis (ph. D.--university Of Amsterdam, 1976) Originally Presented Under The Title: Modal Correspondence Theory. Bibliography: P. [229]-234.