Intensional and Higher-Order Modal Logic

North-Holland Mathematics Studies, 19: Intensional and Higher-Order Modal Logic: With Applications to Montague Semantics focuses on an approach to the problem of providing a precise account of natural language syntax and semantics, including the set-theoretic semantical methods, Boolean models, and two-sorted type theory. The book first offers information on intensional logic and alternative formulations of intensional logic. Topics include two-sorted type theory, normal forms, extensions and intensional logic, modal T-logic, persistence in intensional logic, generalized completeness of intensional logic, and natural language and intensional logic. The text then examines higher-order modal logic and algebraic semantics. Discussions focus on Cohen's independence results, topological models of MLp, modal independence results, Boolean models of MLp, relative strength of intensional logic and MLp, propositional operators, modal predicate logic, and propositions in MLp. The monograph is a valuable reference for mathematicians and researchers interested in intensional and higher-order modal logic.

Part I. Intensional Logic

Chapter 1. Intensional Logic

§1. Natural Language and Intensional Logic

§2. The Logic IL

§3. Generalized Completeness of IL

§4. Persistence in IL

Chapter 2. Alternative Formulations of IL

§5. Modal T-Logic

§6. Extensions of IL and MLT

§7. Normal Forms

§8. Two-Sorted Type Theory

Part II. Higher-Order Modal Logic

Chapter 3. Higher-Order Modal Logic

§9. Modal Predicate Logic

§10. Propositions in MLP

§11. Atomic Propositions and EC

§12. Propositional Operators

§13. Relative Strength of IL and MLP

Chapter 4. Algebraic Semantics

§14. Boolean Models of MLP

§15. Modal Independence Results

§16. Topological Models of MLP

§17. Cohen’s Independence Results

Bibliography