Intensional and Higher-Order Modal Logic
1st Edition
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Description
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.
Table of Contents
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
Details
- No. of pages:
- 158
- Language:
- English
- Copyright:
- © North Holland 1975
- Published:
- 1st January 1975
- Imprint:
- North Holland
- eBook ISBN:
- 9781483274737
About the Author
Daniel Gallin
Affiliations and Expertise
Department of Mathematics, University of San Francisco