Type-Theoretical Grammar [Hardcover]

Constructive type theory was first presented in 1970 by Swedish logician Per Martin-Lof. Since then, it has become one of the main approaches in the foundations of mathematics and computer science. However, although it provides a considerable extension of the concepts and techniques of logic, it remains relatively unknown among linguists and philosophers. This work presents constructive type theory from the point of view of linguistics and the philosophy of language, introducing its valuable approach to those in areas in which it has remained unfamiliar. The theory is then applied to quantification, anaphora, temporal reference, and the structures of text and discourse. Various phenomena of dependence and progression are discussed in the light of concepts of proof object and content, and the solutions to several well-known problems are discussed.

1. Preliminary remarks
2. Gradual introduction to type theory
3. Logical operators in English
4. Anaphoric expressions
5. Temporal reference
6. Text and discourse
7. Context and possible worlds
8. Higher-level type theory
9. Sugaring and parsing
Appendix
Sugaring in ALF
Bibliography
Index

Chapter 2 of this book, the most substantial and most directly linked to computer science, gives a good, gradual account of type theory. This chapter may be recommended to anyone who wants an introduction to these ideas . . . . This is not a book on computer science, but Martin-Lof types are probably the suitable theoretical background for object-oriented programming, because the four basic concepts - objects, abstract data typing, inheritance, and polymorphism - are easy to formalize in type theory. --Computing Reviews