Type-Theoretical Grammar

Abstract

Abstract Constructive type theory was first presented in 1970, by the Swedish logician Per Martin-Lof. It has become one of the main approaches in the foundations of mathematics and computer science. But it has remained relatively unknown among linguists and philosophers, although it provides a comsiderable extension of the concepts and techniques of logic. The book contains an introduction to type theory from the point of view of linguistics and the philosophy of language. Type theory is then applied in the areas of quantification, anaphora, temporal reference, and the structure of text and discourse. In virtue of the type theoretical concepts of proof object and context, various phenomena of dependence and progression in language can be discussed in precise terms, and several well-known problems can be solved.

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