Mathematical Methods in Linguistics

by Barbara B.H. Partee, A.G. ter Meulen, R. Wall

Elementary set theory accustoms the students to mathematical abstraction, includes the standard constructions of relations, functions, and orderings, and leads to a discussion of the various orders of infinity. The material on logic covers not only the standard statement logic and first-order predicate logic but includes an introduction to formal systems, axiomatization, and model theory. The section on algebra is presented with an emphasis on lattices as well as Boolean and Heyting algebras. Background for recent research in natural language semantics includes sections on lambda-abstraction and generalized quantifiers. Chapters on automata theory and formal languages contain a discussion of languages between context-free and context-sensitive and form the background for much current work in syntactic theory and computational linguistics. The many exercises not only reinforce basic skills but offer an entry to linguistic applications of mathematical concepts.
For upper-level undergraduate students and graduate students in theoretical linguistics, computer-science students with interests in computational linguistics, logic programming and artificial intelligence, mathematicians and logicians with interests in linguistics and the semantics of natural language.

Genres: Linguistics, Mathematics, Language, Logic, Nonfiction, Reference, Textbooks

688 pages, Hardcover

First published April 30, 1990

Reviews

[Brian Beakley · Rating 4 out of 5]

When I ended a four-year relationship with a woman, I sat in my office and did every problem in the book through about Chapter 10. Cheaper than therapy.

[for-much-deliberation ...]

I got through a few chapters but I think I will explore this again sometime in the future...

[Nat]

Not exactly a cracking good read, but an approachable and clear guide to the use of set theory in linguistics.