Mathematical Methods in Linguistics

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Springer Netherlands, Apr 30, 1990 - Language Arts & Disciplines - 666 pages
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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.

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About the author (1990)

Paul Portner is Associate Professor of Linguistics and Acting Director of the Interdisciplinary Program in Cognitive Science at Georgetown University. He is the author of numerous articles on topics such as mood and modality, tense and aspect, and the syntax/semantics interface.

Barbara H. Partee is Distinguished University Professor of Linguistics and Philosophy at the University of Massachusetts, Amherst and is the author of several landmark essays in formal semantics. She has written and edited numerous books, including "Mathematical Methods in Linguistics "(with Alice ter Meulen and Robert Wall, 1990), "Montague Grammar "(edited, 1976), and "Quantification in Natural Languages "(edited, with Emmon Bach, Eloise Jelinek, and Angelika Kratzer, 1995).

Patricia Wall is a children's author and teacher with an interest in historical fiction for young readers. Her grandparents came to the state of Washington in the late 1890's and lived through some of the same experiences that are portrayed in the book. This is the first in a series of books about the logging industry in the Pacific Northwest; each book will be told through the eyes of a different family member. She is also the author of the YA title, Beautiful Baby. The book's illustrator is Robert Wall, husband of the author.