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Mathematical Methods in Linguistics [Paperback]

Barbara Partee , Alice ter Meulen , Robert Wall

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Book Description

April 30 1990 9027722455 978-9027722454 Softcover reprint of the original 1st ed. 1993
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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Amazon.com: 5.0 out of 5 stars  6 reviews
26 of 28 people found the following review helpful
5.0 out of 5 stars Not Just for Linguists Oct. 22 2001
By J. putnam - Published on Amazon.com
Mathematical Methods in Linquistics is far more about mathematical methods than about linguistics, although in many places linquistics is used as a source of examples.
Instead it covers such mathematical topics as sets (including infinite sets), relations, a good deal of mathematical logic,
automata (up to turing machines), the lambda calculus, lattices and more.
This would be an excellent book for an advanced undergraduate or graduate student in either mathematics or computer science to use
either as a review text, or as a study guide for further investigation.
6 of 7 people found the following review helpful
5.0 out of 5 stars Extremely good. Jan. 27 2010
By E. Ebrahim - Published on Amazon.com
Format:Paperback|Verified Purchase
This book is incredible. It's a great introduction to axiomatic set theory at the beginning, and it does a great introduction to model theory. I haven't gotten to the linguistics part of it yet, but it covers math and logic in an extremely effective way.
8 of 10 people found the following review helpful
5.0 out of 5 stars Comprehensive March 22 2007
By JDCA - Published on Amazon.com
Format:Paperback|Verified Purchase
This book is well written and detailed. I found it particularly useful for my semantics course. It covers the necessary logic one need to do semantics. It also discuses type theory and the lambda calculus. This book is a great complement to any semantics text.
1 of 1 people found the following review helpful
5.0 out of 5 stars Clear introduction to Linguistics for Math people Aug. 17 2013
By Danny Kerdine - Published on Amazon.com
This is a lovely book that starts in the foundations of mathematics and ends with formal and natural language theory. It can be followed by anyone who wants to spend the time and think about the concepts and do the exercises - which all have solutions in the back of the book. The examples are straight forward and every word can be taken as Hoyle.

Those with a math background will find the first half a delightful review of concepts they have seen in various courses, like abstract algebra and set theory, but with a slightly different twist, one that is more foundational and language theoretic than the standard math treatments.

It would serve well for a course in Linguistics for math majors or conversely as a course in formal languages and Mathematics for language majors.

The ideas presented are timeless so don't let the early publication date lead you astray. There cannot be any better, more current treatment available.
5.0 out of 5 stars Best book available for abstract math! Nov. 24 2012
By Janice Stonestreet - Published on Amazon.com
Format:Paperback|Verified Purchase
Best book available for abstract math students! Thoroughly explains the symbols used in proofs and shorthanding axioms. Glossary is suscinct and accurate.

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