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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23 of 25 people found the following review helpful:
5.0 out of 5 stars
Not Just for Linguists,
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This review is from: Mathematical Methods in Linguistics (Studies in Linguistics and Philosophy) (Paperback)
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, This would be an excellent book for an advanced undergraduate or graduate student in either mathematics or computer science to use
6 of 8 people found the following review helpful:
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Comprehensive,
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This review is from: Mathematical Methods in Linguistics (Studies in Linguistics and Philosophy) (Paperback)
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.
3 of 4 people found the following review helpful:
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Extremely good.,
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This review is from: Mathematical Methods in Linguistics (Studies in Linguistics and Philosophy) (Paperback)
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.
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Key Phrases - Statistically Improbable Phrases (SIPs):
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pumping theorem, universal generalization, complement laws, axiomatizing logic, increasing determiners, finite automaton languages, pda languages, opacity phenomena, weak partial order, auxiliary premise, meet homomorphism, right monotone, permutation closure, intensional model, phrasal conjunction, deterministic pda, join homomorphism, auxiliary alphabet, production schemata, power set algebra, predicate notation, right identity element, natural language determiners, conditional proof, constituent structure tree Key Phrases - Capitalized Phrases (CAPs): (learn more)
Modus Ponens, Swiss German, Halting Problem, Rule of Substitution, Beth Tableaux, Church's Hypothesis, Axiom of Choice, Distributive Laws, Exclusivity Condition, Indirect Proof, Chomsky Hierarchy, New York, Russell's Paradox, Nontangling Condition, Principle of Mathematical Induction, Alonzo Church, Montague Grammar, The Amazon River, Cantor's Theorem, Associative Laws, Function Application, Commutative Laws, United States, Identity Laws Browse Sample Pages:
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pumping theorem, universal generalization, complement laws, axiomatizing logic, increasing determiners, finite automaton languages, pda languages, opacity phenomena, weak partial order, auxiliary premise, meet homomorphism, right monotone, permutation closure, intensional model, phrasal conjunction, deterministic pda, join homomorphism, auxiliary alphabet, production schemata, power set algebra, predicate notation, right identity element, natural language determiners, conditional proof, constituent structure tree Key Phrases - Capitalized Phrases (CAPs): (learn more)
Modus Ponens, Swiss German, Halting Problem, Rule of Substitution, Beth Tableaux, Church's Hypothesis, Axiom of Choice, Distributive Laws, Exclusivity Condition, Indirect Proof, Chomsky Hierarchy, New York, Russell's Paradox, Nontangling Condition, Principle of Mathematical Induction, Alonzo Church, Montague Grammar, The Amazon River, Cantor's Theorem, Associative Laws, Function Application, Commutative Laws, United States, Identity Laws Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
6
books
cite this book:
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- Linguistic Semantics: An Introduction (Cambridge Approaches to Linguistics) by John Lyons in Back Matter
- The Digital Phoenix: How Computers are Changing Philosophy (Metaphilosophy) by Terrell Ward Bynum on page 251
- Natural Language Semantics by Keith Allan in Back Matter
- The Oxford Companion to Women's Writing in the United States by Cathy N. Davidson on page 522
- Negative Contexts: Collocation, Polarity and Multiple Negation (Routledge Studies in Germanic Linguistics) by Ton van der Wouden in Back Matter
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