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Mathematical Methods in Linguistics : Studies in Linguistics & Philosophy - Barbara B. H. Partee

Mathematical Methods in Linguistics

Studies in Linguistics & Philosophy

Hardcover

Published: 30th April 1990
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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.

Preface
Set Theory
Basic Concepts of Set Theory
Relations and Functions
Properties of Relations
Infinities. Appendix A1
Logic and Formal Systems
Basic Concepts of Logic
Statement Logic
Predicate Logic
Formal Systems, Axiomatization, and Model Theory
Algebra
Basic Concepts of Algebra
Operational Structures
Lattices
Boolean and Heyting Algebras
English as a Formal Language
Basic Concepts of Formal Languages
Generalized Quantifiers
Intensionality
Languages, Grammars, and Automata
Basic Concepts of Languages, Grammars, and Automata
Finite Automata, Regular Languages and Type 3 Grammars
Pushdown Automata, Context-Free Grammars and Languages
Turing Machines, Recursively Enumberable Languages, and Type 0 Grammars
Linear Bounded Automata, Context-Sensitive Languages and Type 1 Grammars
Languages Between Context-Free and Context-Sensitive
Transformational Grammars
Review Problems
Index
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9789027722447
ISBN-10: 9027722447
Series: Studies in Linguistics & Philosophy
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 666
Published: 30th April 1990
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 23.5 x 16.51  x 3.81
Weight (kg): 1.14