Mathematical Methods in Linguistics

Barbara H. Partee, Alice Ter Meulen, Robert E. Wall (auth.)9027722447, 9789027722447, 9027722455

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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Table of contents :
Front Matter….Pages i-xxii
Front Matter….Pages 1-1
Basic Concepts of Set Theory….Pages 3-26
Relations and Functions….Pages 27-37
Properties of Relations….Pages 39-53
Infinities….Pages 55-73
Back Matter….Pages 75-84
Front Matter….Pages 85-85
Basic Concepts of Logic and Formal Systems….Pages 87-96
Statement Logic….Pages 97-134
Predicate Logic….Pages 135-178
Formal Systems, Axiomatization, and Model Theory….Pages 179-235
Back Matter….Pages 237-244
Front Matter….Pages 245-245
Basic Concepts of Algebra….Pages 247-253
Operational Structures….Pages 255-274
Lattices….Pages 275-294
Boolean and Heyting Algebras….Pages 295-307
Back Matter….Pages 309-312
Front Matter….Pages 313-313
Basic Concepts….Pages 315-369
Generalized Quantifiers….Pages 371-399
Intensionality….Pages 401-428
Front Matter….Pages 429-429
Basic Concepts….Pages 431-452
Finite Automata, Regular Languages and Type 3 Grammars….Pages 453-484
Pushdown Automata, Context Free Grammars and Languages….Pages 485-504
Turing Machines, Recursively Enumerable Languages and Type 0 Grammars….Pages 505-525
Linear Bounded Automata, Context Sensitive Languages and Type 1 Grammars….Pages 527-532
Front Matter….Pages 429-429
Languages Between Context Free and Context Sensitive….Pages 533-551
Transformational Grammars….Pages 553-557
Back Matter….Pages 559-666