Mathematical Methods in Linguistics

1. Front Matter

   Pages i-xxii

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2. Set Theory

   1. Front Matter

      Pages 1-1

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   2. Basic Concepts of Set Theory

      • Barbara H. Partee, Alice Ter Meulen, Robert E. Wall

      Pages 3-26

   3. Relations and Functions

      • Barbara H. Partee, Alice Ter Meulen, Robert E. Wall

      Pages 27-37

   4. Properties of Relations

      • Barbara H. Partee, Alice Ter Meulen, Robert E. Wall

      Pages 39-53

   5. Infinities

      • Barbara H. Partee, Alice Ter Meulen, Robert E. Wall

      Pages 55-73

3. Back Matter

   Pages 75-84

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4. Logic and Formal Systems

   1. Front Matter

      Pages 85-85

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   2. Basic Concepts of Logic and Formal Systems

      • Barbara H. Partee, Alice Ter Meulen, Robert E. Wall

      Pages 87-96

   3. Statement Logic

      • Barbara H. Partee, Alice Ter Meulen, Robert E. Wall

      Pages 97-134

   4. Predicate Logic

      • Barbara H. Partee, Alice Ter Meulen, Robert E. Wall

      Pages 135-178

   5. Formal Systems, Axiomatization, and Model Theory

      • Barbara H. Partee, Alice Ter Meulen, Robert E. Wall

      Pages 179-235

5. Back Matter

   Pages 237-244

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6. Algebra

   1. Front Matter

      Pages 245-245

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   2. Basic Concepts of Algebra

      • Barbara H. Partee, Alice Ter Meulen, Robert E. Wall

      Pages 247-253

   3. Operational Structures

      • Barbara H. Partee, Alice Ter Meulen, Robert E. Wall

      Pages 255-274

   4. Lattices

      • Barbara H. Partee, Alice Ter Meulen, Robert E. Wall

      Pages 275-294

   5. Boolean and Heyting Algebras

      • Barbara H. Partee, Alice Ter Meulen, Robert E. Wall

      Pages 295-307

7. Back Matter

   Pages 309-312

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8. English as a Formal Language

   1. Front Matter

      Pages 313-313

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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.
Forupper-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.

• computational linguistics
• language
• linguistics
• logic
• predicate logic
• semantics

• Department of Linguistics, University of Massachusetts, Amherst, USA

  Barbara H. Partee

• Departments of Philosophy and Linguistics, Indiana University, Bloomington, USA

  Alice Meulen

• Department of Linguistics, University of Texas, Austin, USA

  Robert E. Wall

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