The Mathematics of Language
eBook - PDF

The Mathematics of Language

  1. 605 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

The Mathematics of Language

About this book

This book studies language(s) and linguistic theories from a mathematical point of view. Starting with ideas already contained in Montague's work, it develops the mathematical foundations of present day linguistics. It equips the reader with all the background necessary to understand and evaluate theories as diverse as Montague Grammar, Categorial Grammar, HPSG and GB. The mathematical tools are mainly from universal algebra and logic, but no particular knowledge is presupposed beyond a certain mathematical sophistication that is in any case needed in order to fruitfully work within these theories. The presentation focuses on abstract mathematical structures and their computational properties, but plenty of examples from different natural languages are provided to illustrate the main concepts and results. In contrast to books devoted to so-called formal language theory, languages are seen here as semiotic systems, that is, as systems of signs. A language sign correlates form with meaning. Using the principle of compositionality it is possible to gain substantial insight into the interaction between form and meaning in natural languages.

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Yes, you can access The Mathematics of Language by Marcus Kracht in PDF and/or ePUB format, as well as other popular books in Languages & Linguistics & Authorship. We have over one million books available in our catalogue for you to explore.

Table of contents

  1. 1 Fundamental Structures
  2. 1 Algebras and Structures
  3. 2 Semigroups and Strings
  4. 3 Fundamentals of Linguistics
  5. 4 Trees
  6. 5 Rewriting Systems
  7. 6 Grammar and Structure
  8. 7 Turing machines
  9. 2 Context Free Languages
  10. 1 Regular Languages
  11. 2 Normal Forms
  12. 3 Recognition and Analysis
  13. 4 Ambiguity, Transparency and Parsing Strategies
  14. 5 Semilinear Languages
  15. 6 Parikh’s Theorem
  16. 7 Are Natural Languages Context Free?
  17. 3 Categorial Grammar and Formal Semantics
  18. 1 Languages as Systems of Signs
  19. 2 Propositional Logic
  20. 3 Basics of λ-Calculus and Combinatory Logic
  21. 4 The Syntactic Calculus of Categories
  22. 5 The AB-Calculus
  23. 6 The Lambek-Calculus
  24. 7 Pentus’ Theorem
  25. 8 Montague Semantics I
  26. 4 Semantics
  27. 1 The Nature of Semantical Representations
  28. 2 Boolean Semantics
  29. 3 Intensionality
  30. 4 Binding and Quantification
  31. 5 Algebraization
  32. 6 Montague Semantics II
  33. 7 Partiality and Discourse Dynamics
  34. 5 PTIME Languages
  35. 1 Mildly-Context Sensitive Languages
  36. 2 Literal Movement Grammars
  37. 3 Interpreted LMGs
  38. 4 Discontinuity
  39. 5 Adjunction Grammars
  40. 6 Index Grammars
  41. 7 Compositionality and Constituent Structure
  42. 8 de Saussure Grammars
  43. 6 The Model Theory of Linguistic Structures
  44. 1 Categories
  45. 2 Axiomatic Classes I: Strings
  46. 3 Categorization and Phonology
  47. 4 Axiomatic Classes II: Exhaustively Ordered Trees
  48. 5 Transformational Grammar
  49. 6 GPSG and HPSG
  50. 7 Formal Structures of GB
  51. Bibliography
  52. Index