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Mathematics | Mathematical Linguistics

Mathematical Linguistics

Kornai, Andras

2008, XIV, 290 p. With online files/update.

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  • Aims to teach linguistics to the reader but presumes knowledge of mathematics only at the undergraduate level
  • The material was hitherto available only in the research literature
  • Wide applicability in information science (information retrieval, information extraction, search engines) and in natural language technologies (speech recognition, OCR, HCI)

Mathematical Linguistics introduces the mathematical foundations of linguistics to computer scientists, engineers, and mathematicians interested in natural language processing. The book presents linguistics as a cumulative body of knowledge from the ground up, with no prior knowledge of linguistics being assumed, covering more than the average two-semester introductory course in linguistics.

This comprehensive, reader-friendly volume offers readers a high-level orientation, discussing the foundations of the field and presenting both the classical work and the most recent results. It covers an extremely rich array of topics including not only syntax and semantics but also phonology and morphology, probabilistic approaches, complexity, learnability, and the analysis of speech and handwriting.

As the first text of its kind, this innovative book will be a valuable tool and reference for those in information science (information retrieval and extraction, search engines) and in natural language technologies (speech recognition, optical character recognition, HCI). Exercises suitable for advanced readers are included as well as suggestions for further reading and an extensive bibliography.

"I'm pleased and impressed. The book is very readable, often entertaining---it tells what the issues are, what they are called, in what health they are, where more meat can be found. Given the enormous amount of material and concepts touched on, and the technical difficulties lying under the surface almost everywhere, the book betrays scholarship in a matter-of-fact way, making due impression on, but without clobbering, the reader. This is a book that invites READING THROUGH…".

Professor Tommaso Toffoli, Boston University, USA

"It is a remarkable achievement, essential reading for every linguist who aspires to be well informed about applications of mathematics in the language sciences."

Professor Geoffrey Pullum, University of Edinburgh, UK

"I really liked this book. First, it is written very well and secondly, the author has taken a rather non-standard but very attractive approach to mathematical linguistics. It is very refreshing."

Professor Aravind K. Joshi, University of Pennsylvania, USA

Content Level » Research

Keywords » Syntax - classification - complexity - computer - hidden markov model - human-computer interaction (HCI) - information - language - learning - linguistics - morphology - natural language processing - semantics - speech processing - speech recognition

Related subjects » Applications - Artificial Intelligence - Mathematics - Philosophy - Signals & Communication - Theoretical Computer Science

Table of contents 

Preface.- Introduction.- The subject matter.- Cumulative knowledge.- Definitions.- Formalization.- Foundations.- Mesoscopy.- Further reading.- The Elements.- Generation.- Axioms, rules and constraints.- String rewriting.- Further reading.- Phonology.- Phonemes.- Natural classes and distinctive features.- Suprasegmentals and autosegments.- Phonological computation.- Further reading.- Morphology.- The prosodic hierarchy.- Word formation.- Optimality.- Zipf’s Law.- Further reading.- Syntax.- Combinatorical theories.- Grammatical theories.- Semantics-driven theories.- Weighted theories.- The regular domain.- External evidence.- Further reading.- Semantics.- The explanatory burden of semantics.- The standard theory.- Grammatical semantics.- Further reading.- Complexity.- Information.- Kolmogorov complexity.- Learning.- Further reading.- Linguistic Pattern Recognition.- Quantization.- Markov processes, Hidden Markov models.- High-level signal processing.- Document classification.- Further reading.- Speech and Handwriting.- Low-level speech processing.- Phonemes as hidden units.- Handwriting and machine print.- Further reading.- Simplicity.- Previous reading.- Bibliography.- Index

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