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Mathematical Linguistics

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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


From the reviews: "Kornai's contribution is refreshingly different in that he treats, in this relatively compact volume, practically all areas of linguistics, phonetics, and speech and language processing. ... A single entry point to the central methods and concepts of linguistics that are made largely ... to the mathematician, computer scientist, or engineer ... . the most likely readership of this book consists of (computational) linguists and others who already know the linguistic issues ... ." (Richard Sproat and Roxana Girju, Computational Lingustics, Vol. 34 (4), 2008) "This is a remarkable book on the mathematics used for linguistics. ... it provides a coherent, well-written view of the math required to model the structure of langiage as used in the main branches of linguistics: phonology, morphology, syntax, and semantics. The intended audience is anyone with sufficient general mathematical maturity, such as advanced undergraduate math. ... The math is presented well, and the material has a strong narrative flow." (Rohan Baxter, Computing Reviews, March, 2009) "The book deals ... with mathematics inspired by linguistics than with applications of mathematics in linguistics. A large part of the book deals with mathematical models of signal, speech, and handwriting recognition. The book consists of ten chapters. Every chapter contains interesting examples, elegant mathematics and many further reading hints. ... The book contains many interesting mathematical models, stimulating examples and elegant proofs, and it is well written." (Jaroslav Kral', Zentralblatt MATH, Vol. 1171, 2009)

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