Mathematical Linguistics

By Rauff, James V. | Mathematics and Computer Education, Winter 2011 | Go to article overview
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Mathematical Linguistics

Rauff, James V., Mathematics and Computer Education

MATHEMATICAL LINGUISTICS by Andras Komai Springer- Verlag, 2008, 289 pp. ISBN: 978-1-84628-985-9

Mathematical Linguistics is a comprehensive introduction to the mathematical study of human languages. This book is written for mathematicians and presupposes no technical knowledge of linguistics or natural language theory. It does, however, require a strong mathematical background. Kornai suggests that the book is accessible to advanced undergraduates but, in my experience, only a special undergraduate with the prerequisite knowledge of algebra, logic, and information theory could truly appreciate its contents. But, for mathematicians and computer scientists, Mathematical Linguistics is an excellent introduction to this important area of applied mathematics.

Kornai organizes the book around the classical subdivisions of linguistics: phonology (the sounds of language), morphology (the words of language), syntax (the sentences of language), and semantics (the meanings of linguistic utterances). He does not address pragmatics (the use of language) but instead offers chapters on some current fundamental linguistic research areas such as pattern recognition and speech and handwriting processing.

The chapters of Mathematical Linguistics break down as follows:

1. Introduction: Here Komai defines mathematical linguistics and specifies the parameters for formalizing human languages.

2. The elements: This chapter reviews the fundamental notions of string rewriting systems familiar to anyone who has studied the theory of computing. Included are Kleene closure, context-free and content-sensitive language, and linear bounded automata.

3. Phonology: Komai discusses natural phonetic classes, distinctive features, and suprasegmentals. He also introduces the use of finite state transducers for phonological modeling.

4. Morphology: This chapter is concerned with word formation and the linguistically controversial Zipf s law (i.e., given some corpus of natural language utterances, the frequency of any word is inversely proportional to its rank in the frequency table).

5. Syntax: In keeping with its prominence in modern linguistics, the chapter on syntax is the longest in the book. Komai discusses a variety of combinatorial theories (e.

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