Mathematical and Computional Linguistics

As Lass (1980) has remarked, "system" is something talked about constantly in linguistics but never beyond paying just lip-service to the concept. This book shows how linguistics constitutes a "system". Linguists (except those who study Formal Language Theory) are confronted with a dilemma. What they study is partially based on physics and is in many respects mathematical; yet the mathematics books are divorced from linguistics and linguistics books are divorced from mathematics and physics. There are no books that teach mathematics for linguists or linguistics with mathematics. This book goes a long way toward accomplishing the integration of mathematics, physics and linguistics into a whole, in other words "a system", just like those that are studied by others in the quantitative disciplines such as physics, engineering, computer science or economics.

The methods of mathematics which are used in the books to elucidate system concepts and others that are needed in linguistics includes boolean algebra, differential equations, and fuzzy logic.

Furthermore it also explains in an intuitive manner,those concepts are not only from mathematics but also from the underlying physics and engineering up to and including acoustic theory of speech, speech recognition, and even nonlinearity/catastrophe theory and quantality of phonemic systems.
All the mathematics needed to form the mathematical foundations of linguistics is illustrated with examples from linguistics and thus may be thought of as "theories", those that should replace the standard literary linguistics tradition in the same way that literary economics is no longer the de facto standard. Physical/acoustic theory of speech is blended naturally into the phonological and phonetic standard, and the standard works are used as springboards to the development of vector space concepts that are necessary for comprehension of new works in speech synthesis and speech recognition. It is rather easy then to show how seemingly nonrelated topics such as sonority scales, child language development, and various linguistics processes such as assimilation, metathesis, fortition/lenition can be seen to be a part of the greater whole. Historical processes are also treated in terms of sound change and also in terms of the most basic ideas which are needed for a thorough understanding of the problems such as multiple scale phenomena, distance and similarity, probability theory, and stochastic processes. A book of this length cannot possibly discuss all of the mathematics necessary in detail, however, there is sufficient material to motivate the topics, and furthermore to point in the direction of further study.