A Theory of Language and Information

A Theory of Language and Information PDF

Author: Zellig Sabbettai Harris

Publisher:

Published: 1991

Total Pages: 456

ISBN-13:

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Written by one of the most respected figures in American linguistics, this book develops an approach to the analysis of language on a mathematical model. Harris presents a formal theory of language structure, in which syntax is characterized as an orderly system of departure from random combinings of sounds, words, and all the elements of language. He argues that the combining of words in a sentence constitutes a mathematical object, and that each departure from randomness is a contribution to the structure and meaning of a sentence. Discussing the differences in the structure and content of language, mathematics, and music, Harris shows that the use of language in a science constitutes a distinguishable sub-language. Remarkable and compelling, Harris's magnum opus will be considered the classical analysis of the structuring of information and development of language.

Mathematical Methods in Linguistics

Mathematical Methods in Linguistics PDF

Author: Barbara B.H. Partee

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 669

ISBN-13: 9400922132

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Elementary set theory accustoms the students to mathematical abstraction, includes the standard constructions of relations, functions, and orderings, and leads to a discussion of the various orders of infinity. The material on logic covers not only the standard statement logic and first-order predicate logic but includes an introduction to formal systems, axiomatization, and model theory. The section on algebra is presented with an emphasis on lattices as well as Boolean and Heyting algebras. Background for recent research in natural language semantics includes sections on lambda-abstraction and generalized quantifiers. Chapters on automata theory and formal languages contain a discussion of languages between context-free and context-sensitive and form the background for much current work in syntactic theory and computational linguistics. The many exercises not only reinforce basic skills but offer an entry to linguistic applications of mathematical concepts. For upper-level undergraduate students and graduate students in theoretical linguistics, computer-science students with interests in computational linguistics, logic programming and artificial intelligence, mathematicians and logicians with interests in linguistics and the semantics of natural language.

The Legacy of Zellig Harris

The Legacy of Zellig Harris PDF

Author: Bruce E. Nevin

Publisher: John Benjamins Publishing

Published: 2002-11-22

Total Pages: 341

ISBN-13: 9027297002

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Zellig Harris had a profound influence in formal systems and applied mathematics, in demonstrations of the computability of language, and in informatics. Volume 2 begins with a commentary by André Lentin on Harris's grounding in constructivist, intuitionist mathematics, drawing a parallel between Harris's central insights and those of Gödel and others which were of like import in the foundations of mathematics. An international array of scholars describe further developments and relate this work to that of others. Fernando Pereira argues that Harrisian 'linguistic information' can effect a reunion of linguistics with information theory that has not been considered possible since Chomsky's declaration of irrelevance in 1957. Chapters by Richard Oehrle and by Terence Langendoen develop two novel formal systems with intriguing properties. Chapters by Naomi Sager and Ngo Thanh Nhan, by Aravind Joshi, and by Stephen Johnson describe the history of work on the computability of language and project exciting prospects ahead. Karel van den Eynde and colleagues describe use of distributional methods, refined beyond those of Harris, to develop comprehensive computer dictionaries for several languages. The chapter by Benoît Habert and Pierre Zweigenbaum surveys the field of automatic acquisition of information categories, and that by Richard Kittredge surveys work on text generation. Richard Smaby shows how distributional analysis can even inform design of computer user interfaces.

General Systems Theory

General Systems Theory PDF

Author: Yi Lin

Publisher: Springer Science & Business Media

Published: 2006-04-11

Total Pages: 386

ISBN-13: 0306469626

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As suggested by the title of this book, I will present a collection of coherently related applications and a theoretical development of a general systems theory. Hopefully, this book will invite all readers to sample an exciting and challenging (even fun!) piece of interdisciplinary research, that has characterized the scientific and technological achievements of the twentieth century. And, I hope that many of them will be motivated to do additional reading and to contribute to topics along the lines described in the following pages. Since the applications in this volume range through many scientific disciplines, from sociology to atomic physics, from Einstein’s relativity theory to Dirac’s quan tum mechanics, from optimization theory to unreasonable effectiveness of mathe matics to foundations of mathematical modeling, from general systems theory to Schwartz’s distributions, special care has been given to write each application in a language appropriate to that field. That is, mathematical symbols and abstractions are used at different levels so that readers in various fields will find it possible to read. Also, because of the wide range of applications, each chapter has been written so that, in general, there is no need to reference a different chapter in order to understand a specific application. At the same time, if a reader has the desire to go through the entire book without skipping any chapter, it is strongly suggested to refer back to Chapters 2 and 3 as often as possible.

Mathematical Linguistics

Mathematical Linguistics PDF

Author: Andras Kornai

Publisher: Springer Science & Business Media

Published: 2007-11-10

Total Pages: 300

ISBN-13: 1846289858

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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: no prior knowledge of linguistics is assumed. As the first textbook of its kind, this book is useful for those in information science and in natural language technologies.

Language and Text

Language and Text PDF

Author: Adam Pawłowski

Publisher: John Benjamins Publishing Company

Published: 2021-12-15

Total Pages: 288

ISBN-13: 9027258384

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Specialists in quantitative linguistics the world over have recourse to a solid and universal methodology. These days, their methods and mathematical models must also respond to new communication phenomena and the flood of data produced daily. While various disciplines (computer science, media science) have different ways of processing this onslaught of information, the linguistic approach is arguably the most relevant and effective. This book includes recent results from many renowned contemporary practitioners in the field. Our target audiences are academics, researchers, graduate students, and others involved in linguistics, digital humanities, and applied mathematics.

The Language of Mathematics

The Language of Mathematics PDF

Author: Mohan Ganesalingam

Publisher: Springer

Published: 2013-03-14

Total Pages: 273

ISBN-13: 3642370128

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The Language of Mathematics was awarded the E.W. Beth Dissertation Prize for outstanding dissertations in the fields of logic, language, and information. It innovatively combines techniques from linguistics, philosophy of mathematics, and computation to give the first wide-ranging analysis of mathematical language. It focuses particularly on a method for determining the complete meaning of mathematical texts and on resolving technical deficiencies in all standard accounts of the foundations of mathematics. "The thesis does far more than is required for a PhD: it is more like a lifetime's work packed into three years, and is a truly exceptional achievement." Timothy Gowers

Mathematical Linguistics

Mathematical Linguistics PDF

Author: Andras Kornai

Publisher: Springer Science & Business Media

Published: 2007-12-16

Total Pages: 290

ISBN-13: 1846289866

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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: no prior knowledge of linguistics is assumed. As the first textbook of its kind, this book is useful for those in information science and in natural language technologies.

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