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LINCOM Handbooks in Linguistics (LHL)

Artikel-Nr.: ISBN 9783895866395

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Beschreibung

**Mathematical and Computational Linguistics**

H. Mark Hubey

*Montclair State University*

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.

Table of Contents:

0: INTRODUCTORY PRELIMINARIES

0.1. Continuous Nature of Speech

0.2. Functions and Mappings

0.3. Stochastic and Fuzzy Functions

0.4. Linear Operators, Relations, and Black Boxes

0.5. Discretization -- Numerical and Closed formSolutions

0.6. Representation, Meaning, and Definition

0.7. Significance, Precision, Accuracy, and Error

0.8. Beads on a String

0.9. Discretization of Speech

0.10. Simple Discretization

0.11. Mappings, Functions, Perception, and Excessive Mentalism

0.12. Binary, Ternary, or Infinity

0.13. Universal Distinctive Features

Appendix 0.A Sets, Classes, Relations, and Functions; Phonemes, Allophones, Semantics, Orthography; Appendix 0.B Dialogue

I: OPPOSITIONS, RELATIONS, GROUPS, AND LATTICES

I.1. Features, Binary Oppositions and Binary Relations

I.2. Simple Structures: Semigroups, Monoids, Groups, Isomorphisms, and Distances

I.3. More Complex Structures: Partial Ordering, Posets, N-cubes, Lattices, Hasse Diagram

I.4. `Lattice' of Vowels: Cardinal Vowel Diagrams, Ladefoged's Modification, Discrete Distance Metric, Trubetzkoy vowels

Appendix I.A Number Systems and Codes:The Binary System, K-maps, Gray codes; Appendix I.B Boolean Algebras

II: PRIVATE AND UNIVERSAL VOWEL SPACES

II.1. Cycles, Distance, Linear Ordering, and Hilbert Curves

II.2. Bloch and Trager Private Spaces

II.3. Chomsky & Halle Private Spaces

II.4. Complement of a Graph

II.5. Pure Vowels in 3-D

II.6. Discrete Universal Spaces

II.7. Karnaugh Maps and Finnish Vowels

II.8. American English Vowels

II.9. Other Spaces -- Stanford Phonology Archive

II.10. Binarity and Simplicity

III: COMPOUND VOWELS, DIPTHONGS, AND VECTORS

III.1. Vector Spaces and Phonemes

III.2. Time Domain Compositions -- Dipthongs and Glides

III.3. Dipthong = Vowel + Vowel

III.4. Dipthong = Vowel + Semivowel

III.5. Vectors and Dependency Phonology

III.6. Trubetzkoy and Stevens

III.7. Nonorthogonality of Features and Fant

IV: SPECTRAL DOMAIN DESCRIPTIONS

IV.1. Time-domain Signals

IV.2. Frequency Domain Descriptions

IV.3. Power Spectrum, Noise, and Autocorrelation

IV.4. Source and Filter

IV.5. Formant Functions and Approximations

IV.6 Dipthongs and Glides

IV.7. Compound Vowels

IV.8. Orthographic Projection of the Vocalic Phonemes of a Generic Language

IV.9. Formant Functions Again

IV.10. Formant Plots and Their Description

IV.11. Summary of Results

IV.12. Further Refinements of the Method

IV.13. The Formant Plots

IV.14. Nonlinearity, Quantality, and Catastrophe Theory

IV.15. Nonlinear Differential Equations and Quantality in Phonetics

Appendix IV.A: Fourier Analysis; Appendix IV.B: Convolution, Correlation, Spectral Density; Appendix IV.C Ordinary Linear Differential Equations; Appendix IV.D Orthogonal Functions; Appendix IV.E: Other Normalizations; Appendix IV.F Exponential Formant Approximations.

V: 3-D VECTOR PHASE SPACE FOR SPEECH

V.1. Properties of Consonants

V.2. Towards a Space

V.3. Consonant Vector Space

V.4. Dimensional Analysis and Buckingham Pi Theorem

V.5. Natural Groupings

V.6. Path Integrals and Minimization

V.7. Acoustic and Auditory Correlates in the Phase Space

V.8. Phones, Phonemes and Allophones

V.9. Sonority, Lenition, Fortition

V.10. Child Language Development and Aphasia

V.11. Vowels in Phase Space

V.12. Distance and Birth of New Phonemes

V.13. Experimental Evidence from Dipthongs

V.14. Implications for Phonological Space

V.15. The Ordinal Vowel Cube

V.16. Sonority Scales

V.17. Vector Representation

V.18. Dynamic Stochastic Processes and Speech Realization

V.19. Forced Binary Discrimination Tests and Probability Theory

V.20. The Ambiguity Function: Another Interpretation

V.21. Entropy, Uncertainty, and Information Theory

V.22. Fuzzy Sets and Catastrophe Theory

V.23. Fuzzy Functions for Multiple Discriminations along a Single Stimulus

V.24. Binary Discriminations for Multiple Stimuli and Stochastic Proceses

VI: UPPER-LEVEL DISTANCE METRICS

VI.1. Consonant Clusters

VI.2. Turkish Vowel Harmony

VI.3. Grammar for Transitions

VI.4. Turkish Syllabification

VI.5. Word Level Measures

VI.6. Topology of Vowel Spaces of Languages Examples from Arabic, English, Chinese, French,German, Italian, Latin, Sanskrit, Irish and Tamil

VI.7. Word Formation Rules and Borrowing

VI.8. Residues of Languages and Distance Functions--Sprachbunde and Sprachfamilien.

VI.9. Propagation, Waves and Diffusion of Innovation

VI.10. Semitic Word Formation Examples

VII: MULTIDIMENSIONAL INHERITANCE

VII.0. Introduction

VII.1. Temporal and Spatial Scaling

VII.2. Time Complexity vs Space Complexity -- Compute vs Memory Bound Processes

VII.3. Order of Magnitude and Complexity

VII.4. Intensive and Extensive Parameters

VII.5. Measurement Scales: Absolute and Relative Measures

VII.6. Stability, Relaxation Time and Correlation Time

VII.7. Process vs State

VII.8. Open Systems vs Closed Systems

VII.9. Time Scales and Linguistics

VII.10 Word Orders and Artificial Non-natural Languages

VII.11. Prehistoric Times and Language

VII.12. Change: Is it infinite ?

VII.13. Family Trees

VII.14. Distance Functions

VII.15. Matching Lexemes and Semantemes

VII.16. Dynamic Stochastic Processes and Language

VII.17. Summary

Appendix VII.A Cognates or Not; Appendix VII.B: Differential Equations Initial Value Problems, Stability and Equilibrium, Static vs Dynamic Equilibrium (Steady State) Appendix VII.C Stochastic Processes; Randomness, Mass and Density Functions, Averaging, Stochastic Differential Equations, Stationarity

VIII: PHONOLOGY, MORPHOLOGY, AND SYNTAX

VIII.0. Modularity

VIII.1. Upper Level Syntactic Structure of the World's Languages

VIII.2. Permutations, Reflections, and Rotations

VIII.3. Same Set Permutations

VIII.4. Tree Traversals and Permutation Groups

VIII.5. Phonology and Morphology

VIII.6. Postfixing Morphology and Morphophonology

VIII.7. Premorphing Languages and Phonology

VIII.8. Transformational Grammar and the H-operators

VIII.9. Infixing and Erase and Replace

VIII.10.Combined Inmorphing and Endmorphing

VII.11. Indonesian and German

VIII.12.Simplicity Metric

Appendix VIII.A: String Quasi-Algebra

IX: SYNTACTIC AND SEMANTIC STRUCTURE OF NEAR NATURAL LANGUAGES

IX.1. Prologue

IX.2. Graphs

IX.3. Binary Trees and Their Growth Patterns

IX.4. Trees and Tree Traversals

IX.5. Operands, Operators and Operations

IX.6. Formal Language Theory

IX.7. Another Kind of Space for Sentences

ISBN 9783895866395. LINCOM Handbooks in Linguistics 09. 450pp.1999.

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