LINGUIST List 10.1483

Fri Oct 8 1999

Books: Mathematical & Computational Ling, Formal Ling

Editor for this issue: Scott Fults <>

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  1. LINCOM EUROPA, H. Mark Hubey, Mathematical & Computational Linguistics
  2. LINCOM EUROPA, Formal Ling - Ping Jiang-King, Tone-Vowel Interaction in OT

Message 1: H. Mark Hubey, Mathematical & Computational Linguistics

Date: Mon, 04 Oct 1999 21:23:43 +0200
Subject: H. Mark Hubey, Mathematical & 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:

0.1. 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.1. Features, Binary Oppositions and Binary Relations
I.2. Simple Structures: Semigroups, Monoids, Groups, Isomorphisms, and
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.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.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.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
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

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
V.24. Binary Discriminations for Multiple Stimuli and Stochastic

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
VI.9. Propagation, Waves and Diffusion of Innovation
VI.10. Semitic Word Formation Examples

VII.0. Introduction
VII.1. Temporal and Spatial Scaling
VII.2. Time Complexity vs Space Complexity -- Compute vs Memory Bound
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.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.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 3 89586 639 3. 
LINCOM Handbooks in Linguistics 09. 
Ca. 450pp. Pb: EUR 70.56 / USD 80 / DM 138 

ISBN 3 89586 924 4. 
LINCOM Handbooks in Linguistics 09 (Hardcover). 
Ca. 450pp. Hb: EUR 101.23 / USD 110 / DM 198 / � 66. 

Ordering information for individuals: Please give us your creditcard no.
/ expiry date or send us a cheque. Prices in this information include
shipment worldwide by airmail. A standing order for this series is
available with special discounts offered to individual subscribers. 

LINCOM EUROPA, Paul-Preuss-Str. 25, D-80995 Muenchen, Germany; FAX +4989
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Message 2: Formal Ling - Ping Jiang-King, Tone-Vowel Interaction in OT

Date: Mon, 04 Oct 1999 21:27:05 +0200
Subject: Formal Ling - Ping Jiang-King, Tone-Vowel Interaction in OT

Ping Jiang-King, University of British Columbia

This study aims at constructing a fully articulated theory of
tone-vowel interaction within the framework of Optimality Theory
(OT). It examines the nature of this phenomenon in Northern Min
languages, as well as various Southeast Asian languages. The questions
addressed are (i) what is the nature of tone-vowel interaction? (ii)
how do they relate to each other? Two important findings emerge from
the investigation. First, tonal types and syllable types are closely
related to each other. That is, different groups of tones occur only
in a certain kind of syllables. These cooccurrence restrictions are
identified as a correlation between tonal contour and syllable weight.

Second, tone does not directly affect vowel distributions and
alternations. Rather, it is the relative syllable positions in which a
vowel occurs and the number of segments present in a syllable that
trigger vowel distributions and alternations. These findings lead to
the conclusion that tone and vowel do not interact directly and that
there is no feature-to-feature correlation between them. Their
interaction lies in the prosodic anchor mediating between them. To
account for the correlation between tonal contour and syllable weight
and the close relationship between syllable structures and vowel
features, a prosodic anchor hypothesis is proposed which attributes
the tone-vowel interaction to the mora and its function as an anchor
for both tone and vowel.

ISBN 3 89586 647 4. 
INCOM Studies in Theoretical Linguistics 16. 
220pp. EUR 57.26 / USD 70 / DM 112 

Ordering information for individuals: Please give us your creditcard no.
/ expiry date or send us a cheque. Prices in this information include
shipment worldwide by airmail. A standing order for this series is
available with special discounts offered to individual subscribers. 

LINCOM EUROPA, Paul-Preuss-Str. 25, D-80995 Muenchen, Germany; FAX +4989
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