Editor for this issue: Richard John Harvey <richardlinguistlist.org>
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 lipservice 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, Ncubes, 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, Kmaps, 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 3D 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. Timedomain 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: 3D 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: UPPERLEVEL 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 FunctionsSprachbunde 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 Nonnatural 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 Hoperators 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 QuasiAlgebra 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 3 89586 639 3. LINCOM Handbooks in Linguistics 09. Ca. 450pp. USD 80 / EUR 73.30 / � 48. 2nd printing. NEW: LINCOM electronic n.e.w.s.l.e.t.t.e.r. Monthly updates. Go to http://www.lincomeuropa.com A Students' and course discount of 40% is offered to the above title. Free copies of LINCOM'S newsflashes 26 & 27 are now available from LINCOM.EUROPAtonline.de. LINCOM EUROPA, Freibadstr. 3, D81543 Muenchen, Germany; FAX +49 89 62269404; http://www.lincomeuropa.com LINCOM.EUROPAtonline.de.Mail to authorRespond to listRead more issuesLINGUIST home pageTop of issue

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