Mathematical Methods in Linguistics (Google eBook)

Front Cover
Springer Science & Business Media, Apr 30, 1990 - Computers - 663 pages
3 Reviews
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.
  

What people are saying - Write a review

Review: Mathematical Methods in Linguistics, Corrected second printing of the first edition (Studies in Linguistics and Philosophy)

User Review  - Nat - Goodreads

Not exactly a cracking good read, but an approachable and clear guide to the use of set theory in linguistics. Read full review

Contents

Basic Concepts
317
1311 A compositional account of statement logic
319
1312 A compositional account of predicate logic
323
1313 Natural language and compositionality
333
132 Lambdaabstraction
338
1322 The syntax and semantics of Aabstraction
341
1323 A sample fragment
343
1324 The lambdacalculus
348

22 Relations
28
23 Functions
30
24 Composition
33
Properties of Relations
39
32 Diagrams of relations
43
33 Properties of inverses and complements
44
34 Equivalence relations and partitions
45
35 Orderings
47
Exercises
51
Infinities
55
42 Denumerability of sets
58
43 Nondenumerable sets
62
44 Infinite vs unbounded
69
Exercises
71
SetTheoretic Reconstruction of Number Systems
75
A2 Extension to the set of all integers
78
A3 Extension to the set of all rational numbers
80
A4 Extension to the set of all real numbers
82
Review Exercises
85
Basic Concepts of Logic and Formal Systems
89
52 Natural languages and formal languages
93
53 Syntax and semantics
94
54 About statement logic and predicate logic
95
Statement Logic
99
Truth values and truth tables
101
622 Conjunction
102
623 Disjunction
103
624 The Conditional
104
625 The Biconditional
105
63 Tautologies contradictions and contingencies
107
64 Logical equivalence logical consequence and laws
110
65 Natural deduction
115
651 Conditional Proof
120
652 Indirect Proof
122
66 Beth Tableaux
123
Exercises
130
Predicate Logic
137
72 Semantics
142
73 Quantifier laws and prenex normal form
148
74 Natural deduction
154
75 Beth Tableaux
165
77 Informal style in mathematical proofs
172
Exercises
175
Formal Systems Axiomatization and Model Theory
181
82 Axiomatic systems and derivations
185
821 Extended axiomatic systems
188
83 SemiThue systems
191
84 Peanos axioms and proof by induction
194
model theory
200
852 Consistency completeness and independence
202
853 Isomorphism
203
854 An elementary formal system
205
855 Axioms for ordering relations
207
856 Axioms for string concatenation
213
857 Models for Peanos axioms
215
858 Axiomatization of set theory
217
86 Axiomatizing logic
219
862 Consistency and independence proofs
222
863 An axiomatization of predicate logic
225
864 About completeness proofs
227
865 Decidability
229
866 Godels incompleteness theorems
230
867 Higherorder logic
231
Exercises
234
Alternative Notations and Connectives
239
Kleenes Threevalued Logic
241
Review Exercises
245
Basic Concepts of Algebra
249
92 Properties of operations
250
93 Special elements
251
94 Maps and morphisms
253
Exercises
255
Operational Structures
257
102 Subgroups semigroups and monoids
263
103 Integral domains
266
104 Morphisms
271
Exercises
273
Lattices
277
112 Lattices semilattices and sublattices
280
113 Morphisms in lattices
285
114 Filters and ideals
287
115 Complemented distributive and modular lattices
290
Exercises
295
Boolean and Heyting Algebras
297
122 Models of BA
300
123 Representation by sets
301
124 Heyting algebra
303
125 Kripke semantics
306
Exercises
309
Review Exercises
311
1325 Linguistic applications
351
Exercises
367
Generalized Quantifiers
373
142 Conditions on quantifiers
375
143 Properties of determiners and quantifiers
380
144 Determiners as relations
391
145 Context and quantification
395
Exercises
400
Intensionality
403
152 Forms of opacity
409
153 Indices and accessibility relations
414
154 Tense and time
423
155 Indexicality
427
Exercises
429
Basic Concepts
433
162 Grammars
437
163 Trees
439
1631 Dominance
440
1632 Precedence
441
1633 Labeling
443
164 Grammars and trees
446
165 The Chomsky Hierarchy
451
166 Languages and automata
453
Finite Automata Regular Languages and Type 3 Grammars
455
1711 State diagrams of finite automata
457
1712 Formal definition of deterministic finite automata
458
1713 Nondeterministic finite automata
460
1714 Formal definition of nondeterministic finite automata
462
172 Regular languages
464
1721 Pumping Theorem for fals
471
173 Type 3 grammars and finite automaton languages
473
1731 Properties of regular languages
477
1732 Inadequacy of rightlinear grammars for natural languages
480
Exercises
482
Pushdown Automata Context Free Grammars and Languages
487
182 Context free grammars and languages
492
183 Pumping Theorem for cfls
494
184 Closure properties of context free languages
497
185 Decidability questions for context free languages
499
186 Are natural languages context free?
503
Exercises
505
Turing Machines Recursively Enumerable Languages and Type 0 Grammars
507
1911 Formal definitions
510
192 Equivalent formulations of Turing machines
514
193 Unrestricted grammars and Turing machines
515
194 Churchs Hypothesis
517
195 Recursive versus recursively enumerable sets
519
196 The universal Turing machine
520
197 The Halting Problem for Turing machines
522
Exercises
525
Linear Bounded Automata Context Sensitive Languages and Type 1 Grammars
529
2011 Lbas and context sensitive grammars
530
202 Context sensitive languages and recursive sets
531
203 Closure and decision properties
533
Exercises
534
Languages Between Context Free and Context Sensitive
535
211 Indexed grammars
536
212 Tree adjoining grammars
542
213 Head grammars
548
214 Categorial grammars
550
Transformational Grammars
555
The Chomsky Hierarchy
561
Semantic Automata
565
Review Exercises
573
Solutions to selected exercises
575
CHAPTER 2
577
CHAPTER 3
578
CHAPTER 4
579
REVIEW PROBLEMS PART A
581
PART B
584
CHAPTER 7
589
CHAPTER 8
596
REVIEW PROBLEMS PART B
599
PART C
603
CHAPTER 10
604
CHAPTER 11
609
CHAPTER 12
610
REVIEW EXERCISES PART C
612
PART D
616
CHAPTER 14
618
CHAPTER 15
621
PART E
622
CHAPTER 18
628
CHAPTER 19
631
CHAPTER 20
632
APPENDIX E II
633
REVIEW PROBLEMS PART E
634
Bibliography
637
Index
643
Copyright

Common terms and phrases

Popular passages

Page ii - PAULINE JACOBSON, Brown University FRANCIS J. PELLETIER, University of Alberta Editorial Board JOHAN VAN BENTHEM, University of Amsterdam GREGORY N. CARLSON, University of Rochester DAVID DOWTY, Ohio State University, Columbus GERALD GAZDAR, University of Sussex, Brighton IRENE...
Page ii - Editorial Board: JOHAN VAN BENTHEM, University of Amsterdam GREGORY N. CARLSON, University of Rochester DAVID DOWTY, Ohio State University, Columbus GERALD GAZDAR, University of Sussex, Brighton IRENE HEIM, MIT, Cambridge EWAN KLEIN, University of Edinburgh BILL LADUSAW, University of California at Santa Cruz TERRENCE PARSONS, University of California, Irvine MATHEMATICAL METHODS IN LINGUISTICS BARBARA H.
Page 11 - C; that is, if every member of A is also a member of B, and...

References to this book

All Book Search results »

About the author (1990)

Paul Portner is Associate Professor of Linguistics and Acting Director of the Interdisciplinary Program in Cognitive Science at Georgetown University. He is the author of numerous articles on topics such as mood and modality, tense and aspect, and the syntax/semantics interface.

Barbara H. Partee is Distinguished University Professor of Linguistics and Philosophy at the University of Massachusetts, Amherst and is the author of several landmark essays in formal semantics. She has written and edited numerous books, including "Mathematical Methods in Linguistics "(with Alice ter Meulen and Robert Wall, 1990), "Montague Grammar "(edited, 1976), and "Quantification in Natural Languages "(edited, with Emmon Bach, Eloise Jelinek, and Angelika Kratzer, 1995).

Patricia Wall is a children's author and teacher with an interest in historical fiction for young readers. Her grandparents came to the state of Washington in the late 1890's and lived through some of the same experiences that are portrayed in the book. This is the first in a series of books about the logging industry in the Pacific Northwest; each book will be told through the eyes of a different family member. She is also the author of the YA title, Beautiful Baby. The book's illustrator is Robert Wall, husband of the author.