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Mathematical methods in linguistics

Mathematical methods in linguistics (Loan 36 times)

Material type
단행본
Personal Author
Partee, Barbara Hall. Wall, Robert Eugene. Meulen, Alice G. B. ter.
Title Statement
Mathematical methods in linguistics / by Barbara H. Partee, Alice ter Meulen, and Robert E. Wall.
Publication, Distribution, etc
Dordrecht ;   Boston :   Kluwer Academic ,   c1990.  
Physical Medium
xx, 663 p. : ill. ; 24 cm.
Series Statement
Studies in linguistics and philosophy ; v. 30
ISBN
9027722455 (pbk. : alk. paper) 9027722447 (alk. paper)
Bibliography, Etc. Note
Includes bibliographical references (p. 637-642) and index.
Subject Added Entry-Topical Term
Mathematical linguistics.
000 00918pamuuu200265 a 4500
001 000000018466
005 19941221105240.0
008 870422s1990 ne a b 00110 eng
010 ▼a 87009893
020 ▼a 9027722455 (pbk. : alk. paper)
020 ▼a 9027722447 (alk. paper)
035 ▼a 87009893
040 ▼a DLC ▼c DLC ▼d DLC
050 0 0 ▼a P138 ▼b .P37 1990
082 0 0 ▼a 410/.72 ▼2 19
090 ▼a 410.72 ▼b P273m
100 1 0 ▼a Partee, Barbara Hall.
245 1 0 ▼a Mathematical methods in linguistics / ▼c by Barbara H. Partee, Alice ter Meulen, and Robert E. Wall.
260 0 ▼a Dordrecht ; ▼a Boston : ▼b Kluwer Academic , ▼c c1990.
300 ▼a xx, 663 p. : ▼b ill. ; ▼c 24 cm.
440 0 0 ▼a Studies in linguistics and philosophy ; ▼v v. 30
504 ▼a Includes bibliographical references (p. 637-642) and index.
650 0 ▼a Mathematical linguistics.
700 1 0 ▼a Wall, Robert Eugene.
700 1 0 ▼a Meulen, Alice G. B. ter.

Holdings Information

No. Location Call Number Accession No. Availability Due Date Make a Reservation Service
No. 1 Location Main Library/Western Books/ Call Number 410.72 P273m Accession No. 111016848 Availability Available Due Date Make a Reservation Service B M
No. 2 Location Main Library/Western Books/ Call Number 410.72 P273m Accession No. 111319801 Availability Available Due Date Make a Reservation Service B M
No. 3 Location Main Library/Western Books/ Call Number 410.72 P273m Accession No. 111529802 Availability Available Due Date Make a Reservation Service B M

Contents information

Table of Contents


CONTENTS
LIST OF SYMBOLS = xiii
PREFACE = xvii
PART A: SET THEORY
 CHAPTER 1. BASIC CONCEPTS OF SET THEORY = 3
  1.1. The concept of a set = 3
  1.2. Specification of sets = 4
  1.3. Set-theoretic identity and cardinality = 8
  1.4. Subsets = 9
  1.5. Power sets = 11
  1.6. Union and intersection = 11
  1.7. Difference and complement = 14
  1.8. Set-theoreticequalities = 17
   Exercises = 23
 CHAPTER 2: RELATIONS AND FUNCTIONS = 27
  2.1. Ordered pairs and Cartesian products = 27
  2.2. Relations = 28
  2.3. Functions = 30
  2.4. Composition = 33
   Exercises = 36
 CHAPTER 3: PROPERTIES OF RELATIONS = 39
  3.1. Reflexivity, symmetry, transitivity, and connectedness = 39
  3.2. Diagrams of relations = 43
  3.3. Properties of inverses and complements = 44
  3.4, Equivalence relations and partitions = 45
  3.5. Orderings = 47
   Exercises = 51
 CHAPTER 4: INFINITIES = 55
  4.1. Equivalent sets and cardinality = 55
  4.2. Denumerability of sets = 58
  4.3. Nondenumerable sets = 62
  4.4 Infinite vs. unbounded = 69
   Exercises = 71
 APPENDIX A: SET-THEORETIC RECONSTRUCTION OF NUMBER SYSTEMS = 75
  A.1 The natural numbers = 75
  A.2. Extension to the set of all integers = 78
  A.3. Extension to the set of all rational numbers = 80
  A.4. Extension to the set of all real numbers = 82
 REVIEW EXERCISES = 85
PART B: LOGIC AND FORMAL SYSTEMS
 CHAPTER 5: BASIC CONCEPTS OF LOGIC AND FORMAL SYSTEMS = 87
  5.1. Formal systems and models = 89
  5.2. Natural languages and formal languages = 93
  5.3. Syntax and semantics = 94
  5.4, About statement logic and predicate logic = 95
 CHAPTER 6: STATEMENT LOGIC = 99
  6.1. Syntax = 99
  6.2. Semantics: Truth values and truth tables = 101
   6.2.1. Negation = 101
   6.2.2. Conjunction = 102
   6.2.3. Disjunction = 103
   6.2.4 The Conditional = 104
   6.2.5 The Biconditional = 105
  6.3. Tautologies, contradictions and contingencies = 107
  6.4. Logical equivalence, logical consequence and laws = 110
  6.5. Natural deduction = 115
   6.5.1. Conditional Proof = 120
   6.5.2. Indirect Proof = 122
  6.6. Beth Tableaux = 123
   Exercises = 130
 CHAPTER 7: PREDICATE LOGIC = 137
  7.1. Syntax = 137
  7.2. Semantics = 142
  7.3. Quantifier laws and prenex normal form = 148
  7.4. Natural deduction = 154
  7.5. Beth Tableaux = 165
  7.6. Formal and informal proofs = 170
  7.7. Informal style in mathematical proofs = 172
   Exercises = 175
 CHAPTER 8: FORMAL SYSTEMS, AXIOMATIZATION, AND MODEL THEORY = 181
  8.1. The syntactic side of formal systems = 181
   8.1.1. Recursive definitions = 181
  8.2. Axiomatic systems and derivations = 185
   8.2.1. Extended axiomatic systems = 188
  8.3. Semi-Thue systems = 191
  8.4. Peano's axioms and proof by induction = 194
  8.5. The semantic side of formal systems: model theory = 200
   8.5.1. Theories and models = 200
   8.5.2. Consistency, completeness, and independence = 202
   8.5.3. Isomorphism = 203
   8.5.4. An elementary formal system = 205
   8.5.5. Axioms for ordering relations = 207
   8.5.6. Axioms for string concatenation = 213
   8.5.7. Models for Peano's axioms = 215
   8.5.8. Axiomatization of set theory = 217
  8.6. Axiomatizing logic = 219
   8.6.1. An axiomatization of statement logic = 219
   8.6.2. Consistency and independence proofs = 222
   8.6.3. An axiomatization of predicate logic = 225
   8.6.4. About completeness proofs = 227
   8.6.5. Decidability = 229
   8.6.6. G$$\ddot o$$del's incompleteness theorems = 230
   8.6.7. Higher-order logic = 231
   Exercises = 234
 APPENDIX B-Ⅰ: ALTERNATIVE NOTATIONS AND CONNECTIVES = 239
 APPENDIX B-Ⅱ: KLEENE'S THREE-VALUED LOGIC = 241
 REVIEW EXERCISES = 245
PART C: ALGEBRA
 CHAPTER 9: BASIC CONCEPTS OF ALGEBRA = 249
  9.1. Definition of algebra = 249
  9.2. Properties of operations = 250
  9.3. Special elements = 251
  9.4. Maps and morphisms = 253
   Exercises = 255
 CHAPTER 10: OPERATIONAL STRUCTURES = 257
  10.1. Groups = 257
  10.2. Subgroups, semigroups and monoids = 263
  10.3. Integral domains = 266
  10.4. Morphisms = 271
   Exercises = 273
 CHAPTER 11: LATTICES = 277
  11.1. Posets, duality and diagrams = 277
  11.2. Lattices, semilattices and sublattices = 280
  11.3. Morphisms in lattices = 285
  11.4. Filters and ideals = 287
  11.5. Complemented, distributive and modular lattices = 290
   Exercises = 295
 CHAPTER 12: BOOLEAN AND HEYTING ALGEBRAS = 297
  12.1. Boolean algebras = 297
  12.2. Models of BA = 300
  12.3. Representation by sets = 301
  12.4. Heyting algebra = 303
  12.5. Kripke semantics = 306
   Exercises = 309
 REVIEW EXERCISES = 311
PART D: ENGLISH AS A FORMAL LANGUAGE
 CHAPTER 13: BASIC CONCEPTS = 317
  13.1. Compositionality = 317
   13.1.1. A compositional account of statement logic = 319
   13.1.2. A compositional account of predicate logic = 323
   13.1.3. Natural language and compositionality = 333
  13.2. Lambada-abstraction = 338
   13.2.1. Type theory = 338
   13.2.2. The syntax and semantics of λ-abstraction = 341
   13.2.3. A sample fragment = 343
   13.2.4. The lambda-calculus = 348
   13.2.5. Linguistic applications = 351
   Exercises = 367
 CHAPTER. 14: GENERALIZED QUANTIFIERS = 373
  14.1. Determiners and quantifiers = 373
  14.2 Conditions and quantifiers = 375
  14.3. Properties of determiners and quantifiers = 380
  14.4. Determiners as relations = 391
  14.5. Context and quantification = 395
   Exercises = 400
 CHAPTER 15: INTENSIONALITY = 403
  15.1. Frege's two problems = 403
  15.2. Forms of opacity = 409
  15.3. Indices and accessibility relations = 414
  15.4. Tense and time = 423
  15.5. Indexicality = 427
   Exercises = 429
PART E: LANGUAGES, GRAMMARS, AND AUTOMATA
 CHAPTER 16: BASIC CONCEPTS = 433
  16.1. Languages, grammars and automata = 433
  16.2. Grammars = 437
  16.3. Trees = 439
   16.3.1. Dominance = 440
   16.3.2. Precedence = 441
   16.3.3. Labeling = 443
  16.4. Grammars and trees = 446
  16.5. The Chomsky Hierarchy = 451
  16.6. Languages and automata = 453
 CHAPTER 17: FINITE AUTOMATA, REGULAR LANGUAGES AND TYPE 3 GRAMMARS = 455
  17.1. Finite automata = 455
   17.1.1. State diagrams of finite automata = 457
   17.1.2. Formal definition of deterministic finite automata = 458
   17.1.3. Non-deterministic finite automata = 460
   17.1.4. Formal definition of non-deterministic finite automata = 462
   17.1.5. Equivalence of deterministic and non-deterministic finite automata = 462
  17.2. Regular languages = 464
   17.2.1. Pumping Theorem for fal's = 471
  17.3. Type 3 grammars and finite automaton languages = 473
   17.3.1. Properties of regular languages = 477
   17.3.2. Inadequacy of right-linear grammars for natural languages = 480
   Exercises = 482
 CHAPTER 18: PUSHDOWN AUTOMATA, CONTEXT FREE GRAMMARS AND LANGUAGES = 487
  18.1. Pushdown automata = 487
  18.2. Context free grammars and languages = 492
  18.3. Pumping Theorem for cfl's = 494
  18.4. Closure properties of context free languages = 497
  18.5. Decidability questions for context free languages = 499
  18.6. Are natural languages context free? = 503
   Exercises = 505
 CHAPTER 19: TURING MACHINES, RECURSIVELY ENUMERABLE LANGUAGES AND TYPE 0 GRAMMARS = 507
  19.1. Turing machines = 507
   19.1.1. Formal definitions = 510
  19.2 Equivalent formulations of Turing machines = 514
  19.3. Unrestricted grammars and Turing machines = 515
  19.4. Church's Hypothesis = 517
  19.5. Recursive versus recursively enumerable sets = 519
  19.6. The universal Turning machine = 520
  19.7. The Halting Problem for Turing machines = 522
   Exercises = 525
 CHAPTER 20: LINEAR BOUNDED  AUTOMATA, CONTEXT SENSITIVE LANGUAGES  AND TYPE 1 GRAMMARS  = 529
  20.1. Linear bounded automata = 529
   20.1.1. Lba's and context sensitive grammars = 530
  20.2. Context sensitive languages and recursive sets = 531
  20.3. Closure and decision properties = 533
   Exercises = 534
 CHAPTER 21: LANGUAGES BETWEEN CONTEXT FREE AND CONTEXT SENSITIVE = 535
  21.1. Indexed grammars = 536
  21.2. Tree adjoining grammars = 542
  21.3. Head grammars = 549
  21.4. Categorial grammars = 550
 CHAPTER 22: TRANSFORMATIONAL GRAMMARS = 555
 APPENDIX E-Ⅰ: THE CHOMSKY HIERARCHY = 561
 APPENDIX E-Ⅱ: SEMANTIC AUTOMATA = 565
 REVIEW EXERCISES = 573
 SOLUTIONS TO SELECTED EXERCISES = 575
  Part A Chapter 1 = 575
   Chapter 2 = 577
   Chapter 3 = 578
   Chapter 4 = 579
  Review Problems, Part A = 581
  Part B. Chapter 6 = 584
   Chapter 7 = 589
   Chapter 8 = 596
  Review Problems, Part B = 599
  Part C Chapter 9 = 603
   Chapter 10 = 604
   Chapter 11 = 609
   Chapter 12 = 610
  Review Exercises, Part C = 612
  Part D. Chapter 13 = 616
   Chapter 14 = 618
   Chapter 15 = 621
  Part E. Chapter 17 = 622
   Chapter 18 = 628
   Chapter 19 = 631
   Chapter 20 = 632
  Appendix E-Ⅱ = 633
  Review Problems, Part E = 634
BIBLIOGRAPHY = 637
INDEX = 643


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