HOME > 상세정보

상세정보

Mathematical methods in linguistics

Mathematical methods in linguistics

자료유형
단행본
개인저자
Partee, Barbara Hall. Wall, Robert Eugene. Meulen, Alice G. B. ter.
서명 / 저자사항
Mathematical methods in linguistics / by Barbara H. Partee, Alice ter Meulen, and Robert E. Wall.
발행사항
Dordrecht ;   Boston :   Kluwer Academic ,   c1990.  
형태사항
xx, 663 p. : ill. ; 24 cm.
총서사항
Studies in linguistics and philosophy ; v. 30
ISBN
9027722455 (pbk. : alk. paper) 9027722447 (alk. paper)
서지주기
Includes bibliographical references (p. 637-642) and index.
일반주제명
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.

소장정보

No. 소장처 청구기호 등록번호 도서상태 반납예정일 예약 서비스
No. 1 소장처 중앙도서관/서고6층/ 청구기호 410.72 P273m 등록번호 111016848 도서상태 대출가능 반납예정일 예약 서비스 B M
No. 2 소장처 중앙도서관/서고6층/ 청구기호 410.72 P273m 등록번호 111319801 도서상태 대출가능 반납예정일 예약 서비스 B M
No. 3 소장처 중앙도서관/서고6층/ 청구기호 410.72 P273m 등록번호 111529802 도서상태 대출가능 반납예정일 예약 서비스 B M

컨텐츠정보

저자소개

Barbara H. Partee(지은이)

Robert E. Wall(지은이)

Alice Ter Meulen(지은이)

정보제공 : Aladin

목차


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


관련분야 신착자료