Mathematical methods in linguistics:
Gespeichert in:
| Beteiligte Personen: | , , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Dordrecht [u.a.[
Kluwer Acad. Press
1990
|
| Ausgabe: | Student ed. |
| Schriftenreihe: | Studies in linguistics and philosophy
30 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003306458&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XX, 663 S. |
| ISBN: | 9027722455 9027722447 |
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Datensatz im Suchindex
| _version_ | 1819294251742134272 |
|---|---|
| adam_text | IMAGE 1
TABLE OF CONTENTS
LIST OF SYMBOLS PREFACE
PART A: SET THEORY
IMAGE 2
APPENDIX A: SET-THEORETIC RECONSTRUCTION OF NUMBER SYSTEMS 75
A.I. 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
IMAGE 3
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. GODEL 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
IMAGE 4
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 ^-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
IMAGE 5
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 4 55
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 5 07
19.1. TURING MACHINES 507
19.1.1. FORMAL DEFINITIONS 510
IMAGE 6
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 TURING 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 548
21.4. CATEGORIAL GRAMMARS 550
CHAPTER 22: TRANSFORMATIONAL GRAMMARS 555
APPENDIX E-1: THE CHOMSKY HIERARCHY 561
APPENDIX E-II: SEMANTIC AUTOMATA 565
REVIEW EXERCISES 573
SOLUTIONS TO SELECTED EXERCISES 5 75
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
IMAGE 7
P A R T 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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| author | Partee, Barbara H. 1940- Meulen, Alice G. ter Wall, Robert E. |
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| id | DE-604.BV005295354 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T08:31:15Z |
| institution | BVB |
| isbn | 9027722455 9027722447 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003306458 |
| oclc_num | 611614294 |
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| owner_facet | DE-473 DE-BY-UBG DE-739 DE-355 DE-BY-UBR DE-29T DE-29 DE-19 DE-BY-UBM |
| physical | XX, 663 S. |
| publishDate | 1990 |
| publishDateSearch | 1990 |
| publishDateSort | 1990 |
| publisher | Kluwer Acad. Press |
| record_format | marc |
| series | Studies in linguistics and philosophy |
| series2 | Studies in linguistics and philosophy Pallas paperbacks |
| spellingShingle | Partee, Barbara H. 1940- Meulen, Alice G. ter Wall, Robert E. Mathematical methods in linguistics Studies in linguistics and philosophy Linguistik (DE-588)4074250-7 gnd Mathematische Methode (DE-588)4155620-3 gnd Mathematische Linguistik (DE-588)4037950-4 gnd |
| subject_GND | (DE-588)4074250-7 (DE-588)4155620-3 (DE-588)4037950-4 |
| title | Mathematical methods in linguistics |
| title_auth | Mathematical methods in linguistics |
| title_exact_search | Mathematical methods in linguistics |
| title_full | Mathematical methods in linguistics by Barbara H. Partee, Alice ter Meulen, Robert E. Wall |
| title_fullStr | Mathematical methods in linguistics by Barbara H. Partee, Alice ter Meulen, Robert E. Wall |
| title_full_unstemmed | Mathematical methods in linguistics by Barbara H. Partee, Alice ter Meulen, Robert E. Wall |
| title_short | Mathematical methods in linguistics |
| title_sort | mathematical methods in linguistics |
| topic | Linguistik (DE-588)4074250-7 gnd Mathematische Methode (DE-588)4155620-3 gnd Mathematische Linguistik (DE-588)4037950-4 gnd |
| topic_facet | Linguistik Mathematische Methode Mathematische Linguistik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003306458&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000018169 |
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