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Partee B.H., Meulen A.T., Wall R.E. — Mathematical Methods in Linguistics
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Название: Mathematical Methods in LinguisticsАвторы: Partee B.H., Meulen A.T., Wall R.E.Аннотация: 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.
Язык: Рубрика: Филология /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1990Количество страниц: 663Добавлена в каталог: 09.12.2005Операции: Положить на полку |
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Subset 9—11 24 28—31 45 46 51 53 57—58 63 65 66 68 69 72 80 123 143 157 171 173 182 185 209 212 219 231 264 265 268 273 283 287 288 299 301 306 338 374 378 381 433 435 462 481 491 503 505 536 562 565 581 582 583 606 Subset of domain 32 Subset of set 10 Subset, definition of 10 17 20 Subset, proper 10 Subset, relation 28 48 85 452 Subset, symbol 10 Substitutability 418 Substitution 115 116 124 196 220 221 224 225 404 405 421 555 Substitution, rule of 114 120 Substring 435 437 449 546 574 Subsystem of rationals 80 Subsystem, isomorphic to the old system 78 Subtraction 77 78 80 81 Subtree 447 544 558 Successor 49 76—78 195 196 217 232 234 237 279 348 350 598 Suffix 435 SUM 36 Suppes, P. 213 Surface structure 555 556 Surjective 253 Syllogism 118 120—122 Syllogism, disjunctive 173 Syllogism, hypothetical 156 163 165 172 Symbol 437—439 446 448 451 455—457 459 461 471 474 476 487 488 490 492 493 497 507 515 517 531 532 536 541 543 544 547 548 551 553 556 557 571 573 580 629 Symbol, auxiliary 6 Symbol, connective 126 Symbol, manipulation 95 Symbol, negation 100 Symbol, subset 10 symmetric 45 Symmetric difference 25 Symmetric relation 43 44 46 47 85 Symmetries, properties of 44 Symmetry 39 40 42 43 52 255 263 266 272 274 275 313 391 394 396 398 400 424 444 459 578 579 588 603 606 608 612 614 615 621 Syntactic component 95 Syntactic component, statement 101 Syntactic constituent 114 Syntactic rule 318 319 Syntactic statement 115 Syntactic structure 101 Syntax 92 95 99 137 140 181 200 232 254 281 300 307 317—320 322—325 328 330 331 333—335 337 338 340—345 349—360 362 364 367 369—373 375 383 389 390 410 414 415 423 425 439 443 535 550 555 Syntax and semantics 94 Syntax, generative 94 system 188—194 202—207 210—212 227 232 235 304 312 318 333 350 357 360 404 414 System of logic 92 System, axiomatic vi 187 System, basic concept of logic and formal 89 System, coordinate 31 System, formal vii 91 92 94 181 System, linearly ordered 86 System, Newtonian 90 91 System, partially ordered 86 System, theorems of the 93 System, well-ordered 86 table 368 Table, truth 101—106 108 110 111 113—116 118 119 125—127 131 229 240 241 250 Tableau 166—168 170 588 589 Tableau, Beth 123—129 135 165 Tableau, semantic 124 130 Takahashi, M. 542 Tarski, A. 305 Tautologies, contradictions and contingencies 106 Tautologous conditional 111 Tautology 107 107 110 111 113 115 116 123 132 143 144 162 220 223 229 236 242 301 388 405 420—422 584 Temporal connotation 102 Temporal order 306 Tense 423 426 427 Ter Meulen, A. v vii 389 390 Term 137 138 142 144 160 324 Terminal alphabet 437 Terminal symbol 438 447 451 Ternary function 36 Ternary relation 30 36 Theorem 94 185 186 189—191 193 195 198 200 218—220 226 229 230 234 236 260—264 267 269 270 276 289 295 299 302 308 311 313 350 351 385 387 388 392—394 437 444 466 471—473 480 496 497 499 502 505 523 524 545 572 608—610 620 Theorem, Cantor's 62 64 73 Theorem, provers 123 Theory 212 215 217 218 228 233 250 251 254 263 274 277 279—281 283 285 295 299 300 306 333 334 338 339 348 351 353 374 375 381 384 385 387 388 390 392 395 400 404 414 415 417 433 434 437 477 502 518 555 557 558 606 Theory of automata 565 Theory of functions 349 Theory of generalized quantifiers 380 Theory of meaning 403 429 Theory, model 92 94 95 181 194 200 201 203 205 208 Theory, number 16 Theory, set 3 6—8 30 80 82 85 93 148 171 208 Theory, type 7 8 Thomason, R. 202 Thue, A. 191—193 236 596 Time 423 Times, New York 65 Top and bottom 298 301 Total order 51 53 Transformation 31 Transformational cycle 555 Transformational grammar vi 555—558 Transformational language 556 558 Transformational rule 555 557 558 Transition 467 468 475 476 478 479 483 487 491 530 624 625 Transition, function 458 459 Transition, relation 462 Transitive 45 272 277 Transitive relation 41 43 46—49 85 Transitive verb 28 138 Transitivity 39 41—43 52 208—210 212 269 275 279 282 305 362 391 393 394 401 424 442 444 459 460 492 511 578—581 588 606 608 609 612 615 620 621 Transitivity, properties 44 Transitivity, relation 207 Translation 96 Translation machine vi TREE 345 359 362 367—370 379 380 400 439 442—450 474 494—497 501 502 515 537—540 542—544 546 547 550 552 555 556 567 570 Tree of numbers 567 Tree structure 556 Tree, adjoining grammar 542—544 546—548 553 Tree, adjoining language vi 545—548 Tree, diagram 439—442 581 Triple 458 459 462 Triple, ordered 27 30 62 Trivial element 262 Trivial partition 46 Truth 94 Truth table 101—108 110—119 125—127 131 229 240 241 250 254 368 Truth value 101 102 104—111 113—115 120 125 131 132 142 144 146 151 165 243 250 320 322 330 335 340 356 368 374 377 405 414 419 421 428 429 584 588 Truth-functional property 101 Turing machine 507—532 556 574 632 Turing machine, theory 502 Turing, A.M. 350 502 507—532 556 574 632 Turing, acceptability 514 520 523 Turing, acceptable language 513 519 522 562 Turing, computability 350 Turing, decidability 520 523 525 Turing, decidable language 513 519 522 Turnstile 459 460 Two-sided identity 255 Two-sided inverse 252 253 Two-sided zero 253 TYPE 340 343—347 351 356 359 362 364 370 374 381 Type 0 grammar 507 515—517 527 531 532 556 Type 1 grammar 529 556 Type 2 grammar 492 Type 3 grammar 455 473 475—477 486 Type free character 351 Type grammar 451 Type language 532 Type raising 552 Type theory 7 8 234 338 339 Ullman, J. 463 466 492 530 531 533 536 Ultrafilter 288 299 301 Ultrafilter theorem 299 Unary operator 100 Unbounded function, infinite vs 69 70 Uncountable set 69 Undecidability 502 union 19 26 218 219 255 300 302 308 314 466 471 485 498 506 526 533 547 576 603 Union and intersection 11 Union, definition of 17 19 20 Union, set-theoretic 12 13 Unique real number 69 Unique string 58 Unique value 32 36 56 458 Uniqueness 250 Universal 383 385 Universal base hypothesis 558 Universal condition 398 Universal determiner 397 Universal generalization 154—156 158 160—164 171—174 593 595 603 Universal instantiation 154—156 158 159 161—166 171 172 174 183 184 196 197 Universal negation 384 Universal quantifier 138 149 150 153 208 397 Universal set 19 21 Universal Turing machine 521 Universe of discourse 16 25 145 147 149 155 157 166 168 169 176 594 Universe, set-theoretic 17 Unordered set 28 Unquantified variable 139 Unrestricted grammar 515 Upper bound 71 558 Vacuous quantification 140 141 Valid argument 115—117 Valuation 307—309 Value 31 70 139 143—146 151 155 165 319—323 327 330 333 335 340—342 356 364 368 370 374 376 377 404 405 414 415 419 421 427 429 458 518 526 529 551 584 588 596 613 629 Value of function 34 Value, truth 101 102 104 106—115 120 125 131 132 243 250 Value, unique 32 36 56 Van Benthem, I. 374 378 379 383 390 391 393 394 413 424 553 565 572 van Eijck, J. 382 Variable 6 138—140 144 148 150 154 157 163 165 171 175 177 187 188 192 212 220 223 224 226 228 229 231 234 308 323 324 326 415 416 425 529 591 Variable, alphabetic 150—153 Variable, convention 345 Variation 379 380 388 392 394 400 620 Variety 393 618 Venn diagram 5 12—15 17 19 20 25 400 606 Verb 231 Verb, phrase 102 424 439—441 Verb, transitive 28 Verkuyl, H. 398 Vet, C. 425 Vijay-Shankar, K. 547 548 Vocabulary 433 435 473 486 525 VP deletion 360—362 Waismann, F. 216 Wall, R. 320 334 352 415 Wave theory, mathematics of vi Weak linear order 211 Weak non-cardinal 389 Weak order 47—49 51 210 Weak partial order 53 208 209 211 212 443 Weak quantity 378 Weir, D. 548 553 Weisler, S. vii Well-formed formula 99—102 114 121 122 183—185 188 190 191 225 235 236 318 320—322 Well-formedness rules 94 Well-ordered set 51 211 Well-ordered system 86 Well-ordering Axiom 269 Westerstahl, D 377 378 390 395 396 398 Wheeler, D. 553 Whitehead, A.N. 220 224 Williams, E. 352 Witness set 399 Word, quantifier 97 Wrapping 548 Yield 447 448 494 495 545 546 Zadeh, L. 6 Zaenen, A. vii Zermelo — Fraenkel axiom 217 218 Zermelo, axiomatization 219 Zermelo, E. 217—219 348 Zero 79 80 86 253 ZFC 219 231 Zorn's lemma 299 Zwarts, F. 391 393 394 Zwicky, A. vii
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