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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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Definition of complement 19 Definition of composition 34 Definition of convergence 82 Definition of intersection 17 19 20 Definition of inverse 174 175 Definition of subset 10 17 20 Definition of union 17 19 20 Definition, recursive 181—186 188 194 196 Deletion 360—362 555 556—558 597 598 Demonstrative 390 DeMorgan's laws 18 20—22 112 136 149 154 173 200 421 499 576 577 592 595 600—602 DeMorgan, A. 18 20—22 112 136 149 154 173 200 294 296 421 576 577 592 595 600—602 DeMorgan, identity 294 296 Denotation 348 Dense relation 51 Denumerability of set 58 59 Denumerably infinite set 59 60 71 Deontic logic 413 Dependence 395 546 Dependence, law of quantifier 150 Dependency 398 481 503 538 541 Derivation 119 185—189 190 192 193 225 227 318 322 327 328 331 337 345 359 362 365 437 438 449 474—477 493 494 496 497 500 501 516 517 530 531 532 536 546 549 558 599 629 Derivation, schema 114 Derivation, tree 367—370 370 537—539 540 542 552 Descartes, R. (Cartesian) 27—30 60 62 464 Designator 419 421 429 Determiner 95 373 374—401 439 440 449 565 567 571 572 Determinism 490 506 508 512 515 530 533 625 Deterministic finite automaton 457—463 477 Deterministic finite language 562 Deterministic pushdown automaton language 562 563 Diagonal argument 65 Diagram 278—280 441 442 457 459 461 476 479 482 484 581 606 Diagram of relation 43 440 Diagram, Venn 5 12—15 17 19 20 25 Difference and complement of arbitrary set 14—16 Difference and complement of arbitrary set, symmetric 25 Discontinuous connective 104 Discourse, domain of 16 142 147 149 158 Discourse, Universe of 16 25 145 147 149 155 157 166 168 169 176 Discrete entities v Discrete mathematics v 82 Disjoint set 73 Disjunction 99 103 107 126—129 149 220 223 227 240 251 308 350 352 354 382 413 Disjunction, inclusive 12 Disjunctive syllogism 118 120—122 173 586 587 593 599—601 Distinct element 42 262 Distinct pair of integers 43 Distinct set 9 Distribution, complementary 52 Distribution, laws of quantifier 149 Distributive 251 309 390 576 577 Distributive lattice 297 302 305 308 Distributive laws 18 19 21 22 25 112 198 199 266 275 290 296 297 421 Distributivity 585 586 607 608 611 Division 31 80 81 Domain 29 30 34 36 45 168 169 170 200 208 212 219 230—232 242 266—272 275—277 286 312 313 325 331 340 346 347 351 360 373 374—379 383 387 390 392 394 395 398—400 415 419 421 423 426 443 514 549 555 Domain of discourse 16 142 147 149 158 Domain of function 31 Domain, subset of 32 Dominance relation 440—445 Double indexing interpretation 428 Double Negation 614 620 Double negation, law of 148 154 Dowty, D. vii 320 334 352 362 364 365 415 425 Dual 384 385 Dual atom 298 Duality 277 278 280 282 283 385 401 Effective enumeration 230 Effectively listing 62 Element 49 51 62 63 67 78 80 86 168 169 203—205 207 212 215 219 232 249 251—253 255 257 258 261—269 274 276—280 283 288—290 292 295 297 298 300 302 303—306 309 311 328 329 366 377 380 390 391 398 399 434 441 446 538 546 578 582 583 603—607 611 612 Element of set 3 Element, distinct 42 Element, finite 76 Element, first and second 29 Element, greatest 50 51 53 Element, least 50 51 53 Element, maximal 50 51 53 Element, minimal 50 51 53 Elementary statement 137 Emptiness 501 Emptiness, question 479 Empty list notation 9 Empty set 4 9 75 218 237 Empty set, axiom 218 Empty string 58 214 215 434 Enderton, H. 231 Entity 346 347 374 380 398 415 419 620 Enumeration 230 Epistemology 409—414 418 Equal relation 76 Equal set 55 Equality 79 81 Equality, set-theoretic 17 18 25 26 equation 34 EQUIVALENCE 118 148 177 313 332 337 342 350 353 367 376 377 392 394 401 417 418 420 421—423 462 463 477 490 492 514 516 530 578 579 585 588 590 591 613—615 Equivalence, class 45—47 56 58 59 135 209 302 306 311 Equivalence, logical 111 113 120 121 172 Equivalence, logical, consequence and laws 110 Equivalence, relation 46 47 52 56 71 79 135 205 272 301 311 Equivalence, relation and partitions 45 Equivalent infinite set 58 Equivalent set 56 57 62 Equivalent set and cardinality 55 Equivalent statement 120 123 132 Etchemendy, J. vii Euclid 89—91 195 200 216 394 Euclidean axiom 90 91 200 Euclidean axiomatization 195 Euclideanness 391 392 Evaluation 331 416—419 423 Even integers, positive 56 Exclusive disjunction 103 Exclusivity condition 442—444 exercises 23 36 51 71 85 130 175 234 255 273 295 309 367 400 429 482 505 525 534 572 Existential generalization 154 157 159 161 162 164 419 592 Existential instantiation 154 157 159 162—165 592 Existential quantifier 138 141 149 150 225 Existentiality 407 408 416 421 424 426 Expression 21 348 352 466 485 513 573 Extended axiomatic system 188—193 Extension 377 379 380 383 385 392 394 395—398 414 415 417—419 421—424 426 428 618 620 621 Extension to the set of all integers 78 Extension to the set of all rational numbers 80 Extension to the set of all real numbers 82 Extension, axiom of 171 Extensional equivalence 417 Extensionality 218 413 Factorization 497 Fallacy 117 False conditional 146 Faltz, L. 354 379 390 Filter 287—289 298 299 301 305—308 389 390 398 399 620 Filtering effect 555 557 Final state 455 457 458 469 475 476 479 488 625 Finite alphabet 66 71 Finite automaton 455—457 460—462 464 467 469 473 475—480 483 486 487 490 507 508 Finite automaton, language 464 466—468 470—472 476 477 479 481 494 497 498 Finite cardinals 63 Finite element 76 Finite linearly ordered set 51 Finite numbers 72 Finite power 73 Finite set 6 9 56 58 70 86 212 266 458 Finite set, class of 59 Finite state 485 Finite string 66 71 86 First and second coordinates, projection onto 28 First and second elements 29 First and second members 42 44 First coordinate 30 First coordinate, projection onto 29 First member 27 First order definability 374 First order definability, logic 93 First order definability, predicate calculus 95 First quantifier law 148 Form, argument 97 Form, prenex normal 151 Form, quantifier laws and prenex normal 148 Formal and informal proofs 170 Formal definition 545 Formal grammar 433 435 438 449 473 481 565 Formal language vi 95 115 155 250 277 306 317 318 322—343 374 385 425 437 481 503 513 561—563 Formal language, natural languages and 93 Formal logic v 96 Formal proof 173 180 Formal semantics 95 Formal system vii 91 92 94 181 202 205 210 212 220 277 304 333 Formal system, basic concept of logic and 89 Formal theory 348 Formalization v vii 89 91 92 Formula 140—142 144 145 148 150—154 156 160 166 167 169 176 177 183—185 188 190 191 208 225 228 235 236 246 308 309 318 320—332 336—338 342 350 353 369 373 414 415 417 429 596 Formula, well-formed 99 100—102 114 121 122 FORTRAN 93 found 440 442 Foundation 348 Fraenkel, A. 217—219 348 Frame 306—308 Frege, G. 317 318 323 333 382 403—405 408 414 415 428 Frege, principle of 317 333 Frequency count vi Friedman, B. 553 Function 30—32 36 37 55 138 142 144 145 163 196 219 231—234 241 249 253 271 307 312 318 326 329 331 335 336 339—343 346 348 349 351 352 355 356 362—364 368 374 388 414 415 417 421 422 424 426 428 434 443 444 454 458 459 462 510 513 514 518 520 526 529—531 551 578 579 584 Function, bounded 70 Function, composition 33 251 552 Function, graph of 31 Function, identity 34 35 Function, infinite vs unbounded 70 Function, into 32 34 Function, inverse of 33 Function, many to one 32 Function, mapping 62 Function, negative 59 Function, one to one 32 34 56 62 Function, onto 32 34 Function, partial 31 32 Function, positive 59 Function, quaternary 36 Function, range of 32 34 Function, relation and 27 Function, ternary 36 Function, value of 34 Fuzzy set 6 Gaifman, C. 552 Gallin, D 350 Gamut 320 Gazdar, G. 354 358 503 536 541 542 547 Geach rule 552 Geach, P.T. 552 Generalization 154—164 171—174 358 407 408 419 421 426 Generalized quantifier vi 358—360 373 374 376 377 387 390 391 395 565 Generalized theory 375 385 Generative grammar 94 Generative sytax 94 Generative transformational theory 433 Generator 454 Ginsburg, S. 555 Glottochronology vi Goedel, incompleteness proof 234 Goedel, incompleteness theorem 230 Goedel, K. 219 227 230 231 234 Goldblatt, R. 250 254 Gradual membership 6 Graetzer, G. 250 303 Grammar 227 234 337 353 363 364 415 433 435 437—439 446—455 473—477 481 482 486 492—494 496—498 500—502 505 515—517 525 527 529—532 534 536—539 542 546 547—550 552 553 555 556 559 565 573 629 632 Grammar, generative 94 Grammar, Montague 7 Grammar, transformational vi Grammatical constituent 138 Graph of function 31 Greatest element 50 51 53 Grelling's paradox 26 Groenendijk, J. 358 Group 257 261—263 266 271—274 311 312 314 434 506 580 606 612 614 Group operation 258 Group theory 263 281 Halfway membership 6 Halting problem 512 513 522—524 Halvorsen, P. 334 Hao Wang 205 Hasse diagram 279 Hayashi, T. 542 Head grammar 548 549 Head language 548 Heim, I. 389 Henkin, L. 227 228 350 Heterological adjective 26 Heuristics 123 Heyting, A. v 215 297 303 305 308 309 414 415 612 Heyting, algebra v 215 297 303 308 Heyting, lattice 612 Hierarchical categorization 503 Hierarchy 436 452 453 535 561 Hierarchy, Chomsky 451 Higginbotham, J. 411 Higher logic 231 234 Higher order analysis 374 Higher quantifier 571 572 Higher system 232 Hilbert, D. 94 220 223 224 Hilbert, program 94 Hoeksema, J. 390 Hofstadter, D. 231 Homomorphism 253 254 271 274 286—289 295 299 302 313 314 334—337 605 606 Hopcroft, D. 463 466 492 530 531 533 536 Hughes, G. 413 Hukari, T. vii Hypothesis 517 531 558 Hypothesis, continuum 65 66 Hypothetical syllogism 118 156 163 165 172 593 Ideal 287—289 298 Idempotence 309 Idempotent 21 251 274 284 293 577 Idempotent law 18 22 112 281 607 609 610 Identity 262 266 269 273 311 403—405 421 428 429 475 576 577 479 585 603 604 606 607 612 Identity and cardinality, set-theoretic 8 Identity element 215 252 257 258 261 263—265 274 434 Identity function 34 35 Identity Law 18 19 21 22 112 114 Identity relation 35 39 Identity set-theoretic 9 Imperative 95 Imperfective paradox 247 Implication 224 Inclusion relation 561 Inclusive disjunction 12 103 Incompleteness theorem 231 Inconsistency 228 Increasing 380—382 385 389 399—401 Increasing determiner 383 Independence 202 203 220 224 Independence of axiom 224 Independence, law of quantifier 150 INDEX 533 537 547 621 Indexed grammar 536 541 542 547 549 553 Indexed language vi 540—542 546 547 Indexical 427 428 Indexicality 427 indices 414—419 422—429 536 538 540 549
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