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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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'At least one' automaton 566 567 'At least one' tree 568 'Every AB' automaton 565 'Every' automaton 566 'Exactly two AB' automaton 568 'Exactly two' automaton 570 'Exactly two' tree 570 'No' automaton 567 Abelian group 257 266 312 607 Abelian group, monoid 264—266 434 Absorption 283 293 Absorption law 282 292 Abstract collection 3 Abstract collection, concept 7 Abstract collection, relation 28 Abstraction, lambda 338—371 Acceptance for ever after state 569 Acceptor 454 Accessibility 414—419 424 429 Ackermann, W. 220—224 Acoustic phonetics vi Action, collective v Action, distributive v Acyclic automaton 572 Adamczyk, K. vii Addition 20 21 31 73 76—80 83 215 413 593 599 Addition law 274 603 608 Ades, A. 553 Adjective, autological 26 Adjective, heterological 26 Adjunction 545—547 555 Agentless passive 363 367 Aho, A. 536 541 Ajdukiewicz, K. 550 Algebra 20 215 247 249—256 257—276 277—296 297—314 334 335 369 388 414 415 609 Algorithm 517—519 523 527 531 533 542 Allophone 52 578 Almost connectedness 391 Alphabet 66 71 188—190 235 254 433 435—437 451 453 454 456 458 465 472 476 478 484 485 487 491 492 494 502 508—515 519—522 529 532 558 573 574 Alphabetic variant 150—153 Alternation 135 Analogue, arithmetic 21 Analysis 3 373—375 388 391 295 399 401 403 408 427 Anaphora 389 419 Andrews, A. vii Anti-euclideanness 391 Anti-symmetric relation 41 Antipersistent 381 Antisymmetric relation 44 47 48 Antisymmetry 44 45 47 48 207 208 209 210 212 213 277 278 282 391—394 398 401 440 444 579 581 583 620 Application 351 Argument 31 34 65 97 115—120 134 135 137 155 159 161 162 164—169 175 178 179 233 303 339—343 348 351 362 363 366 373 376 380 381 398 421 444 513 518 551 588 604 Aristotelian syllogistic logic 333 Aristotle 333 Arithmetic analogue 21 Arithmetic, language of ordinary 93 Aronszajn, M. vii Asher, N. 411 Assertability condition 242 ASSIGNMENT 346 Associative law 18 19 21 22 112 114 120 199 281 292 297 421 Associative operation 73 214 215 251 257 261 263 265 274 284 293 434 576 577 Associativity 270 273 604 606 607 608 609 612 Asymmetric relation 40 42 43 44 45 47 49 85 Asymmetry 208 209 212 213 349 366 391—393 396 424 444 579 atom 298 303 Atomic formula 140 152 308 325 Atomic formula, sentence 100 Atomic formula, statement 99 100 106 107 110 113 115 125—132 155 184 185 191 220 221 235 254 307 319 321 322 368 Autological adjective 26 Automatagu 94 433—574 624 625 627 633 Automorphism 253 274 378 605 Auxiliary alphabet 188—190 236 596 597 Auxiliary premise 120—123 161 162 173 174 586 587 593 595 600—603 614 Auxiliary proof 172 Auxiliary symbol 6 140 Auxiliary tree 543 544 546 Axiom 90—94 185—246 249 250 257 260 266 268 269 299 312 313 314 348 349 437 596 597 599 604 606 Axiom of asymmetry 210 Axiom of Choice 219 232 288 Axiom of extension 171 Axiom of irreflexivity 210 Axiom of regularity 218 Axiom of separation 219 Axiom of transitivity 210 Axiom, schemata 191 225—227 Axiomatic system vi 185—188 191 192 194 211 235 236 Axiomatization 8 89 90 92 181 195 201 208 213 217 219 223 225 226 228 230 234 349 Bach, E. 362 363 364 553 Backward function composition 553 Bar-Hillel, Y. 550 552 Barendregt, H. 351 Barwise, J. 373 384 385 387 389 397 411 Basic alphabet 188 189 Basic clause 320 321 Basic concepts of logic and formal systems 89 Basic concepts of set theory 3 Basic result in recursive function theory 518 Behavioral science vii Bell, J. 231 301 303 Bernays, P. 224 Beth tableaux 123 135 165 168 169 179 229 230 234 246 Beth tableaux, construction rules for 128 Beth, E. 123 124 128 135 165 168 169 179 229 230 234 246 Biconditional 99 105 113 135 171 174 Biconditional laws 112 Biconditional proof 599 602 Biconditional statement 110 Bigelow, J. 405 Bijection 253 285 286 378 Binary connective 100 Binary connective notation 66 69 Binary connective operation 266 267 282 297 312 Binary connective product 191 Binary connective relation 30 39 40 47 174 175 180 205 206 208 374 391 459 460 Binding 150 323 342 373 Birkhoff 52 250 291 292 302 Bolyai, J. 90 91 Bonevac, D. 411 Boole, G.E. v 21 215 297 298 300—304 309 314 352 354 388 478 611 Boolean algebra v 21 215 297 298 301—303 388 478 Boolean algebra, laws 300 Boolean algebra, phrasal conjunction 354 Boolean lattice 611 Bound variable 141 142 144 177 Bound, upper 71 Bounded function 70 Bounded function, lattice 290 Branch 440 497 581 Bresnan, J. 362 364 Brolio, J. vii Brouwer, L.E.J. 305 306 Brouwerian lattice 305 Calculus 82 95 135 142 144 147 160 235 317 339 341 343 348 349 350 351 367 553 Cancellation law 266 Cantor's set theory 7 Cantor's theorem 62 64 73 300 351 520 Cantor, G. 7 62 64 73 82 300 351 520 cardinal number 56 59 62 63 65 73 Cardinality 9 11 58 60 64—72 300 379 390 395 396 398 399 435 580 581 618 Cardinality, equivalent set and 55 Cardinality, set of 82 Cardinality, set-theoretic identity and 8 Carnap, R. 366 Cartesian product 27—30 60 62 464 Categorial grammar 550 552 Categorial language vi Categorical system 206 207 Category 318 320 323 324 339 351 354 359 364 368 373 375 376 386 440 443 503 550 551 553 Category, theory 250 254 281 cell 46 47 Center embedded constituent structure 541 Choice-function 232 Chomsky hierarchy 436 451 452 535 561 Chomsky normal form 505 Chomsky's program 94 Chomsky, N. 94 436 451 452 453 463 481 503 505 535 555 561 Chronological order 86 Church — Rosser Theorem 350 Church's hypothesis 517—519 523 531 Church, A. 317 338 350 352 517 518 519 523 531 Circularity 391 392 394 Circumlocution 101 class 301 306 311 313 379 383 435 464 578 613—615 Class of finite sets 59 Class, context free vi Class, context sensitive vi Class, equivalence 45—47 56 58 59 135 209 Clause 320 321 351 355 357 373 415 505 Clause mate 445 446 Clitic 351 Closed formula 142 150 Closure 249 250 263 335 462 464 492 499 511 533 542 551 553 561 563 604 Coextension 417 Cohen, P.J. 65 219 Collection, abstract 3 Commutative 73 224 251 252 257 262 263 274 284 293 434 576 577 609 613 Commutative group 311 Commutative law 18 20 22 112 114 120 121 281 292 297 421 599 600 601 602 Commutative law, operation 264 Commutativity 270 552 Complement 20 218 293 294 364 405 410 413 418 478 485 576 577 610 625 Complement of arbitrary set, difference and 14 Complement of relation 15 29 33 44 Complement of set 16 17 Complement, definition of 19 Complement, inverse of 36 Complement, inverse relation and 52 Complement, law 18 19 22 112 114 120 123 156 421 Complementary distribution 52 Complementary relation 36 Complementation 26 298 300 477 498 499 542 547 548 563 Complementation laws 298 Complements, properties of inverses and 44 45 Completeness 202 203 Completeness, proof 227 228 Completeness, theorem 308 Complex statement 113 115 126 127 145 Component, semantic 93 95 Component, syntactic 95 Composite 37 composition 33—35 258 285 Composition of operations 263 Compositionality 317—338 339 340 351—357 360 368 369 387 407—409 Compositionality principle 254 337 Computability 350 Computation, mathematics of vi Computational linguistics vi Computing function 454 Concatenation 213—215 318 324 434—436 464—468 471 477 498 533 547 548 Concept of equality 78 Concept of infinity 55 Concept of logic and formal systems, basic 89 Concept of set theory 45 Concept, abstract 7 Conclusion (of deduction) 115—126 129 155 162—168 183 421 Condition 398 442—444 450 Conditional 99 104—106 108 111 115 119 124 129 135 146 147 162 166 173 239 242 243 246 307—309 333 473 Conditional connective 124 Conditional law 112—114 120 154 421 614 Conditional premise 270 608 609 Conditional proof 120—123 133 160 161 171 172 174 198 586 593 599 600 601 602 603 614 Conditional sentence 104 Conditional statement 127 Conjunction 95 99 102 103 118 120 122 125 129 135 149 156 159 161 184 199 239 246 251 333 350 351 352 354 357 364 382 383 407 420 421 547 587 592 593 595 599 600—602 Connected 45 51 Connected relation 42—44 Connectedness 39 42 44 210 211 268 391—393 401 579 620 Connective 100—107 111 115 124—126 130—132 135 139 140 145 153 159 166 169 220 223 225 236 239 240 243 250 318 320 324 368 420 Connective, binary 100 Connective, sentential 95 97 100 Connotation, temporal 102 Conover, L. vii Consequence and laws, logical equivalence, logical 110 Consequence, logical 111 116 Conservative 387 388 Conservativity 376 377 379 380 383 387 388 392 394—398 618 620 621 Consistency 202 203 221 223 Consistency, principle 18 20 22 577 Constancy 377 378 Constant 138 140 141 143 155 156 157 158 160 163 167 168 169 195 225 228 307 308 319 419 496 617 Constituent 101 114 138 360 439 440 441 Constituent sentence 102 Constituent statement 106 110 124 Constituent structure tree 439 442 444 449 Constraint on coordination 382 Construction rules for Beth tableaux 128 Construction, intensional vi Construction, set-theoretic 79 Construction, tableau 130 context 396—399 404 406 408 409 413 418 420 421 425 427—429 Context, dependence 395 398 546 Context, free 449 450 Context, free, class vi Context, free, grammar 492 494 496 497 500 501 502 505 525 535 536 542 544—546 548 552 555 Context, free, language 494 496—500 505 506 525 535 540—542 545 553 562 563 572 Context, sensitive 449—451 Context, sensitive, class vi Context, sensitive, grammar 530—534 556 Context, sensitive, language 529—535 542 553 555 562 563 Contingent 108—110 132 144 584 Continuity 383 Continuous structures v Continuum Hypothesis 65 66 Contradiction 107 110 113 122 123 125 126 132 143 144 228 242 269 301 385 388 389 393 407 421 523 585 Convention 345 353 368 370 Convergence, definition 82 CONVERSE 40 Conversion 342 349 350 353 357 359 360 361 Cooper, R. 334 338 373 384 385 387 389 397 Coordinate, first 30 Coordinate, projection onto first 28 29 Coordinate, projection onto second 28 29 Coordinate, system 31 Copi, I. 202 Correspondence 31 46 63 311 313 318 319 336 579 580 605 606 612 Correspondence, one to one 32—36 55—62 67 69 76 86 198 200 204 205 253 271 Count, frequency vi Countably infinite set 59 Cresswell, M. 352 358 413 Cross-serial dependency 503 538 547 Curry, H. 206 CYCLE 555 558 Dagger 239 Dahl, Oe. 361 daughter 440 441 547 549 De dicto interpretation 409 410 412 De Jong, F. 398 De re interpretation 409 Decidability 229 563 Declarative sentence 95 100 1—2 Decreasing 381 382 389 399 Decreasing determiner 383 Decreasing simple quantifier 384 Dedekind infinite 195 Dedekind, R. 82 194 195 291 Deduction 246 Deduction, natural 115 154 170 Definability 374 Definition 234 236 270 302 325 327 339 346 350 366 367 374 383 384 387 388 389 399 417 421 435 438 443 445 446 447 458 459 460 462 464 465 491 492 510 512 577 594 607 608 609 610
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