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Partee B.H., Meulen A.T., Wall R.E. — Mathematical Methods in Linguistics
Partee B.H., Meulen A.T., Wall R.E. — Mathematical Methods in Linguistics

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Название: Mathematical Methods in Linguistics

Авторы: 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: en

Рубрика: Филология/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1990

Количество страниц: 663

Добавлена в каталог: 09.12.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
'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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