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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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Real numbers, unique 69 Reconstruction of number systems, set-theoretic 75 Reconstruction, set-theoretic 79 Recoverability 556—558 Recursion 555 RECURSIVE 354 recursive clause 320 321 Recursive definition 181—186 188 194 196 234 236 270 Recursive function 513 514 Recursive language 532 533 563 Recursive rule 8 23 335 Recursive set 519 520 531 558 Recursively enumerable language 507 558 563 Recursively enumerable set 520 524 531 556 557 562 Recursively enumerated set 514 516 Reduction, set-theoretic 29 Reference 404 Reference, time 427 Reflexive 45 272 277 Reflexive clitic 351 Reflexive relation 41 43 44 46 47 48 85 Reflexive transitive closure 461 462 Reflexivity 39 42 43 52 208—210 212 213 279 282 305 391 392 394 440 459 460 492 511 578 579 581 588 614 615 621 Reflexivity, properties of 44 Reflexivity, symmetry, transivity and connectedness 39 Regular expression 466 485 Regular expression, grammar 451 Regular expression, language 455 464—466 477 478 480 492 499 503 533 547 562 563 Regular expression, polygons 70 Regularity 218 Reichenbach, H. 427 Rejection with 0 state 569 Rejection with 1 state 569 Relation 28—31 36 37 44 78 80 134 135 174 175 180 186 204—209 211—213 218 219 232 267 268 272 277—280 286 301 311 313 317 329 337 365 374 389 391—394 398 401 409 414 415 418 424 426 436 440—446 452 459 460 462 492 511 551 561 565 578 579 582 583 588 613—615 620 Relation and complement, inverse 52 Relation and function 27 Relation and partition, equivalence 45 Relation of integer 85 Relation of positive integers 43 Relation, abstract 28 Relation, anti-symmetric 41 44 47 48 Relation, asymmetric 40 42—44 47 49 85 Relation, binary 30 39 40 47 Relation, complement 44 29 33 36 Relation, connected 42 43 44 Relation, dense 51 Relation, diagram of 43 Relation, equal 76 Relation, equivalence 46 47 52 56 71 79 Relation, identity 35 39 Relation, inbansitive 41 42 44 Relation, inverse of 29 Relation, irreflexive 39 40 43 47 49 51 85 Relation, membership 4 Relation, n-place 30 Relation, non-reflexive 39 51 Relation, nonconnected 42 43 Relation, nonsymmettic 40 43 44 Relation, nontransitive 41 42 44 Relation, properties of 39 45 51 52 Relation, quaternary 30 36 Relation, reflexive 41 43 44 46 47—48 85 Relation, set-theoretic 29 Relation, subset 28 48 85 Relation, symmetric 43 44 46 47 85 Relation, ternary 30 36 Relation, transitive 41 43 46—49 85 Relative clause 355 357 373 Relative complement 15 replacement 218 219 Representation 334 Representation, ideal 288 Restriction 398 Reuland, E. 389 Reversal 434 435 Reversed members of pair 40 review exercises 85 245 311 573 Rewrite rules 94 Rewriting, string 95 Riemann, B. 90 Right identity element 251 252 Right increasing 398 Right inverse 252 Right linear grammar 451 474 492 Right linear language 562 Right linear tree structure 541 Right monotone decreasing 381 382 399 Right monotone increasing 381 382 384 385 400 620 Right zero 253 Rigid designator 419 421 426 429 Ritchie, R. 555—558 Roach, K. 548 Roberts, C. vii Rogers, H. 518 Rohrer, Ch. 425 427 Root 441 445 447 494 Rooth, M. 354 Ross, J.R. 71 361 Rosser, J. 350 Rozwadowski, K. vii Rule 318—320 322 324 325 328 329 331—333 335 344—346 352 353 356 357 359 362—366 367 474 476 493 536 575 576 629 Rule for Beth tableaux, construction 128 Rule of function application 551 553 Rule of Implication 224 Rule of inference 45 94 118 119 122 151 153 154 162 172 185 196 197 220 221 224—226 235 404 405 437 Rule of substitution 114 120 220 221 224 225 Rule, recursive 8 23 Rule, rewrite 94 Rule, well-formedness 94 Russell, B. 7 10 26 63 216 220 224 339 Russell, paradox 7 10 26 63 Salomaa, A. 536 542 Schema 114 187—193 225—227 235 354 488 617 Schieber, S. 504 Scott, D. 351 463 Second coordinate, projection onto 28 29 Second member 27 28 Second member, first and 44 Second member, nonidentical first and 42 Second, elements, first and 29 Self-dual determiner 384 Semantic automata 565 Semantic component 93 95 Semantic rule 319 346 Semantic tableaux 124 130 Semantic value 142 143 155 Semantics 89 101 104 115 125 138 140 142 144 148 200 231 241 250 254 281 297 306 308 309 317—321 323—327 329 332—335 338—348 351 353—359 361 362 364—368 370 373—375 377 379 380 383—385 387 390 395 399 401 403 404 406—410 412—415 419 422—429 504 550 551 Semantics, formal 95 Semantics, programming 8 Semantics, syntax and 94 Semi-Thue system 191—193 236 596 Semigroup 263—265 274 275 606 Semilattice 280 283—286 295 609 Sense 404 405 407 415 Sensitive, context 449—451 Sentence 104 142 295 Sentence, atomic 100 Sentence, constituent 102 Sentence, declarative 95 100 102 Sentence, set of 67 68 70 Sentential conjunction 103 Sentential connective 95 97 100 102 103 145 Sentential negation 101 Sentential tree 546 Separation 219 Sequence, infinite 69 Sequence, linear 62 64 Set 3 5 19 23 52 57 85 134 142 143 170—174 176 181—185 189 198 205 206 209 211 213 219 227 228 230 232 235 237 249 251 258 262 265 266 273 275 281 288 295 301 302 306 307 308 311 324 325 333 335 338 339 340 342 343 376 377 379 385—388 390 391 396—399 415 417 422—425 433 435 440 442—444 455—458 463 466 474 477 487 491 492 510 514 516 519 520 524 526 529 531 535 536 553 556—558 578 580 582 596 597 603—605 607 611 620 622 Set and cardinality, equivalent 55 Set of all integers, extension to the 78 Set of all rational numbers, extension to the 80 Set of all real numbers, extension to the 82 Set of axioms 92 Set of cardinality 82 Set of elements 203 Set of entities 375 Set of integers 31 32 267 Set of languages 68 Set of n-tuples 62 Set of ordered n-tuples 36 Set of ordered pairs 30 31 Set of positive and negative integers 51 Set of positive integers 55 56 Set of primitives, non-empty 92 Set of real numbers 66 Set of rules 437 Set of sentences 67 68 70 295 Set of sets 12 Set of statements 245 307 Set of strings 186 214 438 464 481 484 Set of transition rules 483 Set theory 3 6—8 30 80 82 85 93 148 171 208 212 217—219 251 254 255 274 277 279 280 295 299 300 302 348 381 383 384 388 392 400 434 477 606 Set theory and logic v vi Set theory, axiomatization of 8 Set theory, basic concepts of 3 Set theory, concepts of 45 Set theory, laws of 45 Set, arbitrary 12 13 14 Set, Cantor's theory 7 Set, class of finite 59 Set, complement of 16 Set, countably infinite 59 Set, denumerability of 58 Set, denumerable 59 Set, denumerably infinite 59 60 Set, disjoint 73 Set, distinct 9 Set, empty (null) 4 9 75 Set, equal 55 Set, equivalent 56 57 62 Set, finite 6 9 56 58 70 86 Set, finite, linearly ordered 51 Set, fuzzy 6 Set, infinite 6 8 9 55—60 65 70 86 Set, member of 5 7 8 10—12 15 21 24 25 27 30 32 36 43 52 53 56 58—60 62 63 66 69 70 75 76 155 Set, non-empty 46 Set, nondenumerable 62 64 69 Set, nondenumerably infinite 69 86 Set, null (empty) 4 10 19 21 123 Set, ordered pairs of 30 Set, ordinary 27 Set, partially ordered 51 Set, power 11 62—65 Set, product 498 Set, properties of 7 Set, specification of 4 Set, subset of 10 Set, uncountable 69 Set, universal 19 21 Set, unordered 28 Set, well-ordered 51 Set-theoretic complement 17 Set-theoretic concept 55 Set-theoretic construction 79 Set-theoretic difference 15 16 Set-theoretic equality 17 18 25 26 Set-theoretic expression 21 Set-theoretic identity 9 Set-theoretic identity and cardinality 8 set-theoretic intersection 14 Set-theoretic notation 4 Set-theoretic operation 12 Set-theoretic paradox 8 Set-theoretic reconstruction 79 Set-theoretic reconstruction of number systems 75 Set-theoretic reduction 29 Set-theoretic relation 29 set-theoretic union 12 13 Set-theoretic universe 17 Sextuple 491 Shamir, E. 552 Sheffer stroke 240 Sikorski, R. 306 Simple decreasing 389 Simple increasing 389 simplification 118 121 127 156 159 161 162 172—174 183 184 362 586 587 592 595 599 600—603 Single root condition 441 443 Single-value 31 Single-value mapping 32 Singleton 4 12 27 Sister 441 442 444 Situation 458—460 462 Skolem, function 23 232 Skolem, normal form 229 232 233 237 Solutions 575 Soundness Theorem 308 Specification of set 4 Square of opposition 566 STACK 487 489 490 536 542 571 572 Stack, alphabet 487 491 Stack, automata 541 Stack, symbol 491 Standard model 91 Standard notation 135 136 Standard Theory vi 555 557 Star 464—466 471 477 547 Star, Kleene 469 498 533 State 306 307 453 454—459 461 463 466 469 471 472 474—477 479 485 487—489 492 507—510 512 517 520 521 529 567—569 572 573 625 State, diagram 457 461 476 479 482 484 State, transition 478 Statement 106 107 110 111 113 115 117 119 120 122 123—132 137—140 142—145 147—150 154 155 157 159 161 162 164—166 168 170 171 176 180 182 183 185 191 206 207 216 219—221 223 227 239 241 242 245 250 252 254 270 283 300 301 306 307 319 322 323 327 335 350 359 364 367 368 392 403—405 407 408 413 414 418 420—422 425 428 429 444 489 519 520 588 596 617 Statement calculus 95 137 234 235 Statement logic 99 100 102 118 119 130 190 199 219 220 223 226 229 319—322 Statement logic and predicate logic 95 Statement logic, laws of 112 Statement syntactic component 101 Statement, atomic 99 100 Statistics, probability and vi Status, membership 6 Steedman, M. 553 STEP 510 511 Stokhof, M. 358 Stone, M.F. 301 303 Stone, representation 301 303 Strict linear order 211 Strict order 47—49 51 Strict partial order 209 210 443 444 Strict total order 444 String 181—183 186—192 200 214 215 234 311 312 433—438 447—449 451 453—455 457—460 462—469 471—473 476—481 483—485 488 489 491—494 496—498 500—502 506 507 509—514 517 519 521 523—525 527 530—536 538 545 546 548 549 551—553 556 558 573 574 583 596 612 613 622 626 629 String, concatenation 213 String, empty 58 String, finite 66 71 86 String, rewriting 95 String, unique 58 Stroke 240 strong 387 388 394 Strong connectedness 391 392 Strong conservativity 377 Strong order 47 Structure 322 Structure, algebraic v Structure, continuous v Structure, syntactic 101 Subalgebra 301 Subformula 113 114 329 Subgroup 263—265 274 311 313 605 606 Sublattice 280 283 284 287 292 302 Submonoid 265 Subposet 284 Subscript 99 138
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