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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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Indirect proof 122 123 133 580 595 601 602 Individual constant 138 Individual variable 138 Induced partition 47 52 Induction 235 276 309 434 596 608 609 Induction, principle of mathematical 195—199 217 269 270 Induction, step 197 198 Inductive proof 194—199 Inference 221 224—226 235 375 404 405 409 437 Inference, productions of 186 189 Inference, rules of 45 95 118 119 122 151 153 154 162 172 185 196 197 220 Infinite cardinal number 65 73 Infinite denumerably 71 Infinite numbers 72 Infinite sequence 69 Infinite set 6 9 55—60 65 70 86 212 Infinite set, countably 59 Infinite set, denumerably 59 60 Infinite set, equivalent 58 Infinite set, nondenumerably 69 Infinite vs unbounded function 69 70 Infinite, Dedekind 195 infinity 218 219 Infinity, concept of 55 Informal proof 173—175 180 Informal proof, formal and 170 Information-state 306 307 309 Initial state 455 457 458 461 469 475 476 479 484 488 507 510 517 520 Initial symbol 437 Initial tree 543 544 547 Input 453—457 461 463 484 489 512 514 519 529—531 567 573 Input, alphabet 484 485 491 Input, string 477 483 489 490 508 521 532 Input, symbol 491 Input, tape 487 488 507 Instantiation 154—174 183 184 196 197 617 INTEGER 62 64 73 75 78 79 177 178 196—200 235 253 257 258 263 265 267 269—273 311 313 434 527 556 575 576 581 585 591 606 608 609 613 Integer, distinct pair of 43 Integer, extension to the set of all 78 Integer, negative 62 71 79 80 Integer, nonnegative 80 Integer, odd 60 Integer, ordered pair of 81 Integer, positive 6 9 49 59—61 79 80 Integer, relation of 85 Integer, relation of positive 43 Integer, set of 31 32 Integer, set of, positive 55 56 Integer, set of, positive and negative 51 Integral domain 266—272 275 276 312 313 Integral power 71 Intended model 91 Intension 414—429 Intensional construction vi Intensional equivalence 417 Intensional logic 429 Intensionality 403 413 414 Interpretation 409 410 412 414 415 422 425 428 429 Interrogative 95 Intersection 12 19 20 26 300 302 308 382 388 477 481 498 499 533 542 546 547 573 576 Intersection, definition 17 19 20 Intersection, operation of 255 Intersection, set-theoretic 14 Intersection, union and 11 Into function 32 34 443 Intransitive 45 Intransitive relation 41 42 44 Invalid argument 115 116 119 Inversal instantiation 592 593 603 Inverse 30 34 35 37 218 225 252 253 261—263 265—267 274 275 286 311 313 434 578 603 604 606 607 Inverse element 255 257 Inverse law 613 614 Inverse of complement 36 inverse of function 33 Inverse of relation 29 Inverse relation and complement 44 52 Inverse schema 192 Inverse, definition of 174 175 Inverse, properties 45 Irrational numbers 64 Irreflexive relation 39—51 85 205 Irreflexivity 208 209 213 391—393 429 442 444 578 579 Isomorphic model 206 207 Isomorphic subsystem to the old system 78 Isomorphic system 204 Isomorphism 80 81 203—205 253 254 267 271 272 274 275 285 286 292 300 301 303 311 378 476 605 612 Isotone 285 Jacobson, P. vii James, W. 72 Janssen, Th. 250 334 352 Joshi, A. 535 542 546 548 553 Kalish, D. 318 Kamp, H. 424 425 427 Karttunen, L. vii Keenan, E. 354 361 379 388—390 Kernel 271 Kleene, closure 542 Kleene, S. 241—243 464 465 466 469 471 477 498 518 533 542 547 Kleene, star 464—466 469 471 477 498 533 547 Kripke, S. 254 306—309 414 415 419 429 Kripke, semantics 254 306 308 Kripke, valuation 307 Kuroda, Y. 556 Labeling 443 446 447 545 624 Labeling function 444 Ladusaw, W. 334 385 390 LAMBDA 351 352 354—367 374 Lambda abstraction 338 341 348 Lambda calculus 317 339 348—351 Lambda conversion 353 Lambda rule 347 Lambek, calculus 553 Lambek, J. 206 553 Landman, F. vii 303 Langacker, R. 445 Language 67 104 115 137 138 140 155 230 231 242 250 254 277 300 303 306 309 317—324 326 333 334 338 340—347 351—353 355 360 373 375 378—380 383 385 389 392 393 395 399 401 403 405 406 409 413—115 421 423 424 425 427 429 433 435—438 448 451—157 460 462—472 474—484 486—489 491 492 494 496—501 503 505—507 511—513 515—517 519 520 522—525 527 529—535 540—542 545—549 556—558 561—563 572 573 Language of logic 93—97 Language of ordinary arithmetic 93 Language, categorial vi Language, formal vi 95 Language, indexed vi Language, logical 100 102 Language, meta 92 93 Language, natural 3 7 92 95 96 100 101 103 Language, object 92 Language, programming 7 8 93 Language, tree adjoining vi Lasersohn, P. vii Lattice 277 280 282—297 302 304 306 308 309 314 389 609—612 Lattice theory 281 283 390 Law 148 149 267 268 275 282 291 Law of Double Negation 148 Law of quantifier dependence 150 Law of quantifier independence 150 Law of transivity 275 Law of trichotomy 268 Law, associative 18 19 21 22 Law, commutative 18 20 22 Law, complement 18 19 22 Law, DeMorgan's 18 20—22 Law, distributive 18 19 21 22 25 Law, idempotent 18 22 Law, identity 18 19 21 22 Laws and prenex normal form, quantifier 148 Laws of quantifier disttibution 149 Laws of quantifier movement 151 Laws of set theory 45 Laws of statement logic 112 Laws, logical equivalence, logical consequence and 110 Leaf 441 444 447 449 556 557 Least element 50 51 53 212 232 441 Least number 395 Left identity element 251 252 Left increasing 398 Left inverse 252 Left linear grammar 474 Left linear tree structure 541 Left monotone decreasing 381 382 Left monotone increasing 380—382 400 620 Left zero 253 Lemma 299 302 303 Level of representation 334 Levy, L. 542 Lewis, D. 463 466 492 Lexical rule 364—367 Lexicon 347 356 364 550 Lindenbaum algebra 301 Linear bounded automata 529—533 Linear function 529—531 Linear grammar 474 Linear list 67 Linear order 51 66 69 76 210 434 Linear sequence 62 64 Linearly ordered set, finite 51 Linearly ordered system 86 Linguistic object 5 Linguistic theory 437 559 Link, G. 334 390 Lisp 93 214 351 List, linear 67 List, notation 4—6 Listing, effectively 62 Lo Cascio, V. 425 Lobachevsky, N. 90 91 Logic vi 95 140 142 143 147 148 153 169 175 177 183 190 199 212 214 219 220 223 225—232 234 236 241 246 307 308 317—330 333 348 350 359 360 362 368 369 373 378 382 385 403 405 408 409 413—415 417 419—421 423 429 Logic and formal systems, basic concept of 89 Logic and predicate logic, statement 95 Logic of statement 140 144 239 241 250 307 335 Logic, first-order 93 Logic, formal v 96 Logic, language of 93—97 Logic, laws of statement 112 Logic, predicate vi 95—97 99 100 102 118 119 130 Logic, system of 92 Logical connective 102 103 Logical consequence 111 116 Logical consequence and laws, logical equivalence 110 Logical equivalence 111 114 113 118 120 121 172 417 418 Logical language 100 102 104 137 300 550 logical negation 101 Logical omniscience 422 Logical paradox 7 Logical predicate 138 Logics 306 Machine Translation vi Machover, P. 231 301 303 MacLane, S. 52 250 302 Manipulation, symbol 95 Many to one function 32 MAP 31 Mapping 31 33 34 36 57 58 63 200 234 249 253 254 271 272 285—287 302 312 313 326 334—336 346 373 434 443 555 556 581 605 Mapping function 62 Mapping, one to one 56 Mapping, single-valued 32 Markov 518 Marsh, W. 542 Mass terms v Massey, G. 236 Mate, clause 445 Mathematical and linguistic analysis 3 Mathematical induction 596 608 609 Mathematical induction, principle of 195—199 Mathematics of Computation vi Mathematics of wave theory vi Mathematics, discrete v 82 Matrix 141 Maximal element 50 51 53 May, R. 334 338 McCawley, J. 361 McKinsey, J. 305 Meaning 403 429 Meaning, postulate 364—366 Member 465 Member of set 3 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 76 142 143 155 171 173 182 184 237 262 Member, first 27 Member, second 27 28 Members, first and second 44 Members, nonidentical 42 membership 500 501 510 533 573 578 579 581 582 596 Membership, gradual 6 Membership, halfway 6 Membership, multiple 6 Membership, question 479 Membership, relation 4 Membership, status 6 Memory 453 meta-language 92 93 230 319 320 322—324 424 Miller, G. 463 481 Minimal element 50 51 53 Modal logics 306 Modality 413 418 Model 90 91 143—146 168 170 206 207 209—211 214 221 223 224 232 237 246 266 267 269 300 301 303 307 325—327 329—332 337 338 346—348 351 368 369 376 378 380 383 389 391 398 399 401 414—417 421—425 428 429 433 535 594 617 Model, intended 91 Model, standard 91 Model, theoretic semantics v Model, theory 92 94 95 181 194 200 201 203 205 208 215 228 233 353 374 375 387 414 415 417 Modified head grammar 548 549 553 Modified language 549 Modular law 290 291 Modularity 293 modus ponens 116—118 121 122 155 161 174 182—184 196 197 220 221 226—228 586 587 599 600 602 603 Modus Tollens 118 123 164 586 587 599 601 Monadic predicate logic 229 Monoid v 215 263 264 266 271 274 275 434 606 Monotone 285 383 Monotone decreasing 383 384 389 620 Monotone decreasing determiner 381 Monotone decreasing set 385—387 Monotone increasing 383 384 389 399 401 620 Monotonicity 381—383 385 397 400 Montague Grammar 7 234 250 363 415 Montague semantics 233 Montague, R. 7 233 234 250 317 318 333 334 338 339 352 353 359 363 366 374 415 425 550 Morpheme 203 351 433 Morphism 253 254 271 Morphology 365 424 Morse, S. 93 Moss, L. 390 Move 491 492 Move, produces in one 459—462 Movement, laws of quantifier 151 Multiple 575 Multiple membership 6 Multiplication 20 21 31 73 76—78 80 81 204 215 Multiplication law 267 N-place relations 30 n-tuple, ordered 27 n-tuple, set of 62 Named object 5 Natural deduction 115 154 170 Natural language 3 7 92 95 96 100 101 103 104 115 137 138 230 231 242 250 254 277 303 306 309 317 322 333 338 351 360 373 375 379 380 383 385 392—395 399 401 403—406 409 413—415 421 423 427 429 433 436 453 482 503 535 542 550 551 557 558 Natural language, formal languages and 93 Natural number 3 9 11 36 51 56—60 62 66 75 76 78—80 85 86 194—196 200 216 217 230 237 263 Negated determiner 566 Negated quantifier 565 Negation 99 101 122 123 125 126 135 159 167 220 223 228 231 236 239 240 243 307 308 351 352 368 383 384 385 400 567 602 Negation, law of double 148 Negation, symbol 100 Negative function 59 Negative integers 62 71 79 80
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