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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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Negative rational numbers 62 86 Negative, set of positive and 51 Negative, strong 387 388 New York Times 65 Newton, I. 89 91 Newtonian system 90 91 Node 440—447 544 545 547 567 568 581 619 Node admissibility condition 450 Non-Abelian group 612 Non-determinism 490—492 497 499 512 515 516 530—533 Non-deterministic automata 457 485 486 Non-deterministic finite automata 460 462 477 484 Non-deterministic finite language 562 Non-deterministic linear bounded automaton language 562 Non-deterministic pushdown automaton language 562 Non-distributivity 291—293 Non-empty set 46 206 219 232 281 288 Non-empty subset 283 287 Non-finite automaton 462 463 Non-finite of primitives 92 Non-modularity 291 292 Non-monotone 382 Non-reflexive relation 39 40 Non-terminal alphabet 437 Non-terminal symbol 439 446 451 Non-triviality 379 Non-Turing acceptable language 562 Nonconnected relation 42 43 Nonconnectedness 578 579 Nondenumerable set 62 64 69 Nondenumerable set, infinite 69 86 Nonidentical first and second members 42 Nonnegative integers 80 Nonreflexive relation 51 Nonsymmetric 45 Nonsymmetric relation 40 43 44 Nonsymmetry 578 579 Nontangling condition 442—444 Nontransitive relation 41—44 Nontransitivity 578 579 Normal form, prenex 151 Normal form, quantifier laws and 148 Not every automaton 566 Notation 34 135 136 234 236 239 Notation, binary 66 69 Notation, empty list 9 Notation, list 4—6 Notation, predicate 6 11 12 14 16 28 31 33 Notation, set-theoretic 4 Notion, primitive 27 Noun 231 439 440 Noun phrase 102 395 399 404—408 410 411 418 419 426 439 440—443 480 504 Null set 4 10 19 21 123 189 Null string 192 NUMBER 230 263 267 274 340 395 Number theory 16 400 Number, cardinal 56 59 62 63 73 Number, extension to the set of all rational 80 Number, extension to the set of all real 82 Number, finite 72 Number, infinite 72 Number, infinite, infinite cardinal 65 73 Number, irrational 64 Number, natural 3 9 11 36 51 56—60 62 66 75 76 78—80 85 86 194—196 200 Number, negative rational 86 Number, positive rational 86 Number, rational 60 64 81—83 Number, real 51 64 65 69 70 Number, set of real 66 Number, systems, set-theoretic reconstruction 75 Number, theoretic tree 379 380 Number, unique real 69 Object 3 4 11 16 28 29 31 Object, language 92 319 Object, linguistic 5 Object, named 5 Odd integers 60 Oehrle, R. 553 Omniscience 422 One to one correspondence 32—36 55—63 67 69 76 78 86 198 200 204 205 253 271 311 579 580 612 One to one function 32 34 37 56 62 One to one mapping 56 Onto function 32 34 37 Opacity 405 406 408—415 418—421 423 425 426 Open formula 142 208 Open statement 138 139 144 Operation 250 252 253 257—261 263 264 266 267 271 273—275 281—284 297 311 312 314 318—321 324 325 334 335 348 350 362—364 420 612 Operation, complementation 477 Operation, intersection 255 477 Operation, order and v Operation, set-theoretic 12 Operator, unary 100 Order 50 208—213 232 264 267 278 280—283 306 363 391 393 434 435 442—444 580 588 607 Order and operation v Order, chronological 86 Order, linear 51 66 69 76 Order, partial 51 Order, strict 47—49 51 Order, strong 47 Order, theory 277 285 Order, total 51 53 Order, weak 47—51 Order, weak, partial 53 Ordered n-tuple 27 Ordered n-tuple, set of 36f Ordered pair 28 29 34 39 40 41 44 47 48 60 62 79 81 143 145 146 174 186 313 438 444 Ordered pair and Cartesian products 27 Ordered pair, set of 30 31 Ordered quadruples 30 62 Ordered set, finite linearly 51 Ordered set, finite partially 51 Ordered system, linearly 86 Ordered system, partially 86 Ordered triple 27 30 62 Ordering 47 79 81 Ordinary arithmetic, language of 93 Ordinary set 27 Output 453 454 565 pair 313 Pair, ordered 28 29 34 39 40 41 44 47 48 60 62 79 81 143 145 146 174 186 Pair, reversed members of 40 Pairing 218 Papadimitriou, Ch. 463 466 492 Paradox 427 Paradox, Grelling's 26 Paradox, logical 7 Paradox, Russell's 7 10 26 63 Paradox, set-theoretic 8 Parallel postulate 89 90 PARAMETER 395—397 422 425 427—429 Parse tree 494 495 501 502 Parsing vi Parsons 334 Partee, B.H. v vii 334 352 254 257 358 366 379 427 555 Partial function 31 32 Partial order 51 277 278 280 282 306 393 Partial order, weak 53 Partial recursive function 520 Partially ordered set 51 Partially ordered system 86 Partition 135 Partition, equivalence relation and 45 Partition, induced 47 52 Partition, trivial 46 Partitioning 46 Pascal, B. 93 passive 363 367 Peano, axiom 194 197 200 212 215—217 230 234 237 Peano, axiomatization 232 Peano, fifth postulate 269 Peano, G. 194 195 197 200 212 215—217 230 232 234 237 269 Performative 95 Permutation invariance 572 persistent 381 Peters, S. 320 334 352 415 555—558 Phoneme 3 52 433 578 Phonemic overlap 578 Phones 52 Phonetics, acoustic vi Phrasal conjunction 103 352 354 Phrasal passive rule 363 Phrasal rule 364 phrase 102 480 Phrase, structure 322 Phrase, structure tree 474 515 PNF 152 153 159 178 229 Polarity 386 Polarity, reversal 385 Polish notation 135 136 234 236 Pollard, C. 548 Polygons, regular 70 POSET 277—285 288 295 306 308 609 Positive and negative integers, set of 51 Positive closure 533 Positive element 268 269 Positive even integers 56 Positive function 59 Positive integer 6 9 49 59 60 61 79 80 235 265 434 Positive integer, relation of 43 Positive integer, set of 55 56 Positive rational numbers 86 257 Positive, strong 387 388 394 Possessive 390 Post Correspondence Problem 525 Post, E. 518 Postulate 364—366 Postulate, parallel 89 90 Power, finite 73 Power, integral 71 Power, set 11 62 63—65 185 218 219 232 235 275 280 295 300—302 376 435 596 Power, set, lattice 304 Precedence 441 442 Precedence relation 444 446 Predecessor 49—53 76 217 442 Predicate 8 23 42 138 139 140 143 144 166 170 171 173 176 178 182 183 185 195 196 199 205 216 242 Predicate calculus 95 142 144 147 160 341 343 Predicate logic vi 96 97 137 140 142 143 147 148 153 169 175 177 212 214 225—231 234 236 241 246 307 308 318 323 324—328 330 333 350 359 360 362 363 368 369 373 382 385 405 408 409 413—415 419—421 Predicate logic, statement logic and 95 Predicate notation 6 11 12 14 16 28 31 33 Prefix 435 Premise 115 117 119 120 122—126 129 155 156 160—168 171 173 174 197 221 236 270 412 418—421 Prenex normal form, quantifier laws and 148 151 Preorder 209 Presupposition 242 243 398 Prime 99 128 188 primitive 94 217 220 237 319 414 415 434 Primitive non-empty set of 92 Primitive notion 27 Primitive predicate 216 Principal filter 620 Principal ideal 288 Principle of compositionaiity 254 317 318 Principle of Finite Induction 269 270 Principle of Mathematical Induction 195—199 235 596 608 609 Principle, consistency 18 20 22 Probability and statistics vi Problem 512 513 523 524 Produces in one move 459 460 462 491 492 510 511 PRODUCT 498 Product, cartesian 28 29 30 60 62 Production 187 191 192 536 537 549 596 Production, schemata 187 189—191 193 197 Productions of inference 186 189 PROGRAM 455 Program, Chomsky's 94 Program, Hilbert's 94 Programming language 7 8 93 348 351 491 Programming semantics 8 Projection onto first and second coordinates 28 Projection onto first coordinate 29 Projection onto second coordinate 29 Projection, problem 243 PROLOG 93 214 Proof, conditional 120—122 Proof, formal and informal 170 Proper ideal 289 Proper subset 10 Properties 251 Properties of complements 45 Properties of connectedness 44 Properties of inverses 45 Properties of operation 250 Properties of reflexivity 44 Properties of relations 39 45 51 52 Properties of set 7 Properties of symmetries 44 Properties of transitivity 44 Properties truth-functional 101 Properties, inverses and complements 44 Proposition 100 162 Propositional calculus 95 135 138 142 144 145 163 Propositional logic 142 Pseudo-complement 304 611 Pseudo-complementation 305—309 314 Pseudocleft 358 Pullum, G. 503 542 Pumping lemma 571 Pumping theorem 471—473 480 481 494 496 497 499 502 505 506 545 Push and copy rule 536 Pushdown automata 487—493 497 499 506 508 512 529 530 541 571—573 Quadruple 438 491 508 510 520 526 548 551 Quadruple, ordered 30 62 Quantification 395 418 424 Quantification, vacuous 140 141 Quantified variable 140 Quantifier 138—156 159—161 163 164 167 169 170 177 208 225 229 231—233 308 318 323 324 358—360 373 374 375—380 383—385 387 388 390—393 395 397—400 409 416 424 426 565 567 571 572 591 Quantifier, automata 565 Quantifier, dependence, law of 150 Quantifier, distribution 172 Quantifier, distribution, laws of 149 161 171 Quantifier, generalized vi Quantifier, independence, law of 150 Quantifier, law, first 148 Quantifier, laws and prenex normal form 148 Quantifier, movement, laws of 151 154 Quantifier, negation 159 164 595 Quantifier, negation, laws 154 173 Quantifier, word 97 quantity 378—380 383 392 394—397 618 621 Quasi-model 223 Quasi-order 209 Quasi-reflexivity 620 Quaternary function 36 Quaternary relation 30 36 Question 479 Quine's dagger 239 Quine, W.V.O. 239 406 Quintuple 458 462 Rabin, M. 463 RANGE 29 30 36 56 Range of function 32 34 Rasiowa, H. 306 Rational numbers 60 64 75 81—83 257 267 274 Rational numbers, extension to the set of all 80 Rational numbers, negative 62 86 Rational numbers, positive 86 Rational numbers, subsystem of 80 Real numbers 51 64 65 69 70 267 340 Real numbers, extension to the set of all 82 Real numbers, set of 66
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