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| Barwise J., Etchemendy J., Allwein G. — Language, Proof and Logic |
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| Предметный указатель |
Game rules for  75
Game rules for  72
Game rules for quantifiers 237—238
Game rules, winning strategy 78
Game, Henkin — Hintikka 67
General conditional proof 323—327 329 332 342 442
Goedel Incompleteness Theorem 552—555
Goedel numbering 553
Goedel, Kurt 526 546
Grade Grinder 5—10 12—13
Grice's cancellability test 188
Grice, H.P. 188
Henkin construction 528 540—545
Henkin Construction Lemma 540
Henkin theory 528 532
Henkin — Hintikka game 67
Henkin, Leon 67
Hintikka, Jaakko 67
Horn sentence 479
Horn sentence, conditional form of 481
Horn sentence, satisfaction algorithm for 479 481 484
Horn, Alfred 479
Idempotence of 119
Idempotence of 119
Identity 25 37
Identity in proofs 49
Identity, elimination 55
Identity, introduction 55
Identity, reflexivity of 50 51
Identity, symmetry of 50 51
Identity, transitivity of 51
if  then else 194
IFF 182
Implicature 187 188 244—247 381
Inclusive disjunction 74
Incompleteness theorem 526 552—555
Inconsistent premises 140
Independence 297
Independence lemma 531
Indirect proof 136—138
Indiscernibility of identicals 49 51
Individual constants 19 20 32
Induction 376
Induction and proving programs correct 458—464
Induction on the natural numbers 453—455
Induction step of proof by induction 449
Induction, mathematical 70 442
Inductive clause of inductive definition 444 445
Inductive definition 39 442—445
Inductive definition in set theory 451—453
Inductive definition, base clause 444 445
Inductive definition, inductive clause 444 445
Inductive definition, theory of 465
Inductive hypothesis 446
Inductive proof 445—449
Infix notation 23 33 37 38 90
Inherently vacuous claim 246
Instantiation, existential 322—323
Intended domain of discourse 236
Interpreted language 15
Intersection 415 416
Introduction rules 142
Intuitionism 355
Invariance under motion 400 401
Inventor's paradox 447
Inverse 52
Irrational numbers 131 136 205
Irreflexivity 422
Jabberwocky 268
Jeffrey, Richard 555
Kleene, Stephen 515
Language of first-order logic 2
Language of first-order logic for arithmetic 38
Language of first-order logic for set theory 37
Language of first-order logic, expressive limitations 71 85 176 383
Language, artificial 2—4
Language, blocks world 19 21
Language, first-order 28
Language, interpreted 15
Language, natural 4
Language, uninterpreted 15
Law of excluded middle 97
Laws of logic 1
Lemma 452
Levy, Azriel 435
Liar's paradox 555
Literal 68 69 118 122 123 479
Loeb's paradox 556
Loewenheim, Leopold 546
Logical consequence 2 4—5 505 526
Logical dependence 51 105
Logical truth 94 505
Logical validity 42
Logically equivalent wffs 276
Los, J. 400
Lower predicate calculus 2
Lowwenheim — Skolem Theorem 546
Mary Ellen's World 496 498 499
Material biconditional 181 198
Material conditional 178
Material conditional, usefulness of 198
Meaning 84
Meaning postulates 284
Method of counterexample 5 15 63
Method of proof 5 46 128 198 329
Method of proof by cases 131—134
Method of proof by contradiction 136—138
Method of proof, conditional 199
Method of proof, conditional, general 325
Mixed quantifiers 293 296 329
modus ponens 198 199 206
Modus Tollens 203 212
Monkey principle 187
Monotone operator 465
Multiple quantifiers 289
Names 19 20
Names in English 20
Names, introducing new 29
Natural deduction 142
Natural language 4
Necessary condition 179
Necessary TT- 102
Necessary TW- 102
Necessary, logically 103 137
Negation 67 68
Negation, double 68 83 83
Negation, elimination 155
Negation, introduction 136 155
Negation, normal form 118—122
Negation, scope of 80
Non-logical truth in all worlds 363
Nonstandard models of arithmetic 548
Nonstandard models of set theory 547
Normal form, conjunctive (CNF) 121—125 312 479
Normal form, disjunctive (DNF) 121—125
Normal form, negation 118—122
Normal form, prenex 281 311—315
Normal form, Skolem 515
Noun phrase 239
Noun phrase, complex 243
Noun phrase, plural 398
Noun phrase, quantified 298 304
Noun phrase, quantified, existential 243 247
Noun phrase, quantified, universal 243 248
Null quantification 281
Numerical claim 366 374
Ordered pair 420 421
PA 456
Palindrome 448 450
Paraphrasing English 300
| Parentheses 79 80 101 147 148 233
Parentheses, alternatives to 90
Partition 426
Peano arithmetic 456—457
Peano, Giuseppe 3 456
Peirce, Charles Sanders 3
Persistence through expansion 400
Persistence under growth 401
PHRED 260—261
Plural noun phrases 398
Polish notation 90 91 196
Possessives 515
Possible TT- 102
Possible TW- 102
Possible, logically 95 137
powerset 429
Powerset axiom 436
Predicate 19 21 25
Predicate argument 21
Predicate arity 21
Predicate symbols 20
Predicate vs function symbol 32
Predicate, extension of 422 497 498
Predicate, introducing new 28
Prefix notation 23 33 90
Premises 41 44
Premises, inconsistent 140
Prenex form 281 289 311—315 520
Presuppositions 286
Presuppositions and determiners 380
Presuppositions and the axiomatic method 287
Prime number 242 332 333
PROLOG 3
proof 46 49 103
Proof by cases 131—134
Proof by contradiction 136—138
Proof by induction, basis 449
Proof by induction, induction step 449
Proof of nonconsequence 15 63
Proof of uniqueness claims 375
Proof strategy 167 171 206 210 352
Proof with no premises 173
Proof, advantages over truth tables 127
Proof, conditional 199
Proof, discovery of the notion of 287
Proof, formal vs informal 48—49
Proof, general conditional 323—327 329 342
Proof, indirect 136—138
Proof, informal, purposes of 129—130
Proof, informal, style 48 129
Proof, involving numerical determiners 374—376
Proof, involving the identity symbol 49
Proof, purported 327
Proof, step 198 319
Proof, working backwards 167
Proposition 24
Quantification, numerical 366—371
Quantification, numerical, and proofs 374—376
Quantified noun phrase 227 298 304
Quantifier equivalences 280 282
Quantifier scope 233
Quantifier uniqueness 375
Quantifier, existential 230—231
Quantifier, universal 230
Quantifiers 3 32 227 230—231 239
Quantifiers, alternations of 312
Quantifiers, alternative notation for 255—256
Quantifiers, DeMorgan laws for 279
Quantifiers, first-order 257
Quantifiers, game rules for 237—238
Quantifiers, generalized, adding to fol 383
Quantifiers, generalized, and vagueness 387
Quantifiers, generalized, logic of 389
Quantifiers, generalized, semantics of 499—500
Quantifiers, mixed 293 296 329
Quantifiers, monotone 390
Quantifiers, multiple 289
Quantifiers, second-order 257
Quantifiers, semantics for 234—238
Range of a function 428
Rational inquiry 1—2 4
Rational number 131
Reasoning, invalid 1
Reasoning, valid 1
Reductio ad absurdum 136—138
Reference columns 96
Referent of a name 497 498
Reflexivity 52 422
Reflexivity of identity 50
Reit 56
Reiteration 56 151
Relations, antisymmetric 422
Relations, asymmetric 422
Relations, binary 422
Relations, equivalence 424—425
Relations, functional 427
Relations, inverse 423
Relations, irreflexive 422
Relations, modeling in set theory 422—425
Relations, reflexive 422
Relations, transitive 422
Relative complement 440
Replacement method 270—271
Resolution clause 488
Resolution method 54 489—491 519 524
Resolution method for fol 516 521
Resolution method, completeness of 493
Resolution method, soundness of 493
Resolvent 489 490
Rules, default use of 143 145 153 161 208 345 349
Rules, elimination 142
Rules, introduction 142
Russell paradox 406 432 433
Russell set for a set 430 431
Russell set for a set, absolute version 432
Russell's Theorem 362
Russell, Bertrand 430
Russellian analysis of both and neither 382
Russellian analysis of definite descriptions 379 382
Russellian analysis of definite descriptions, Strawson's objection 381
Satisfaction 234 500 502 506
Satisfaction, algorithm for Horn sentences 479 481 484
Satisfiability 373 469
Satisfiable truth table (tt-) 469
Saturday Night Live 304
Scope 80
Second-order logic 257
Semantics for connectives 68 72 75 178 182
Semantics for quantifiers 234—238
Semi-wff 449
Sentence 232 231—233
Sentence, atomic 19 23 23 25 32 51
Sentence, complex 67
Sentence, existential 400
Sentence, Horn 479 481
Sentence, normal forms 124
Sentence, satisfiable 373
Sentence, universal 520
Set theory 435
Set theory, first-order language of 37
Set, conception of, naive 405—411 416 432—434 436 439
Set, conception of, von Neumann's 435 436 438
Set, conception of, Zermelo's 438
Set, empty 407 412
Set, membership 37
Set, singleton 412 420 440
Sets, cummulative 438—439
Sets, infinite 437—438
Sets, size of 437
simplification 129
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