Barwise J., Etchemendy J., Allwein G. — Language, Proof and Logic :: Электронная библиотека попечительского совета мехмата МГУ

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Barwise J., Etchemendy J., Allwein G. — Language, Proof and Logic

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Название: Language, Proof and Logic

Авторы: Barwise J., Etchemendy J., Allwein G.

Язык:

Рубрика: Математика/Алгебра/Математическая логика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1999

Количество страниц: 587

Добавлена в каталог: 09.12.2004

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

$g+{\emptyset}$       501
$\cap$       415
$\cup$       415
$\emptyset$       412
$\exists$       228 230—231
$\exists$ Elim      348
$\exists$ Intro      347
$\forall$       228 230
$\forall$ Elim      342
$\forall$ Intro      343
$\in$       37 406
$\leftrightarrow$       181
$\leftrightarrow$ Elim      209
$\leftrightarrow$ Intro      209
$\mathcal{F}$       54 142 342
$\mathcal{F}_T$       215 470
$\mathcal{H}$       532
$\mathfrak{M}$       498
$\neg$       68
$\neg$ Elim      155 161
$\neg$ Intro      155
$\neq$       68
$\perp$       137 155 157
$\perp$ Elim      159
$\perp$ Intro      156
$\star$       7
$\subseteq$       413
$\to$       178
$\to$ Elim      206
$\to$ Intro      206
$\vdash_T$       470
$\vee$       74
$\vee$ Elim      150
$\vee$ Intro      148
$\wedge$       71
$\wedge$ Elim      143
$\wedge$ Intro      144
$\wp$       429
=      25 37
= Elim      50 51 56
= Intro      50 51 55
Absolute complement      419 440
AC      436
Aczel, Peter      441 465
Addition      129
AFA      441
Affirming the consequent      203 212
Alternative notation      40 66 89 90 196 255—256
Ambig-wffs      444
Ambiguity      4 79 307
Ambiguity and context      304
Ambiguity and inference      308
Ana Con      60 61 114 115 158 272 286
Analytic consequence      60
Antecedent of a conditional      178
Antecedent of a conditional, strengthening      203 212
Anti-foundation axiom      441
Antisymmetry      422
Appropriate variable assignment      501
Arbitrary individual      348
Argument      41 44
Argument of a predicate      21
Argument, sound      43 44 140
Argument, valid      42 44 140
Aristotelian forms      239—242
Aristotle      3 239
Arithmetic, first-order language of      38
Arity      21 23 25
Arity of function symbols      33
Artificial language      2—4
Associativity of $\vee$       118
Associativity of $\wedge$       118
Assumption for conditional proof      200
Assumption for existential instantiation      322
Assumption for general conditional proof      324 343
Assumption for indirect proof      136
Assumption for proof by cases      132
Asymmetry      422
Atomic sentences      19 23 23 25 32
Atomic wff      228—229 231
Automated theorem proving      312
Axiom, Anti-foundation      441
Axiom, Choice      436
Axiom, comprehension      406 409 408—410 433 435
Axiom, Extensionality      407 406—408 435
Axiom, Infinity      436
Axiom, Powerset      436
Axiom, Regularity      436 440 441
Axiom, Replacement      436
Axiom, Separation      435
Axiom, union      435 440
Axiom, Unordered Pair      435
Axiomatic method      283 287 288
Axiomatic method and presuppositions      287
Axioms      47 288
Axioms of Peano arithmetic      456—457
Axioms of set theory      435
Axioms, shape      285 338—340
Axioms, shape, completeness of      512
Background assumptions      287
Barber paradox      333 362
Base clause of inductive definition      444 445
Basis of proof by induction      449
BETWEEN      25
Biconditional      181 198
Biconditional elimination      199 209
Biconditional introduction      209
Binary function symbol      33
Binary relation symbol      308
Binary truth-functional connective      190
Boole      5—10 100
Boole, George      67
Boolean searches      91
Boolos, George      555
Bound variable      232 282
Boxed constant      343 347
Cancellability test      188
Cantor, Georg      406 437 467
Carroll, Lewis      268
Cartesian product      421 440
Cases, proof by      131—134
Chain of equivalences      120 128
Claim      24
Claim, inherently vacuous      246
Clause for resolution      488
Clause, empty      489 524
CNF      124
Commitment      79
Commitment in game      77 78
Commutativity      146
Commutativity of $\vee$       119
Commutativity of $\wedge$       119
Compactness Theorem for first-order logic      527 548
Compactness Theorem for propositional logic      477
Complete deductive system      214 219 361
Complete set of axioms      338
Complete truth-functionally      190 193
Completeness of resolution      491
Completeness theorem      219 526
Completeness Theorem for first-order logic      527
Completeness Theorem for propositional logic      470
Completeness Theorem for propositional logic, reformulation of      472
Completeness Theorem, use of      220
Complex noun phrase      243
Complex term      32 34
Con procedures in Fitch      61
Conclusion      41 44
Conditional      176 178 198 398
Conditional antecedent of      178
Conditional antecedent of strengthening      203 212

Conditional consequent of      178
Conditional consequent of affirming      203 212
Conditional consequent of strengthening      203 212
Conditional consequent of weakening      203 212
Conditional contrapositive of      199
Conditional elimination      198 206
Conditional introduction      206
Conditional proof      199 203 206
Conditional proof, general      323 329 442
Conjunction      67 71 129
Conjunction, elimination      129 143
Conjunction, introduction      129 144
Conjunctive normal form (CNF)      121—125 479
Connectives, truth-functional      67 93 177
Connectives, truth-functional, binary      190
Connectives, truth-functional, Boolean      67
Connectives, truth-functional, semantics for      68 72 75 178 182
Connectives, truth-functional, ternary      195
Consequence      297
Consequence, analytic      60
Consequence, first-order      267 266—273
Consequence, FO      267
Consequence, logical      2 4—5 41 42 44 46 93 110 181 267
Consequence, tautological      110—113 219
Consequence, tautological, in Fitch      114
Consequent of a conditional      178
Consequent of a conditional affirming      203 212
Consequent of a conditional strengthening      203 212
Consequent of a conditional weakening      203 212
Conservativity      389—390
Constructive dilemma      203 212
Context sensitivity      27 304 307
Contradiction      137 155
Contradictory TT-      138
Contradictory, TT-      158
Contraposition      199
Contrapositive      201
Conversational implicature      187 188 244—247 381
Corollary      218
Correctness of axioms      338
Counterexample      5 15 63
Counterexample, first-order      270
Date of Birth Lemma      530
Deduction Theorem      535
Deductive system      54
Definite descriptions, Russellian analysis      379
Definite descriptions, Strawson's objection      381
DeMorgan laws      81 82 83 106 182 312
DeMorgan laws and first-order equivalence      275—279
DeMorgan laws for quantifiers      279 355
Determinate property      22 24
Determiners      227 364
Determiners, anti-persistent      392
Determiners, general form      384
Determiners, generalized, adding to fol      388
Determiners, generalized, binary      397
Determiners, generalized, logic of      394
Determiners, generalized, semantics of      387
Determiners, monotone      366 392
Determiners, monotone, decreasing      391
Determiners, monotone, increasing      390
Determiners, persistent      392—394
Determiners, reducible      385
Discharged assumption      164
Disjunction      67 74
Disjunction, elimination      149
Disjunction, exclusive      74 75
Disjunction, inclusive      74
Disjunction, introduction      129 148
Disjunctive normal form (DNF)      121—125
Distributive laws      122
Distributive laws of $\wedge$ over $\vee$       122 124
DNF      124
DNF sentence      125
Dodgson, Charles      268
Domain of a function      427
Domain of discourse      236 348 496 498
Domain of quantification      236
dot notation      90
Double Negation      68 83 83
Elimination rules      142
Elimination Theorem      528 534
Elimination Theorem, proof of      538
Empty clause      489 524
Empty set      412
Enderton, Herbert      435 555
Equivalence classes      424—425
Equivalence relations      424—425
Equivalence, first-order      267
Equivalence, first-order, and DeMorgan laws      275—279
Equivalence, logical      93 106—109 267
Equivalence, logical, of wffs with free variables      276
Equivalence, tautological      106—109
Euclid's theorem      332
Even number      200 242
Excluded Middle      97 128 174
Exclusive disjunction      74 75
Existential elimination      322 347
Existential generalization      320 321
Existential instantiation      322—323 329 332
Existential introduction      320 347
Existential noun phrase      243
Existential quantifier      230—231
Existential sentence      400
Existential wff      450
Extended discourse      306 307
Extension of a predicate      422 497 498
files, naming      6—7
Files, submitting      5—10
First-order consequence      267 505
First-order languages      2
First-order languages, arithmetic      38
First-order languages, expressive limitations of      397—398
First-order languages, set theory      37
First-order logic      2
First-order logic, language of, (fol)      2
First-order structure      498 495—498 500
First-order validity      267 505
First-order vs. second-order      257
Fitch      5—10 14 58
Fitch bar      43 54
Fitch format      43
Fitch, Frederic      43 54
Fitch-style deductive system      14 54 149 163
Fitch-style deductive system, extended      376
FO Con      115 158 271 272 286 524
Fo-satisfiable      506
Formal proof      54 142 206 376
Formally complete theory      472
Formally consistent theory      471
Free logic      20n
Free variable      232
Frege, Gottlob      3
Function      427
Function symbols      31 31—34 229 308 514 516
Function symbols and quantification      251—253
Function symbols of arithmetic      38
Function symbols, completeness for languages with      544
Function, domain of      427
Function, modeling in set theory      427—428
Function, partial on a domain      427
Function, partial, defined on an object      428
Function, range of      428
Function, total on a domain      427
Functional calculus      2
Game      67 77
Game rules      78 237
Game rules for $\leftrightarrow$       182
Game rules for $\neg$       68
Game rules for $\to$       178

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