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Kneebone G.T. — Mathematical Logic and the Foundations of Mathematics: An Introductory Survey
Kneebone G.T. — Mathematical Logic and the Foundations of Mathematics: An Introductory Survey

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Название: Mathematical Logic and the Foundations of Mathematics: An Introductory Survey

Автор: Kneebone G.T.

Аннотация:

Graduate-level historical study is ideal for students intending to specialize in the topic, as well as those who only need a general treatment. Part I discusses traditional and symbolic logic. Part II explores the foundations of mathematics, emphasizing Hilbert’s metamathematics. Part III focuses on the philosophy of mathematics. Each chapter has extensive supplementary notes; a detailed appendix charts modern developments.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1963

Количество страниц: 435

Добавлена в каталог: 30.11.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
AND-OR tree      186
And-parallelism      188
Apt, K.      212 292
assertion      203
ASSIGNMENT      17 105
atom      13
Atom, ground      140
Axiom      27 43 48 61
Axiom, Gentzen system      45 62 128
Axiom, Hilbert system      48 60—61 129
Axiom, Hoare logic      210
Axiom, number theory      136
Axiom, temporal logic      257
Ben-Ari, M.      292
Binary decision diagram      81—95
Binary decision diagram, apply      86 90
Binary decision diagram, complexity      90
Binary decision diagram, definition      85
Binary decision diagram, implementation      92—95
Binary decision diagram, model checking      278
Binary decision diagram, ordered      89
Binary decision diagram, quantify      92 279
Binary decision diagram, reduce      83 89
Binary decision diagram, restrict      91 279
Boolean operator      2 9
Boolean operator, associativity      16 22
Boolean operator, commutativity      22
Boolean operator, conjunction      10
Boolean operator, disjunction      10
Boolean operator, equivalence      10
Boolean operator, exclusive or      10
Boolean operator, implication      10
Boolean operator, minimal set      23—24
Boolean operator, nand      10 23
Boolean operator, negation      9
Boolean operator, nor      10 23
Boolean operator, precedence      16
Boolean operator, principal operator      16
Bryant, R.      89—90 291
Cantor, G.      289
Cardinality      288
Cartesian product      287
Characteristic predicate      202
Church's Theorem      122
Church, A      121
Clausal form      68 142
Clause      68
Clause, clashing      71 152 164
Clause, empty      70
Clause, fact      176
Clause, goal      173 176
Clause, ground      142
Clause, guarded      192
Clause, Horn      176
Clause, parent      72 152
Clause, parity      97
Clause, program      176
Clause, subsume      70
Clause, unit      68
Clocksin, W.      292
Closed, atomically      33
Closure, existential      104
Closure, reflexive transitive      240 246 287
Closure, universal      104
co-NP=NP?      96
Compactness theorem, predicate calculus      121
Compactness theorem, propositional calculus      59
Completeness, Hoare logic      218
Completeness, predicate calculus, Gentzen system      128
Completeness, predicate calculus, Hilbert system      131
Completeness, predicate calculus, resolution      169
Completeness, predicate calculus, semantic tableaux      141
Completeness, predicate calculus, SLD-resolution      178
Completeness, propositional calculus, Gentzen system      47
Completeness, propositional calculus, Hilbert system      56—57
Completeness, propositional calculus, resolution      74—78
Completeness, propositional calculus, semantic tableaux      34—38
Completeness, relative      202
Completeness, strong      58
Completeness, temporal logic      262—264
complexity      95 99
Component graph      250 254
Computation rule      175
Conjunctive normal form      67
Consistency      57 136—137
Consistent      see "Theory consistent"
Consistent, maximally      65
Constant      102
Constrain-and-generate      196
Cook, S.      96
Correct answer substitution      176
Creswell, M      292
De Morgan's laws      23 68
Decision procedure      25 43
Decision procedure, predicate calculus      102 112 121—124 153 165
Decision procedure, predicate calculus, solvable cases      124
Decision procedure, propositional calculus      25 34 100
Decision procedure, temporal logic      252
Deductive system      43
Derivation tree      13
Derived rule      48
Deterministic algorithm      95
Diller, A.      292
Disjunctive normal form      99
Domain      105 117 140 149 196 202 210 288
Dreben, B.      124 291
Duality      25 108 138 208 239 240 257 259 260
Eight-queens problem      194
Even, S.      250
Existential quantifier      103
Exponential time      95
Expression      154
Factoring      164
Failure node      75 169
Falsifiable predicate calculus      106
Falsifiable propositional calculus      24
Fitting, M.      291
Flip-flop      272 281
Formation tree      13
Formula, atomic      103
Formula, closed      104 106
Formula, complementary      30
Formula, condensable      125
Formula, future      241 250 260
Formula, ground      140
Formula, monadic      124
Formula, next      241
Formula, predicate calculus      103
Formula, propositional calculus      13
Formula, pure      120 124
Frame      241
Francez, N.      292
Fulfil      244 248 250 254
Function      139
Galil, Z.      291
Generalization      see "Rule of inference generalization"
Generate-and-test      194
Gentzen system, Hauptsatz      64
Gentzen system, predicate calculus      127—128
Gentzen system, propositional calculus      45—48
Gentzen system, sequent      62
GHC      192—194
Goedel, K.      136
Goldbach's conjecture      5
Goldfarb, W.      124 291
Grammar      3 12
Gries, D.      291
Ground instance      140 142
Haken, A.      98
half-adder      3 99
Harel, D.      291
Herbrand base      149
Herbrand interpretation      149
Herbrand model      149
Herbrand universe      148
Herbrand's theorem      150—151
Hilbert system, predicate calculus      129—135
Hilbert system, propositional calculus      48—59
Hilbert system, variants      60
Hilbert's program      2
Hintikka set, predicate calculus      117
Hintikka set, propositional calculus      36
Hintikka structure, temporal logic      243 247 248
Hintikka's lemma, predicate calculus      117
Hintikka's lemma, propositional calculus      37
Hintikka's lemma, temporal logic      249
Hoare logic      209—219
Hopcroft, J.      13 122
Horn clause      172
Hughes, G.      292
Huth, M.      63 266 291
Idempotent      22 171
Incompleteness theorem      136
Induction      290
Inference node      76 169
Instance      154
Integers      283
Interpretation, finitely presented      245
Interpretation, predicate calculus      105 140
Interpretation, propositional calculus      17
Interpretation, temporal logic      237
Intuitionistic logic      6
Invariant      206 211 263
Jaffar, J.      199 292
Lewis, H.      124 291
Lifting lemma      167
Lindenbaum's Lemma      137
Literal      30 113 124
Literal, complementary      30 72 152
Lloyd, J.      179 180 292
Logic programming      5 173—199
Logic programming, concurrent      186—194
Logic programming, constraint      194—199
Logical consequence      27 107
Logical equivalence      19 107
Loveland, D.      292
Lowenheim — Skolem theorem      121
Lowenheim's theorem      121
Lukasiewicz, J.      15
Maher, M.      199 292
Manna, Z.      267 277 292
Martelli, A.      292
Matrix      142
McMillan, K.      292
Mellish, C.      292
Mendelson, E.      61 124 134 136 291
Metalanguage      19
Minsky, M.      122
Modal logic      6 236
Model      24 26
Model checking      272—280
Model checking, implementation      279—280
Model checking, symbolic      277
Model, finite      112 120
Model, finitely presented      252
Model, predicate calculus      106
Model, temporal logic      238
modus ponens      see "Rule of inference modus
Monk, D.      61 291
Montanari, U.      292
n-tuple      286
Natural deduction      63
Natural numbers      284
Nerode, A.      124 291
Nondeterministic algorithm      95
NP-complete      96
Object language      19
Olderog, E.-R.      212 292
Or-parallelism      188
P=NP?      96
Partial correctness      203 211
Peterson's algorithm      269 272
Pnueli, A.      267 277 292
Polish notation      15
Polynomial time      95
Postcondition      203 222
Potter, B.      292
Precondition      203 222
Predicate calculus      3 101—138
Predicate transformer      204
Prefix      124 142
Prenex conjunctive normal form      124 142
preorder traversal      14
Procedure      176
PROGRAM      202
Program specification      4
Program specification in Z      221
Program specification, concurrent      266—267
Program verification      4 211—213
Program verification, concurrent      269—272
Program, concurrent      266
Program, logic      176
Program, semantics      4 202—209
Program, synthesis      213—216
Programming language, CHIP      198
Programming language, CLP($\mathcal{R}$)      199
Programming language, PASCAL      4 5 104 205 269
Programming language, PROLOG      5 181—185
Programming language, Prolog, cut      184
Programming language, Prolog, non-logical predicate      183
proof      43
Proof checker, predicate calculus      134—135
Proof checker, propositional calculus      59—60
Propositional calculus      2 9—100
RANGE      288
Reductio ad absurdam      see "Rule of inference reductio
Refutation      25 73 180
Relation      101 105 287
Renamable-Horn      172
renaming      71
Rescher, N.      292
Resolution      5
Resolution, general      164—169
Resolution, ground      152—153
Resolution, predicate calculus      139—172
Resolution, predicate calculus, implementation      170
Resolution, propositional calculus      67—80
Resolution, propositional calculus, complexity      96—98
Resolution, propositional calculus, implementation      78—80
Resolvent      72 152
Robinson, J.      67 153 159
Rule of inference      43
Rule of inference, C-Rule      133
Rule of inference, contrapositive      50
Rule of inference, cut      64
Rule of inference, deduction      49 130
Rule of inference, double negation      52
Rule of inference, exchange of antecedent      51
Rule of inference, generalization      129 257
Rule of inference, Gentzen system      45 62 128
Rule of inference, Hilbert system      129
Rule of inference, modus ponens      48 129 257
Rule of inference, modus tollens      64
Rule of inference, reductio ad absurdum      53
Rule of inference, structural induction      17
Rule of inference, temporal logic      257
Rule of inference, transitivity      51
Ryan, M.      63 266 291
Satisfiable predicate calculus      106
Satisfiable propositional calculus      24 26
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