Davis R.E. — Truth, Deduction, and Computation: Logic and Semantics for Computer Science :: Электронная библиотека попечительского совета мехмата МГУ

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Davis R.E. — Truth, Deduction, and Computation: Logic and Semantics for Computer Science

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Название: Truth, Deduction, and Computation: Logic and Semantics for Computer Science

Автор: Davis R.E.

Язык:

Рубрика: Технология/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1989

Количество страниц: 281

Добавлена в каталог: 28.01.2014

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

Предметный указатель

$( )_{i}$       133
      165
      185
      164 216
-solvable      158
th main argument      171
      216
      166
$P((\underline{S}))$       72
$y_{\lambda}$       171
$\alpha$ -conversion      150
$\beta$ -contraction      157
$\beta$ -expansion      157
$\beta$ -red      157
$\beta$ -redex      157
$\beta$ -reduction      150 157
$\bot$ (bottom)      179
$\circ$ (composition)      165
$\eta$ -contraction      157
$\eta$ -expansion      157
$\eta$ -red      157
$\eta$ -redex      157
$\eta$ -reduction      157
$\exists$ (existential quantifier)      45
$\forall$ (universal quantifier)      45
$\lambda$ -calculus      147
$\lambda$ -calculus, axioms      155
$\lambda$ -calculus, language      151—152
$\lambda$ -calculus, rules of inference      155
$\lambda\beta\eta$ -calculus      155
$\lambda\Omega$ -calculus      201
$\lambda\Omega$ -terms      201
$\mathbf{h}(A)$       58
$\mathbf{k}$       164
$\mathbf{s^*}$       51
$\mathcal{A}(\mathcal{M})$       202
$\mathcal{B}$       164
$\mathcal{B}\mathcal{V}(\mathcal{M})$       153
$\mathcal{F}\mathcal{V}(\mathcal{M})$       153
$\mathcal{H}$ (Herbrand expansion)      72
$\mathcal{L}$       see "Propositional Logic"
$\mathcal{P}\mathcal{C}$       see "Predicate Calculus"
$\mathcal{V}$       189
$\mu$ -operator      108
$\omega$       200
$\Omega$ -conversion      201
$\Omega$ -match      201
$\Omega$ -normal form      201
$\Omega$ -redexes      201
$\Omega$ -reductions      201
$\Phi$       188
$\Psi$       188
$\sqcap$ (box)      25—27
$\sqcap$ (greatest lower bound)      179
$\sqcup$ (least upper bound)      179 185
$\sqsubseteq$ (approximates)      178
$\star$       133
$\tau$       25—27
$\top$ (top)      179
${\eta}_{\infty}$       217
Abstraction      152
Applicative order      160
Approximate      200 201 206
Approximate normal form      200 201 206
Approximate reduction      199
Approximate terms      201
Approximates ( $\sqsubseteq$ )      178
Approximation      175
Arithmetization      130
Arity      44
Atomic formula      45
Axioms      2
Axioms of $\lambda$ -calculus      155
Axioms of $\mathcal{E}\mathcal{N}\mathcal{T}$       117
Axioms of $\mathcal{L}$       20
Axioms of $\mathcal{P}\mathcal{C}$       57
Basis      186
Best direct approximant      201
body      149 152
Boehm, C.      194
Bottom ( $\bot$ )      179
Bound occurrence      46 153
Bound variable      46 149 152 153
Bounded $\mu$ -operator      114
Bounded product      113
Bounded quantifiers      114
Bounded sum      113
Box ( $\sqcap$ )      25—27
Bv (bound variable)      152
Call-by-name      160
Call-by-value      160
Chain      185
Characteristic function of a relation      110
Characteristic function of a set      110
Church — Rosser Theorem      161
Church's thesis      125
Church, Alonzo      107
Clash      73
Clausal form      64
Clause      64—65
Clause ground      29
CLE      25
Closed term      158
Closed wff      49
Closure      53 68
Combination      152
Combinators      158
Common instance      74
Compactness      5
Complementary literal elimination      25
complete      195
Complete lattice      179
Complete partial orders      182
Complete, computation scheme      7
Complete, theory      6
Composition (f $\circ$ g)      165
Computation, vi      167
Computationally semi-discrete      215
Consistent      162
Consistent, theory      7 122
context      156
continuous      184
Contractum      157
Contradictory      54
conversion rules      155
Convertible      157
Countable      2
Currying      150
Decidable property      7
Decidable theory      7
Deducibility, properties of      4
Deducible from      4
Deduction      vi
Deductive system      vi 1
Definition by cases      115
Denumerable      2
Depends upon      60
Derivation      4
Deterministic computation      vi
Direct approximant      201
Direct consequence      2
Directed set      183
Directed set, interesting      185
Disagreement set      75
Domain      49 178
Effective procedure      7
Elementary number theory      105
Elementary Number Theory, $\mathcal{E}\mathcal{N}\mathcal{T}$ , axioms      117—118
Elementary Number Theory, $\mathcal{E}\mathcal{N}\mathcal{T}$ , language      105—106
Elementary Number Theory, $\mathcal{E}\mathcal{N}\mathcal{T}$ , rules of inference      118

Enumeration model      176
Environment      188
Equal in $D_{\infty}$       190
Essentially undecidable      142
Existential quantifier ( $\exists$ )      45
Expressible      128
Expression      2
Extended environment      189 190
False in a given interpretation      52
Finite approximations      175
Finite extension      140
First-order predicate calculus      57
First-order theory      44
First-order theory with equality      121
First-order theory, axioms      57
First-order theory, language      44
First-order theory, language, symbols      44
First-order theory, language, wffs      45
Fixed point      184
Fixed point operator      184
Formal theory, vi      2
Free for      47
Free occurrence      46 153
Free variable      46 153
Functional extensionality      156
General recursive function      107 109
General recursive relation      110
Goedel number of expression      131
Goedel number of sequence of expressions      132
Goedel number of symbol      130
Greatest lower bound ( $\sqcap$ )      179
Ground (gr)      28
Ground (gr) clause      29
Ground (gr) resolution      25 32
Ground (gr) resolvent      29
H.n.f.      171
Head context      159
Head normal form      viii 170—172
Head redex      171
Head reduction      172
Head variable      171
Herbrand domain      72
Herbrand expansion ( $\mathcal{H}$ )      72
Herbrand's theorem      73
Hereditarily undefined      168
Higher-order theory      44
Hilbert programme      106
Hilbert, David      106
Horn clause      83
Identifier      152
Incomparable      180 194
Incompleteness      107
Infinite objects      175
Initial functions      107
Instance      3
int      107
Interconvertible in the limit      217
Interpretation      49
Interpretation of a theory      5
Intuitive Number Theory      107
Invertibility      90
Join      179 185
Juxtaposition      133
Lambda calculus      147
Lambda Calculus, axioms      155
Lambda Calculus, language      151—152
Lambda Calculus, rules of inference      155
Lattice, complete      179
Lattice, flat      181
Least fixed point operator      185
Least upper bound ( $\sqcup$ )      179
Lexical order      66
LIMIT      185
Limit point      186
Limiting completeness      196
Logical axioms      57
Logical consequence      55
Logically equivalent      55
Logically false      55
Logically imply      55
Logically true      55
Logically valid      54
Matrix      67
Meet      179
META      5
Metavariables      2
Model      6
Modus ponens (MP)      2
Monotonic      5 183
Monotonicity      5
Most general unifier      75
MP      see "Modus ponens"
NeXT      107
Non-monotonic      5
Nondeterministic computation      vi
Nonterminating programs      173
Normal form      viii 160 164
Normal order reduction      163
Normal-order      160
Paradoxical combinator      160
Parentheses      152
Partial normal form      200
Partial objects      176
Partial order      178
Partial terms      199
PR (primitive recursive)      111
Predicate calculus      43
Predicate Calculus, $\mathcal{P}\mathcal{C}$ , axioms      57
Predicate Calculus, $\mathcal{P}\mathcal{C}$ , language      44—45
Predicate Calculus, $\mathcal{P}\mathcal{C}$ , rules of inference      58
Prefix      67
Prenex form      67
Primitive recursive function      108
Primitive recursive relation      110
Primitive recursive set      110
Projection function      108
proof      vi 4 5
Proper axioms      57
Proper elements      181
Proper normal form      201
Propositional logic      11
Propositional Logic, $\mathcal{C}$ , axioms      20
Propositional Logic, $\mathcal{C}$ , language      11—12
Propositional Logic, $\mathcal{C}$ , rule of inference      20
Provable      4
R (recursive)      111
rand      152
Rator      152
Recursion rule      108
Recursive function      109
Recursive function theory      107
Recursive relation      110
Recursive set      110
Reduced approximant      201
Reduction      157
Reduction, approximate      199
Refutation      31 77
Representable      127 128
Resolution      31 77
Resolution, ground      32
Resolvent      76
Resolvent ground      29
Robinson, Raphael      107
Rules of Inference      2
Satisfiable      54
Satisfies      52
Satisfy      52
Schema      2
Scope      152
Scope of connectives      45

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