For alphabetization purposes, (a) differences in fonts and case are ignored; (b) quotation marks are ignored; (c) other punctuation symbols—hyphens, underscores, parentheses, etc.—are treated as blanks; (d) numerals precede letters; (e) blanks precede everything else.
≠ (inequality), 54
| (Sheffer stroke), 403
↓ (Peirce arrow), 403
∈ (member of), 91
∉ (not member of), 92
≡ (equivalent to), 125, 209, 367, 400, 412
⇔ (bi-implies, equivalent to), 367
⊂ (properly included in), 93
⊃ (properly includes), 93
⊆ (included in), 93
⊇ (includes), 93
→ (functional dependency), 152, 291
→→ (multivalued dependency), 348
!! (image relation reference), 224
∃ (existential quantifier), 375
∀ (universal quantifier), 375
θ-join, 194-195
1NF, see first normal form
2NF, see second normal form
2VL, see two-valued logic
3NF, see third normal form
3VL, see three-valued logic
4NF, see fourth normal form
5NF, see fifth normal form
access method, 16
ACID properties, 295
aggregate operators, 228-235
relation valued, 252
vs. summaries, see summary
algebra, see relational algebra
ALL BUT, 181-182
ALL or ANY comparison, 63, 432-436
ALTER TABLE, 32, 179, 199, 220
alternate key, 151
AND (aggregate operator), 229, 288, 391
antecedent, 368
Anthony, Susan B., 173
antijoin, 219
Appleby, Sir Humphrey, 443
architecture, 33
Aristotle, 467
arity, 18
arrow (FD), 152
required with subquery, 99, 213, 222, 315, 447, 508, 540
assignment
database, see database assignment
multiple, see multiple assignment
relational, see relational assignment
tuple, see tuple assignment
Assignment Principle, 149, 165, 341, 484
associativity, 199
Atkinson, Malcolm, 468
atomicity
scalar value, 48-52
statement, 145
transaction, 295
attribute-name: type-name pair, 18
extracting value from tuple, 85
heading, 82
“multivalued,” 49
pictured as column, 7
relation, 89
relvar, 141
tuple, 82
SQL, 313
attribute constraint, see constraint
attribute FROM, 85
attribute naming, reliance on, 199-201
attribute ordering (left to right)
in SQL tables, 19
not in relations, 20
attribute value, 82
axiom (database), 160
axiom (logic), 373
bag, 51
Bancilhon, François, 468
bang bang, 224
base relation, 23
base relvar, 141
see also base relation
base table constraint, 293-295
BCNF, see Boyce/Codd normal form
“Big Data,” 532
see also recursion
Billings, Josh, iii
binary relation (mathematics), 466
BNF grammar
SQL, 454-458
Tutorial D, 512-514
body, 89
relvar, 141
BOOLEAN
SQL, 59-60
Boswell, James, 533
bound variable, 377-378
Boyce, Raymond F., 534
Boyce/Codd normal form, 166
Breazu-Tannen, Val, 200
Buneman, Peter, 200
Bush, George W., 374
calculus, see relational calculus
California, 411
candidate key, see key
Cardelli, Luca, 41
cardinality, 89
relvar, 141
cartesian join, 11
cartesian product, see product
CASCADE, 155
CASE, 415
Chaudhuri, Surajit, 533
Chudnovsky, Gregory, 485
Closed World Assumption, 158, 163, 170, 483
closed expression, see expression
closure, 11, 173, 177-180, 202, 330
CNF, see conjunctive normal form
COALESCE, 125-126
Codd, E. F., passim
coercion, 47
SQL, 61-65
UNKNOWN to TRUE, 122, 289, 317
collation, 63
column, see attribute
column constraint, 294
column naming, 97-100
commalist, 7-8
common attribute, 174
commutativity, 198
compensatory action, 337
component (tuple), 82
conjunct, 407
conjunction, 407
conjunctive normal form, 407
CONNECT BY (Oracle), 257
eventual, see eventual consistency
vs. correctness, 302
consequent, 368
attribute, 286
base table, see base table constraint
column, see column constraint
database, see database constraint
inference, 340
is a proposition, 304
multirelvar, see relvar constraint
relvar, see relvar constraint
single relvar, see relvar constraint
state, 305
transition, 305
tuple, 288
type, see type constraint
vs. performance, 305-306
vs. predicate, 301-303
contrapositive, 370-371
contrapositive law, 427
Cornford, Frances, 493
correlated subquery, see subquery
correctness, see consistency
correlated subquery, see subquery
correlation name, 176, 380, 446
not in Tutorial D, 176
cost based optimizing, 196
CREATE ASSERTION, 287-293
cross join, 11
cross product, 11
cursor, 143
CWA, see Closed World Assumption
D_INSERT, 146
expansion, 146
n-adic, 189
Darwen, Hugh, passim
data independence, 17
logical, 200-201, 349-350, 353, 354, 358-359
data model, 18
two meanings, 15
data type, see type
database, passim
collection of propositions, 157-158
logical system, 160
is a tuple, 481
vs. DBMS, 43
database administrator, 45
database assignment, 481
database constraint, 281, 287-295
checked immediately, 296-301
SQL, 293-295
the (total) database constraint, 303
database management system, 43
vs. database, 43
database statistics, 196
database variable, 478, 480-482
Date, C. J., passim
DBA, 45
DBMS, 43
dbvar, see database variable
DCO, 44
de Haan, Lex, iii, xiv, 295, 306, 546
decomposition (missing information)
horizontal, 496-498
vertical, 495-496
DEE, see TABLE_DEE
deferred checking, 299
degree
foreign key, 153
relvar, 141
DELETE, 145
via cursor (SQL), 143
delimited identifier, 313
Derbyshire, John, 217
dereferencing, 67
derived relation, 23
derived relvar, see snapshot; view see also derived relation
DeWitt, David, 468
see also semidifference
direct image, 24
disjoint INSERT, see D_INSERT
disjoint union, see D_UNION
disjointness of types, 52
disjunct, 407
disjunction, 407
disjunctive normal form, 407
DISTINCT, 119-120
“distinct, considered equal,” 64, 453
distributivity, 198
Dittrich, Klaus, 468
DIVIDEBY, 227
DNF, see disjunctive normal form
see also type
domain calculus, 382
“domain check override,” 44
“don’t know” answers, 505-508
dot qualification, 176, 379-380, 445-446
not in Tutorial D, 176
double bang, 224
double negation law, 413
double underlining, 8, 19, 112, 163, 171-172, 231, 264
DUM, see TABLE_DEE
duplicate elimination, 181, 187
in SQL tables, 118-120
not in relations, 19
see also tuple equality
durability, 295
Efrem, Emil, 523
Einstein, Albert, 472
Eliot, T. S., 489
Elmasri, Ramez, 544
Emerson, Ralph Waldo, 281
empty argument, see aggregate operator
empty range, 388-389
empty relation, 90-91
empty set, 85
SQL, 454
empty tuple, 85
empty type, 77-78
encapsulation, 56
EQD, see equality dependency
relation, see relation equality
SQL, 60
tuple, see tuple equality
see also “the same”
equijoin, 195
essentiality, 483
Euclid, iii
euclidean geometry, 469
eventual consistency, 525-527
EXCEPT, 190
exclusive union, 218-219
existential quantifier, 375
EXISTS, 374
iterated OR, 390
see also existential quantifier
explicit table, 444-445
expression
vs. statement, 179
expression transformation, 112, 128-129, 131, 133-134, 411ff
expression vs. statement, 179
EXTEND, 220-222
multiple, 244
see also “what if”
Extensible Markup Language, see XML
extension vs. intension, 158, 170
FD, see functional dependency
Fernandez, Iggy, 511, 527-532, 545
fifth normal form, 360
relvar, 75
“flat relation,” 92
FORALL, 374
iterated AND, 390
vs. COUNT, 395
see also universal quantifier
not fundamental, 156
shorthand, 293
values are tuples, 153
fourth normal form, 348
free variable, 377-378
see also bound variable
functional dependency, 152, 243, 291-292
nontrivial, 167
functional segmentation, see segmentation
Gehrke, Johannes, 547
generated type, 58
generic type, 74
Gennick, Jonathan, 118
Gilbert, W. S., 511
googol, 130
googolplex, 130
Graunt, John, 81
Graves, Robert, 364
gross requirements, 255
GROUP, 246
GROUP BY
redundant, 240-241
Haldeman, H. R., 324
Hall, Patrick, 545
Hardy, G. H., iii
HAVING redundant, 242
relvar, 141
Held, G. D., 545
Hitchcock, Peter, 545
Hodge, Alan, 364
Hodges, Wilfrid, 546
hold (constraint), 282
horizontal decomposition, see decomposition see also sharding
Hynes, Ed, 116
I_DELETE, 147
expansion, 147
identity (equivalence), 412
identity projection, 181
identity restriction, 180
identity value, 184-185
image relation, 223-226, 235-236
implementation, 15
vs. model, 15
implementation defined, 433
implementation dependent, 433
implication, see logical implication
implication law, 413
inclusion, 93
proper, 93
information equivalence, 106, 245, 326, 353, 360-361
Information Principle, 58, 113, 124, 477, 483
INSERT, 145-146
expansion, 146
SQL, 148
integrity constraint, see constraint
intended interpretation, 156
interpretation, see intended interpretation
special case of join, 183
interval, 486-487
introduced name, see WITH
involution law, 413
irrational number, 42
irreducibility (key), 149-150
IS_EMPTY, 93
IS NOT NULL, 131, 137, 138, 502 see also NOT NULL
Jay, Antony, 443
Johnson, Samuel, 533
see also equijoin; θ-join
JOIN (SQL), 185-186
not at outermost level, 4
alternate, see alternate key
foreign, see foreign key
irreducibility, 149-150
primary, see primary key
shorthand, 290
uniqueness, 149
values are tuples, 151-152
see also candidate key
Koppelaars, Toon, xv, 295, 306, 516
Korth, Henry F., 547
lateral subquery, see subquery
Lincoln, Abraham, 398
literal, 71
relation, 89-90
table, see VALUES
tuple, 83-84
see also selector
logical data independence, see data independence
logical implication, 368-369
logical operator, see connective
logical system, 160
Lynn, Jonathan, 443
Magritte, René, 20
Maier, David, 468
Marx, Groucho, iii
MATCHING, 219
materialization (vs. substitution), 331
“materialized view,” see snapshot
MAYBE, 130
McGoveran, David, 493, 544, 546
Melton, Jim, 546
method (SQL), 3
MINUS, see difference
missing information (without nulls), 493-510
model, 18
vs. implementation, 14-18
modus ponens, 373
modus tollens, 373
multidimensional databases, 92
multirelvar constraint, 292
multiple assignment, 254, 300-301
multiple RENAME, 236
multiple SUMMARIZE, 244
multiset, 51
multivalued dependency, 348
MVD, see multivalued dependency
n-adic predicate, 373
n-ary relation, 7
n-ary tuple, see tuple
n-place predicate, 373
n-tuple, see tuple
Nagel, Ernest, 364
NAND, 403-404
natural join, 13
see also join
Navathe, Shamkant, 544
Newman, James, 364
Newton, Isaac, 472
niladic, 373
NO CASCADE, 169
NO PAD, 64
nonscalar, 56
NOR, 403-404
normalized, see first normal form
“NoSQL,” 521-532
NOT MATCHING, 220
NOT NULL, 36, 66, 124-125, 139, 294
not in relational model, 9
not in types, 123
“null value,” 84, 96, 132, 133, 139, 234, 495
nullary relation, 181
object ID, 326
“object oriented model,” 467
“object/relational,” 52
Ohori, Atsushi, 200
Open World Assumption, 163, 170
open expression, see expression
operator, passim
SQL, 3
cost based, 196
see also expression transformation
ORDER, 259
ORDER BY, 19, 259-260, 263, 278
not in views, 259
ordinal position (SQL columns), 20
orthogonality (language design), 47
OWA, see Open World Assumption
PAD SPACE, 64
parameterized type, 74
part explosion, 256
part implosion, 256
performance
not a model issue, 16, 17, 116, 189
vs. constraint, 305-306
see also optimization
Peirce arrow, 403
physical data independence, see data independence
physical representation hidden, 45-46, 54, 58, 282
physical storage
not in relational model, 23-24, 34
Pietarinen, Lauri, 364
pipelining, 177
placeholder, 372
PNF, see prenex normal form
pointer, 67
not in relational model, 67, 78
polymorphic type, 74
possible representation, 72, 282
possibly nondeterministic, 64-65, 341, 452-453
positioned update, 143
predicate, 156
compound, 373
n-adic, 373
n-place, 373
relational expression, 193-194
relvar, see relvar predicate
simple, 373
SQL, 158
vs. boolean expression, 379
vs. constraint, 301-303
predicate calculus, see predicate logic
“predicate transitive closure,” 131, 212
prenex normal form, 382
SQL, 151
primitive operators, 191
principle, 5
Principle of Identity of Indiscernibles, 133, 484
Principle of Interchangeability, 325-327, 484
procedural, 28
procedure (SQL), 3
product (cartesian), 11, 183-184
expanded, 11
extended, 11
special case of join, 183
projection, 181
precedence, 182
proper inclusion, see inclusion
proper subkey, see subkey
proper subset, see subset
proper superkey, see superkey
proper superset, see superset
compound, 367
simple, 367
proto tuple, 379
pseudovariable, 481-482
QBE, see Query-By-Example
quantification, 374-378, 387-394
quantification law, 414
quantifier
don’t need both, 387-388
existential, 374-375
other kinds, 391-394
sequence, 376
universal, 374-375
see also EXISTS; FORALL; UNIQUE
Quarles, Francis, 1
query, 452
query expression, 3
quota query, 259, 262, 276-277
Ramakrishnan, Raghu, 547
RANK, 277
rational number, 42
Reagan, Nancy, 501
real number, 42
recommendations summarized, 516-519
recursion, 254-259
SQL, 256-259
reducibility, see irreducibility
referenced relvar, 153
referencing, 67
referencing relvar, 153
referential constraint, see foreign key
referential integrity, 9
metaconstraint, 304
refresh, see snapshot
Rel, 529
relation, 88-93
n-dimensional, 92
vs. relvar, 24-26
vs. table, 103-104
vs. type, 158-159
see also relvar
relation constant, 327-328
RELATION H, 89
relation heading, 89
relation literal, see relation selector
inference, 178
name, 89
RELATION type generator, 57
relation value, see relation
relation valued attribute, 51, 105, 245-252
relation variable, see relvar
relational algebra, 10-13, 467
generic, 173
purpose, 479
read-only, 174
relational assignment, 10, 25, 145-147, 478-479
not part of algebra, 174
relational calculus, 13, 379-387, 467
relational comparison, 92-93, 251
relational completeness, 396-397, 479-480
relational database, see The Information Principle
relational inclusion, see inclusion
relational model, passim
formal definition, 473-480
informal definition, 6-13
objectives, 482-483
vs. other models, 467-468
relations, tuples, and attributes, 3
relcon, 328
relvar, 26
base vs. stored, 23
constraint, see relvar constraint
predicate, see relvar predicate
virtual, see view
vs. relation, 26
see also relation
relvar constraint, 292
the (total) relvar constraint, 303
relvar predicate, 157
relvar reference, 174
multiple, 236
repeating group, 49
representation vs. type, 45-46, 47, 68, 73
restriction condition, 180
rewrite rule, see expression transformation
rhetoric, 112
Riemann, Bernhard, 472
Robson, Peter, 544
Robinson, Ian, 523
routine (SQL), 3
row, 86-88
row comparison, 87-88
row constraint, 288
row expression, 63
row extraction, 91
row literal, 86
row type (SQL), 65
row type constructor (SQL), 65
row value constructor (SQL), 86
row variable (SQL), 65
relation types, see relation type
RVA, see relation valued attribute
Sagan, Carl, 472
satisfy (constraint), 151, 282
satisfy (predicate), 372
scalar, 56
schema, 523
segmentation, 524-525
SELECT *, 444
SELECT - FROM - WHERE
too rigid, 221
selection, see restriction
scalar, 46, 54, 55-56, 283-284
tuple, 83
self-referencing relvar, 162
semantic optimization, 297-298
semidifference, see NOT MATCHING
semijoin, see MATCHING
“semistructured model,” 467
SEQUEL, 534-535
set level operations, 142-145, 304-305
set membership, 91
Shakespeare, William, 157
sharding, 525
Sheffer stroke, 403
Silberschatz, Avi, 547
Simon, Alan R., 546
single relvar constraint, 292
snapshot, 350-351
Snodgrass, Rick, 469
SQL, passim
departures from relational model, 489-492
expression evaluation, 195
legacy, 488
means the SQL standard, xiv
not the same as the relational model, 2
pronunciation, xiv
vs. Tutorial D, 174-176
SQL:1992, 3, 4, 59, 71, 124, 175, 222, 330 363, 449, 453, 478, 538, 546
SQL:2003, 3, 4, 59, 124, 342, 449, 538, 546
state constraint, see constraint
statement (two meanings), 158, 372
statement vs. expression, 179, 372
Stoll, Robert R., 547
strong typing, 47
Strozzi, Carlo, 521
subject database, 524
subject to (constraint), 282
proper, 167
lateral, 451
subset, 22
proper, 22
substitution procedure, 330
subtuple, see subset
subtype, see type inheritance
Sudarshan, S., 547
SUMMARIZE BY, 238
summary, 238
superkey, 152
proper, 152
superset, 22
proper, 22
symmetric difference, see exclusive union
table
picture of relation, 20
SQL, 95-97
see also relation; relvar
TABLE (conversion operator), 97, 247
TABLE (explicit table), see explicit table
TABLE_DEE
and TABLE_DUM, 74, 94-95, 108, 132, 181, 328, 505-507
identity with respect to join, 184-185
not in SQL, 410
TABLE_DUM, see TABLE_DEE
table equality, see equality
table expression, 3
SQL, 4
table literal, see VALUES
table value constructor (SQL), 95
“tables and views,” 24, 323-324
tables, rows, and columns, 3
target relvar
assignment, 141
foreign key, 153
teddy bear, 171
temporal data, 486
theorem (database), 160
theorem (logic), 373
theory, 471-473
theory is practical, xiii
Third Manifesto, 26, 77, 247, 271, 277, 287, 321, 409, 478, 480, 484-485, 488, 529, 542-543
third normal form, 167
three-valued logic, 120
truth tables, 121
TIMES, 183-184
Todd, Stephen, 545
total database constraint, 303
total relvar constraint, 303
transaction, 295-296
transition constraint, see constraint
transitive closure, 254-256
TransRelationalTM Model, 24, 33, 485, 523, 538
“trigger,” 155
triggered action, 144
truth functional completeness, 130, 369
truth table, see two-valued logic; three-valued logic
truth vs. consistency, see consistency
extracting attribute value from, 85
pronunciation, 3
tuple assignment, 58
tuple calculus, 382
tuple constraint, 288
tuple equality, 22, 85-86, 152
TUPLE H, 83
tuple heading, see heading
tuple join, 108
tuple literal, see tuple selector
tuple projection, 108
tuple selector, 83-84
tuple type, 83
name, 83
TUPLE type generator, 57
tuple union, 108
tuple value, see tuple
tuple valued attribute, 105
Tutorial D, passim
used in The Third Manifesto, 26
vs. SQL, 174-176
TVA, see tuple valued attribute
two-valued logic, 120
scalar vs. nonscalar, 56-58, 475
types are disjoint, 52
user vs. system defined, 42
vs. physical representation, 53
vs. possible representation, see possible representation
vs. relation, see relation
checked on selector invocation, 285
type constructor, 74
type error, 47
type generator, 57
CHAR, 59
RELATION, 57
ROW, 65
TUPLE, 57
type inheritance, 52, 286, 287, 321
type template, 74
“typed table,” 66-67
U_operators, 487
Uhren, Thomas, xvi
UNGROUP, 246
disjoint, see D_UNION
n-adic, 189
with coercion, 62
UNIQUE (quantifier), 391-392
SQL analog, see UNIQUE (SQL)
vs. COUNT, 395
UNIQUE (SQL), 138, 151, 290-291, 392-394, 430-431
UNNEST, 247
uniqueness (key), 149
universal quantifier, 375
see also coercion
UPDATE, 146
via cursor (SQL), 143
update vs. UPDATE, 10
“updating attributes,” 144
“updating tuples,” 143-144
updating views, see view
value, 27
can’t be updated, 27
vs. variable, 27
variable, 27
can be updated, 27
vs. value, 27
vertical decomposition, see decomposition
“materialized,” see snapshot
retrieval, 329-331
two different purposes, 349
updating, 336-349
view constraint, 331-336
view defining expression, 324
view predicate, 328-329
violate (constraint), 282
virtual relation, 23
virtual relvar, see view see also virtual relation
Webber, Jim, 523
Wegner, Peter, 41
Weikum, Gerhard, 533
“what if,” 252-254
“where used,” 256
SQL, 192-193
WITH CHECK OPTION, 325, 341-342
Wittgenstein, Ludwig, 21, 233, 363
Wong, E., 545
Wright, Andrew, 72
wrong answers, 123, 128, 381, 419
XML, 51, 52, 53, 276, 477, 522
XMINUS, 219
XUNION, see exclusive union
Zdonik, Stanley, 468
Zloof, Moshé, 547