Unknown values the relational database model [PhD Thesis]

Karen Laura Kwast “Unknown values the relational database model” (PhD Thesis, 1992) ......Page 1
Table of contents ......Page 6
1. Introduction ......Page 10
Part I. Formalization of the model ......Page 20
2.1 The relational scheme ......Page 22
2.2 The database model ......Page 25
2.3 Database integrity ......Page 27
2.4 Relational views ......Page 28
3.1 Relational algebra ......Page 32
3.2 Cylindric algebra ......Page 37
3.3 The relational calculus ......Page 43
3.4 Codd-completeness ......Page 47
4.1 Renaming attributes ......Page 54
4.2 Relational equivalences ......Page 55
4.3 Normalization through renaming ......Page 57
4.4 A normal form for almost all terms ......Page 60
4.5 Normalization and predicate logic ......Page 63
Part II. Integrity Constraints ......Page 64
5.1 Constraint satisfaction ......Page 66
5.2 Modal logic ......Page 67
5.3 What should hold ......Page 69
5.4 Believing what is acceptable ......Page 71
5.5 Nested constraint sets ......Page 75
5.6 Partitioned constraint sets ......Page 76
5.7 Related work ......Page 78
5.8 Sources of accessibility ......Page 80
6.1 The Closed World Assumption ......Page 82
6.2 Reiter’s “On Integrity Constraints” ......Page 84
6.3 A knowledge base must be closed ......Page 88
6.4 The proper expression of constraints ......Page 90
6.5 Accidental constraint satisfaction ......Page 93
Part III. Weak equivalence ......Page 94
7.1 Aggregate functions ......Page 96
7.2 General selections ......Page 98
7.3 The calculation operator ......Page 100
7.4 The projection-selection operator ......Page 103
7.5 Equivalent selection clauses ......Page 106
7.6 Weak equivalence ......Page 107
8.1 Definition of weak implication ......Page 112
8.2 Rules for strong implication ......Page 117
8.3 Rules for weak implication ......Page 120
8.4 System WJ is complete ......Page 126
8.5 Turning rules into axioms ......Page 132
8.6 Strong implications and classical logic ......Page 137
8.7 Inferences among weak implication ......Page 141
9.1 Substitution ......Page 146
9.2 Weak equivalence and constraint satisfaction ......Page 149
9.3 Weak equivalence and constraint solving ......Page 151
9.4 Weak equivalence and integrity constraints ......Page 154
Part IV. Nulls in a relational database ......Page 158
10.1 Codd’s null values ......Page 160
10.2 Indexed nulls ......Page 167
10.3 Nulls in SQL ......Page 168
11.1 Presuppositions ......Page 176
11.2 A Kripke model for nulls ......Page 178
11.4 Nulls and integrity ......Page 181
12.1 Alternative proposals ......Page 190
12.2 Choices made ......Page 196
12.3 Correlations ......Page 198
12.4 Aside: Dishkant’s finite predicate logic ......Page 199
13.1 The underlying model ......Page 206
13.2 The semi-classical model ......Page 208
13.3 The partial model ......Page 210
13.4 Answers known to be true ......Page 211
13.5 Fairness ......Page 215
13.6 Full safety ......Page 218
13.7 Codd tables ......Page 225
13.8 The meaning of nulls ......Page 227
13.9 Computable queries ......Page 229
14. Conclusion ......Page 232
Bibliography ......Page 234
Index ......Page 241
Acknowledgements ......Page 246
Samenvatting ......Page 247
Stellingen ......Page 249