Logic and Databases: The Roots of Relational Theory

Voorkant
Trafford Publishing, 2007 - 445 pagina's
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Logic and databases are inextricably intertwined. The relational model in particular is essentially just elementary predicate logic, tailored to fit the needs of database management. Now, if you're a database professional, I'm sure this isn't news to you; but you still might not realize just how much everything we do in the database world is - or should be! - affected by predicate logic. Logic is everywhere.

So if you're a database professional you really owe it to yourself to understand the basics of formal logic, and you really ought to be able to explain (and perhaps defend) the connections between formal logic and database management. And that's what this book is about. What it does is show, through a series of partly independent and partly interrelate essays, just how various crucial aspects of database technology-some of them very familiar, others maybe less so- are solidly grounded in formal logic. It is divided into five parts:

*Basic Logic
*Logic and Database Management
*Logic and Database Design
*Logic and Algebra
*Logic and the Third Manifesto

There's also a lengthy appendix, containing a collection of frequently asked questions (and some answers) on various aspects of logic and database management. Overall, my goal is to help you realize the importance of logic in everything you do, and also- I hope- to help you see that logic can be fun.

 

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Geselecteerde pagina's

Inhoudsopgave

A little history
207
Sixth normal form
209
Answers to exercises
210
Denormalization Considered Harmful
215
Denormalize for performance?
216
What does denormalization mean?
217
Definitions
218
Examples
219

A closer look at quantifiers
19
Customer must place order
25
How logic helps
28
Concluding Remarks
30
Terminology
31
Answers to exercises
33
Some Operators Are More Equal than Others
41
The universe of discourse
42
Identity
43
Equality
45
Logical equivalence
47
Other kinds of equivalence
54
Biimplication
55
Concluding remarks
61
References and bibliography
62
Equality in SQL
63
LOGIC AND DATABASE MANAGEMENT
65
Constraints and Predicates
67
Values and variables
69
The suppliersandparts database
70
A closer look at Example 1
73
Constraints are propositions
76
Relvar and database constraints
78
A note on constraint checking
79
All checking is immediate
80
Multiple assignment
82
Relvar predicates
84
Correctness vs consistency
86
A note on database design
87
Predicates for derived relvars
88
A constraint classification scheme
89
Concluding remarks
91
Acknowledgments
92
References and bibliography
93
The Closed World Assumption
95
Basic assumptions
96
Why the CWA is preferred
100
Relvar predicates revisted
104
Putting it all together
106
Dealing with uncertainty
107
Negation and disjunction
109
Concluding remarks
113
Acknowledgments
114
What about outer join?
116
Why Relational DBMSs Must Be Based on Logic
119
Propositional calculus
121
Logical systems is general
123
Predicate calculus
127
The DBMS as a logical system
129
Concluding remarks
131
References and bibliography
132
Why Relational DBMS Logic Must Not Be ManyValued
135
A classification scheme
137
Fragments
138
Extensions and deviants
139
Additional complexities
142
Other manyvalued logics
147
Relational threevalued logics
148
References and bibliography
149
Some useful 2VL tautologies
150
LOGIC AND DATABASE DESIGN
153
All for One One for All
155
How many case are there?
157
Examples of confusion
161
Concluding remarks
172
References and bibliography
175
Normalization from Top to Bottom
177
Relvars and keys
178
Defining the problem
180
Join dependencies
183
Fifth normal form
188
Join dependencies are integrity constraints
189
Multivalued dependencies
191
Fourth normal form
199
BoyceCodd normal form
201
Concluding remarks
202
Acknowledgments
203
Wheres do we stop?
221
What denormalization isnt
222
What denormalization isns bis
225
The usability argument
226
The integritry argument
228
Concluding remarks
232
LOGIC AND ALGEBRA
235
Why Is It Called Relational Algebra?
237
Basic algebra
238
Generalizing basic algebra
242
Isomorphism
246
Boolean algebra
248
The algebra of sets
252
Matrix algebra
255
Relational algebra
256
Concluding remarks
262
Acknowledgments
269
References and bibliography
270
Why is it called relational calculus?
272
Semijoin and Semidifference
275
Semijoin
276
Semidifference
277
More on semijoin
278
More on semidifference
280
The Theory of Bags An Investigative Tutorial
283
Containment and inclusion
284
Union intersection difference and product
285
Union plus and intersection star
288
Restriction
289
What about complements?
290
The algebra of set
292
An algebra of bags
294
Concluding remarks
297
Acknowledgments
298
LOGIC AND THE THIRD MANIFESTO
299
Godel Russell Codd A Recursive Golden Crowd
303
Discussion
304
Remarks on Tutorial D
305
A remark on the third
306
References and bibliography
308
To Be Is to Be a Value of a Variable
309
Critic As objections
311
Critic objections
316
Multiple assignment
324
Database values and variables
326
Concluding remarks
327
And Now for Something Completely Computational
329
Decidability
330
Computational completeness implies undecidability
331
Does Codd avoid the trap?
332
Why we want computational completeness
334
Does it all matter?
335
References and bibliography
337
The Logic of View Updating
339
Database variables
341
Compensatory updates
344
The principle of interchangeability
346
Database inclusion and equivalence
347
Total mapping
349
Partial mappings
353
Darwens overall objections
358
Darwens detailed objections
359
Darwens objections to orthogonality
367
Darwens proposals
369
Conclusion remarks
373
References and bibliography
374
Frequently Asked Questions
377
Relational algebra
381
Relvar predicates
387
Relation valued attributes
391
Keys and further normalization
397
Missing information
409
Variables types and constraints
412
SQL criticisms
422
References and bibliography
434
Index
439
Copyright

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Over de auteur (2007)

C.J. Date has a stature that is unique within the database industry. C.J. is a prolific writer, and is well-known for his best-selling textbook: An Introduction to Database Systems (Addison Wesley). C.J. is an exceptionally clear-thinking writer who can lay out principles and theory in a way easily understood by his audience.

Bibliografische gegevens