Chapter10(pdf) - KFUPM Open Courseware

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Inference Rules for FDs • Given a set of FDs F, we can infer additional FDs that hold whenever the FDs in F hold • Armstrong's inference rules: • IR1. (Reflexive) If Y subset-of X, then X -> Y • IR2. (Augmentation) If X -> Y, then XZ -> YZ • (Notation: XZ stands for X U Z) • IR3. (Transitive) If X -> Y and Y -> Z, then X -> Z • Some additional inference rules that are useful: • Decomposition: If X -> YZ, then X -> Y and X -> Z • Union: If X -> Y and X -> Z, then X -> YZ • Psuedotransitivity: If X -> Y and WY -> Z, then WX -> Z • The last three inference rules, as well as any other inference rules, can be deduced from IR1, IR2, and IR3 (completeness property) Copyright © 2007 Ramez Elmasri and Shamkant B. Navathe Slide 10- 22
Normalization of Relations • Normalization: • The process of decomposing unsatisfactory "bad" relations by breaking up their attributes into smaller relations • Normal form: • Condition using keys and FDs of a relation to certify whether a relation schema is in a particular normal form • Normal form of a relation is the highest NF condition that it meets, and hence indicates the degree to which it has been normalized • 2NF, 3NF, BCNF • based on keys and FDs of a relation schema • 4NF • based on keys, multi-valued dependencies : MVDs • 5NF • based on keys, join dependencies d : JDs Copyright © 2007 Ramez Elmasri and Shamkant B. Navathe Slide 10- 23
Page 1 and 2: Copyright © 2007 Ramez Elmasri and
Page 3 and 4: Chapter Outline • Informal Design
Page 5 and 6: Informal Design Guidelines for Rela
Page 7 and 8: A simplified COMPANY relational dat
Page 9 and 10: Two relation schemas suffering from
Page 11 and 12: EXAMPLE OF AN UPDATE ANOMALY • Co
Page 13 and 14: EXAMPLE OF AN DELETE ANOMALY • Co
Page 15 and 16: Null Values in Tuples • GUIDELINE
Page 17 and 18: Copyright © 2007 Ramez Elmasri and
Page 19 and 20: Functional Dependencies (1) • Fun
Page 21: Examples of FD constraints • Soci
Page 25 and 26: Definitions of Keys and Attributes
Page 27 and 28: Normalization into 1NF Copyright ©
Page 29 and 30: Second Normal Form (1) • Uses the
Page 31 and 32: Normalizing into 2NF Copyright © 2
Page 33 and 34: Third Normal Form (2) • A relatio
Page 35 and 36: Normal Forms Defined Informally •
Page 37 and 38: General Normal Form Definitions (2)
Page 39 and 40: BCNF (Boyce-Codd Normal Form) • A
Page 41 and 42: A relation TEACH that is in 3NF but

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