Appendix B - Advanced relational database design, first covers the theory of multivalued dependencies; recall that multivalued dependencies were introduced in Chapter 8. The project-join normal form, which is based on a type of constraint called join dependency is presented next; join dependencies are a generalization of multivalued dependencies. The chapter concludes with another normal form called the domain-key normal form. | Appendix B: Advanced Relational Database Design Database System Concepts, 6th Ed. ©Silberschatz, Korth and Sudarshan See for conditions on re-use Appendix B: Advanced Relational Database Design Reasoning with MVDs Higher normal forms Join dependencies and PJNF DKNF Database System Concepts - 6th Edition ©Silberschatz, Korth and Sudarshan Theory of Multivalued Dependencies Let D denote a set of functional and multivalued dependencies. The closure D+ of D is the set of all functional and multivalued dependencies logically implied by D. Sound and complete inference rules for functional and multivalued dependencies: 1. Reflexivity rule. If α is a set of attributes and β ⊆ α, then α →β holds. 2. Augmentation rule. If α → β holds and γ is a set of attributes, then γ α→γ β holds. 3. Transitivity rule. If α → β holds and β →γ holds, then α →γ holds. Database System Concepts - 6th Edition ©Silberschatz, Korth and Sudarshan Theory of Multivalued Dependencies (Cont.) 4. Complementation rule. If α holds. β holds, then α 5. Multivalued augmentation rule. If α ⊆ γ, then γ α δ β holds. 6. Multivalued transitivity rule. If α then α γ – β holds. 7. Replication rule. If α R–β–α β holds and γ ⊆ R and δ β holds and β β holds, then α γ holds, β. 8. Coalescence rule. If α β holds and γ ⊆ β and there is a δ such that δ ⊆ R and δ ∩ β = ∅ and δ γ, then α γ holds. Database System Concepts - 6th Edition ©Silberschatz, Korth and Sudarshan Simplification of the Computation of D+ We can simplify the computation of the closure of D by using the following rules (proved using rules 1-8). Multivalued union rule. If α α βγ holds. Intersection rule. If α holds. Difference rule. If If α β holds and α holds and α γ – β holds. Database System Concepts - 6th Edition β holds and α β holds and α γ holds, then γ holds, then α γ holds, then α β∩γ β–γ ©Silberschatz, Korth and .
