Converting Subclass Structures to Relations

When we have an isa-hierarchy of entity sets, we are presented with numerous choices of strategy for conversion to relations. Recall we assume that:

Using Null Values to Combine Relations - Comparison of Approaches

There is another way to representing information regarding a hierarchy of entity sets. If we are allowed to use NULL (the null value as in SQL) as a value in tuples, we can handle a hierarchy of entity sets with a single relation. This relation has all the attributes belonging to

Keys of Relations

We say a set of one or more attributes {A1, A2,. . . ,An} is a key for a relation R if: 1. Those attributes functionally determine all other attributes of the relation. That is, because relations are sets, it is impossible for two different tuples of R to agree on all of A1, A2, ... ,An.

Rules About Functional Dependencies

In this section, we shall learn how to reason about FD's. That is, suppose we are told of a set of FDs that a relation satisfies. Sometimes, we can deduce that the relation must satisfy

Trivial Functional Dependencies

A FD A1A2 . . . An → B is said to be trivial if B is one of the A's. For instance, title year → title is a trivial FD. Every trivial FD holds in every relation, since it says that "two tuples that agree in all of A1,

Why the Closure Algorithm Works

In this section, we shall show why the closure algorithm correctly decides whether or not a FD A1A2 . . . An → B follows from a given set of FDs S. There are two parts to the proof:

Decomposing Relations

The accepted way to remove these anomalies is to decompose relations. Decomposition of R involves splitting the attributes of R to make schemas of two new relations. Our decomposition rule also includes a way of populating those relations with tuples by "projecting" the tuples

Boyce-Codd Normal Form

The objective of decomposition is to replace a relation by several that do not exhibit anomalies. There is, it turns out, a simple condition under which the anomalies discussed above can be guaranteed not to exist. This condition is called Boyce-Codd

Multivalued Dependencies

A "multivalued dependency" is an assertion that two attributes or sets of attributes are independent of one another. This condition is, as we shall see, an overview of the notion of a functional dependency, in the sense that every FD implies a corresponding multivalued dependency.

Definition of Multivalued Dependencies

A multivalued dependency (often abbreviated MVD) is a statement about some relation R that when you fix the values for one set of attributes, then the values in certain other attributes are independent of the values of all the other attributes in the relation. More specifically, we say the MVD

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