Question

What is a functional dependency? What are the possible sources of the information that defines the functional dependencies that hold among the attributes of a relation schema?

Short answer

A functional dependency is a constraint between two sets of attributes in a relation. It exists when a relationship between or among attributes allows you to predict with certainty the value of one attribute given the value of another. The sources of the information that defines the functional dependencies that hold among the attributes of a relation schema are primarily the semantics of the attributes, the constraints and conditions inherent in the data model, and the business rules imposed on the attributes and their relationships.

Step-by-step solution

Define Functional Dependency

A functional dependency is a constraint between two sets of attributes in a relation from a database. If we have an attribute set \(A\) and an attribute set \(B\), then \(B\) is functionally dependent on \(A\) (denoted as \(A \rightarrow B\)), if each value of \(A\) is associated with exactly one value of \(B\). It shows the relationship of one attribute towards another.

Explain the Idea of Relation Schema

A relation schema is a logical definition of a database including relations and the types of attributes. It includes the relation name, attribute names, and the domain of each attribute. Functional dependencies in a relation schema define the constraints between attributes.

Identify Sources of Functional Dependency

The information that defines the functional dependencies among the attributes of a relation schema can come from several sources. The most common sources of this information are the semantics of the attributes, the constraints and conditions specified by the data model, and the business rules that apply to the attributes and their relationships.

Key concepts

Relation Schema

In the realm of databases, a relation schema can be viewed as the blueprint of a database table. It not only names the table but also meticulously defines each column (attribute) and prescribes the type of data each can hold—a date, a number, or a string of text, for example. Much like an architect's plan, the relation schema conveys the structure, but not the content of data stored in the actual table records.

A clear relation schema is essential because it enforces consistency. Every entry in a database table conforms to the schema, which means, for instance, that you always expect a date in a 'birthdate' column and never an arbitrary string or number. Understanding the relation schema is key to grasping how functional dependencies play a role. These dependencies act as a set of rules that dictate how the values of one attribute relate to the values of another—often guiding how data is organized and ensuring its integrity across the database.

Database Constraints

Think of database constraints as the rules and regulations of the data world. They're the essential guidelines that assure the data in a database remains accurate and reliable. Constraints are often set up to enforce business rules, ranging from the straightforward—such as a primary key constraint which keeps each record unique—to the complex, like referential integrity constraints that make sure associations between tables stay solid.

A considered set of constraints can prevent data corruption by stopping entries that don't fit the established rules. Within constraints, we find our functional dependencies, which require that the relationship between attributes stays consistent. For example, a Social Security Number uniquely identifies a taxpayer; hence, given a Social Security Number (attribute A), only one possible name (attribute B) should correspond to it.

Attribute Semantics

The semantics of an attribute refer to the inherent meaning and business logic it carries. It's not just about what the data is, but what it signifies in the broader context. For example, in a relation schema for a university database, the attribute 'student_id' doesn't merely hold a random integer; it uniquely identifies a student within the institution.

Attribute semantics inform functional dependencies because they dictate how different attributes should relate to one another based on their meanings. This goes beyond the technical structure of the database and delves into understanding the nature of the data itself—its origin, its use, and its implications. Real-world understanding contributes largely to establishing functional dependencies. For instance, knowing that each course has a unique course number and title can lead to the functional dependency where the course number (A) dictates the course title (B).

Data Model

The data model is a conceptual tool used to describe the structure of a database—how data is stored, organized, and manipulated. Essentially, it outlines the blueprint for the entire database system, dictating not only the schematics of data representation (like the relation schema) but also the relationships and rules that govern these data elements.

When thinking about functional dependencies within the data model, one can view them as the specific routes data takes in this blueprint, defining how one data element influences another. The data model includes various constraints including entity integrity and referential integrity, which help preserve the accuracy and consistency of the data. By establishing how attributes are functionally dependent on one another, the data model ensures that the database adheres to its intended design and business logic, leading to more reliable and maintainable databases.