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A notion of logical implication is defined for functional dependencies in the following way: a set of functional dependencies logically implies another set of dependencies , if any relation R satisfying all dependencies from also satisfies all dependencies from ; this is usually written .
Given a set of functional dependencies , an Armstrong relation is a relation which satisfies all the functional dependencies in the closure + and only those dependencies. . Unfortunately, the minimum-size Armstrong relation for a given set of dependencies can have a size which is an exponential function of the number of attributes in the dependencies conside
The following unify package management for several or all Linux and sometimes Unix variants. These, too, are based on the concept of a recipe file. AppImage (previously klik and PortableLinuxApps) aims to provide an easy way to get software packages for most major distributions without the dependency problems so common in many other package ...
Every non-trivial functional dependency begins with a superkey (a stricter form of 3NF) — Every non-trivial multivalued dependency begins with a superkey — Every join dependency has a superkey component [8] — Every join dependency has only superkey components — Every constraint is a consequence of domain constraints and key constraints
A canonical cover for F (a set of functional dependencies on a relation scheme) is a set of dependencies such that F logically implies all dependencies in , and logically implies all dependencies in F. The set has two important properties:
Dependency theory is a subfield of database theory which studies implication and optimization problems related to logical constraints, commonly called dependencies, on databases. The best known class of such dependencies are functional dependencies , which form the foundation of keys on database relations .
There is a functional dependency from the candidate key to all the attributes in the relation. The superkeys of a relation are all the possible ways we can identify a row. The candidate keys are the minimal subsets of each superkey and as such, they are an important concept for the design of database schema.
A trivial multivalued dependency X Y is one where either Y is a subset of X, or X and Y together form the whole set of attributes of the relation. A functional dependency is a special case of multivalued dependency. In a functional dependency X → Y, every x determines exactly one y, never more than one.