| [Relational Theory] | [Carol's HomePage] |
| Unnormalised Form (UNF) | A table that contains one or more repeating groups. |
A relational table which is not an instance of a proper relation is in unnormalised form (UNF).
A relational table which is not in First Normal Form (1NF) is in unnormalised form (UNF).
| First Normal Form | A relation is in first normal form if and only if every non-key attribute is functionally dependent upon the primary key |
A relation is in first normal form if it contains no repeating attributes and no repeating groups of attributes.
| First Normal Form (1NF) | A relation in which the intersection of each row and column contains one and only one value. |
A relation is in first normal form if
First normal form (1NF) is now considered to be part of the formal definition of a relation in the basic (flat) relational model; historically, it was defined to disallow multivalued attributes, composite attributes, and their combinations. It states that the domain of an attribute must contain only atomic (simple, indivisible) values and that the value of any attribute in a tuple must be a single value from the domain of the attribute. Hence, 1NF disallows having a set of values, a tuple of values, or a combination of both as an attribute value for a single tuple. In other words, 1NF disallows "relations within relations" or "relations as attributes of tuples". The only attribute values permitted by 1NF are single atomic (or indivisible) values.
The first normal form (1NF), as introduced by Codd, is equivalent to the definition of the relational data model. In particular, the value of an attribute must be atomic. It cannot be anything that has structure, such as a record (with multiple fields) or a set.
| Second Normal Form | A relation is in second normal form if and only if it is in first normal form and every non-key attribute is fully functionally dependent upon the primary key |
A relation is in second normal form if and only if it is in first normal form and every non-key attribute is fully functionally dependent on the primary key.
| Second Normal Form (2NF) | A relation that is in First Normal Form and every non-primary-key attribute is fully functionally dependent on the primary key. |
| Second Normal Form (2NF) | A relation that is in first normal form and every non-primary-key attribute is fully functionally dependentt on any candidate key. |
A relation is in second normal form if
A relation is in second normal form if
A relation is in second normal form if
A relation schema R is in 2NF if every nonprime attribute A in R is fully functionally dependent on the primary key of R.
A relation schema R is in second normal form (2NF) if every nonprime attribute A in R is not partially dependent on any key of R.
The second normal form (2NF) says that a schema must not have an FD, X → Y, where X is a strict subset of that schema's key.
| Third Normal Form | A state in which all relations in a database are fully normalised |
A relation is in third normal form if and only if it is in 2NF and every non-key attribute is nontransitively dependent on the primary key. (Date,1990)
A relation is in third normal form if and only if the non-key
attributes are:
(a) mutually independent, and;
(b) fully dependent on the primary key. (Date,1990)
A relation is in third normal form if and only if it is in second normal form there are no functional dependencies between the non-key attributes.
| Third Normal Form (3NF) | A relation that is in First and Second Normal Form, and in which no non-primary-key attribute is transitively dependent on the primary key. |
| Third Normal Form (3NF) | A relation that is in First Normal Form and Second Normal Form, and in which no non-primary-key attribute is transitively dependent on any candidate key. |
A relation is in third normal form if
A relation is in third normal form if
A relation schema R is in third normal form (3NF) if, whenever a nontrivial functional dependency X → A holds in R, either (a) X is a superkey of R, or (b) A is a prime attribute of R.
| Boyce-Codd Normal Form | A stronger normal form than third normal form. A BCNF schema is one in which every functional determinant is a candidate key |
BCNF is essentially a clearer formulation of Codd's 3NF definition which also caters for two additional cases:
Relations with more than one candidate key, and;
relations with overlapping candidate keys.
Let us start with the definition of BCNF:
A relation is in Boyce-Codd normal form (BCNF) if and only if every determinant is a candidate key.
| Boyce-Codd Normal Form (BCNF) | A relation is in BCNF if and only if every determinant is a candidate key. |
A relation is in Boyce-Codd Normal Form if
A relation is in Boyce-Codd Normal Form if
A relation is in Boyce-Codd Normal Form if
every determinate in the minimal FD list is a candidate key
A relation schema R is in BCNF if whenever a nontrivial functional dependency X → A holds in R, then X is a superkey of R.
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URL: http://computer/people/Carol.Edmondson/theory/NormalForms.shtml
Last modified: 05 January 2007 15:03:03 EST |