Content deleted Content added
m →Logical Interpretation: MOS:CAPS, punct. |
|||
Line 55:
[[Relation (database)|Relation]]s are classified based upon the types of anomalies to which they're vulnerable. A database that is in the [[first normal form]] is vulnerable to all types of anomalies, while a database that is in the ___domain/key normal form has no modification anomalies. Normal forms are hierarchical in nature. That is, the lowest level is the first normal form, and the database cannot meet the requirements for higher level normal forms without first having met all the requirements of the lesser normal forms.<ref name="Normalization">David M. Kroenke, ''Database Processing: Fundamentals, Design, and Implementation'' (1997), Prentice-Hall, Inc., pages 130–144</ref>
== Logical
The relational model is a [[formal system]]. A relation's attributes define a set of [[logic]]al [[propositions]]. Each proposition can be expressed as a tuple. The body of a relation is a subset of these tuples, representing which propositions are true. Constraints represent additional propositions which must also be true. [[Relational algebra]] is a set of logical rules that can [[Validity (logic)|validly]] [[inference|infer]] conclusions from these propositions.<ref name="professionals"/>{{rp|95–101}}
The definition of a ''tuple'' allows for a unique empty tuple with no values, corresponding to the [[empty set]] of attributes. If a relation has a degree of 0 (i.e. its heading contains no attributes), it may have either a cardinality of 0 (a body containing no tuples) or a cardinality of 1 (a body containing the single empty tuple). These relations represent [[Boolean ___domain|Boolean]] [[truth values]]. The relation with degree 0 and cardinality 0 is ''False'', while the relation with degree 0 and cardinality 1 is ''True''.<ref name="professionals"/>{{rp|221–223}}
Line 67 ⟶ 66:
Furthermore, if ''{ID}'' is a key, then a relation containing the tuples ''{Alice, 1}'' and ''{Bob, 1}'' would represent the following [[contradiction]]:
# There exists an employee with the name ''Alice'' and the ID ''1''.
# There exists an employee with the name ''Bob'' and the ID ''1''.
| |||