Perusrelaatio

Perusrelaatio, literally meaning “basic relation” in Finnish, is a term used in mathematics, logic, and database theory to refer to a primitive or base relation in a formal system. It denotes a relation symbol in the signature of a relational structure that is taken as given, rather than defined by formulas in terms of other relations.

In a relational structure, a perusrelaatio is defined by its arity and its interpretation: for a given domain, the perusrelaatio corresponds to a specific set of tuples of the appropriate length. While most commonly binary, higher-arity base relations are also possible in some theories.

The perusrelaatio acts as a building block for defining other relations or properties. Derived or defined relations can be obtained from the perusrelaatio through logical formulations, combinations, and operations such as composition or converse. For example, a relation like ancestor can be defined from a primitive parent relation using transitive closure, while other theories may impose axioms that determine how base relations interact.

In practice, the term can also appear in database contexts to describe a base relation or base table that stores raw data, as opposed to derived views that are defined from base relations. In such cases, perusrelaatio often corresponds to the fundamental tables in a schema, from which queries and analytical views are constructed.

Properties of a perusrelaatio depend on the theory in which it is used; there is no single intrinsic property beyond its arity and its interpretation in a model. Its role is to serve as a primitive symbol from which other concepts are defined or inferred.

See also: primitive relation, arity, relational structure, definability, relational algebra, database schema.