[woolcap]

One way to think about it is with a mathematical relation, like 'X > Y'. A relational database relation representing this relation would consist of a header tuple, <X, Y>, and a set of tuples whose values satisfy the relation, such as <10, 2>, <8, 3>, <9, 4>. In more common terms, the rows of this table would contain pairs of numbers in which the value of the X attribute is greater than the value of the Y attribute. This table describes the relation(ship) of certain pairs of numbers.

"Each tuple in a relation represents an n-ary relationship...among a set of n values..., and the full set of tuples in a given relation represents the full set of such relationships that happen to exist at some given time--and, mathematically speaking, that's a relation."[1]

[1] Chris Date, Database in Depth, page 46

[talaketu]

This points to the dual view of a relation - intensional vs extensional. The beauty of the relational model of data is the morphism: by evaluating relational operations on the extensional model (data) we gain can answer questions corresponding to intensional model (concept).

For example given the extensional data ALBUM(TITLE, ARTIST) corresponding to the intention "the albums, each with a title and artist", we can compute "the eponymous albums, each with a title" via EPONYMOUS_ALBUM = ALBUM where (TITLE = ARTIST)

We started with some data for a relation corresponding with a concept, and were able to operate on the data to produce a new relation - data corresponding to a new concept.