# Grounded relation

A **grounded relation** over a sequence of sets is a mathematical object consisting of two components. The first component is a subset of the cartesian product taken over the given sequence of sets, which sets are called the *domains* of the relation. The second component is just the cartesian product itself.

For example, if *L* is a grounded relation over a finite sequence of sets, *X*_{1}, …, *X*_{k} , then *L* has the form *L* = (*F*(*L*), *G*(*L*)), where *F*(*L*) ⊆ *G*(*L*) = *X*_{1} × … × *X*_{k} , for some positive integer *k*.

The default assumption in almost all applied settings is that the domains of the grounded relation are nonempty sets, hence departures from this assumption need to be noted explicitly.