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, X1, …, Xk , then L has the form L = (F(L), G(L)), where F(L) ⊆ G(L) = X1 × … × Xk , 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.