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A '''grounded relation''' over a [[sequence]] of [[set]]s 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 ''[[domain of discourse|domain]]s'' of the relation.  The second component is just the cartesian product itself.

A '''grounded relation''' over a [[sequence]] of [[set]]s 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 ''[[domain of discourse|domain]]s'' of the relation.  The second component is just the cartesian product itself.

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

For example, if ''L'' is a grounded relation over a finite sequence of sets, 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.

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.