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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.
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''<sub>1</sub> × … × ''X''<sub>''k''</sub>, 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.
==See also==
* [[Logic of relatives]]
* [[Relation (mathematics)|Relation]]
* [[Relation composition]]
* [[Relation construction]]
* [[Relation reduction]]
* [[Relation theory]]
* [[Relation type]]
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''<sub>1</sub> × … × ''X''<sub>''k''</sub>, 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.
==See also==
* [[Logic of relatives]]
* [[Relation (mathematics)|Relation]]
* [[Relation composition]]
* [[Relation construction]]
* [[Relation reduction]]
* [[Relation theory]]
* [[Relation type]]