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==Discussion==
==Discussion==
The main thing that keeps the general problem of relational reducibility from being fully well-defined is that one would have to survey all of the conceivable ways of "getting new relations from old" in order to say precisely what is meant by the claim that the relation ''L'' is reducible to the set of relations {''L''<sub>''j''</sub> : ''j'' in ''J'' }. This is tantamount to claiming that if one is given a set of "simpler" relations ''L''<sub>''j''</sub> , for indices ''j'' in some set ''J'', that this collection of data would somehow or other fix the original relation ''L'' that one is seeking to analyze, to determine, to specify, or to synthesize.
The main thing that keeps the general problem of relational reducibility from being fully well-defined is that one would have to survey all of the conceivable ways of "getting new relations from old" in order to say precisely what is meant by the claim that the relation ''L'' is reducible to the set of relations {''L''<sub>''j''</sub> : ''j'' in ''J'' }. This is tantamount to claiming that if one is given a set of "simpler" relations ''L''<sub>''j''</sub> , for indices ''j'' in some set ''J'', that this collection of data would somehow or other fix the original relation ''L'' that one is seeking to analyze, to determine, to specify, or to synthesize.
In practice, however, apposite discussion of a particular application typically settles on either one of two different notions of reducibility as capturing the pertinent issues, namely:
In practice, however, apposite discussion of a particular application typically settles on either one of two different notions of reducibility as capturing the pertinent issues, namely:
==See also==
==See also==
{|
{{col-begin}}
{{col-break}}
* [[Binary relation]]
* [[Binary relation]]
* [[Cartesian product]]
* [[Cartesian product]]
* [[Image (mathematics)|Functional image]]
* [[Image (mathematics)|Functional image]]
* [[Reconstruction conjecture|Graph reconstruction]]
* [[Reconstruction conjecture|Graph reconstruction]]
{{col-break}}
* [[Projection (set theory)|Projection]]
* [[Projection (set theory)|Projection]]
* [[Relation (mathematics)|Relation]]
* [[Relation (mathematics)|Relation]]
* [[Tacit extension]]
* [[Tacit extension]]
* [[Triadic relation]]
* [[Triadic relation]]
{{col-end}}
