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Definition:

Type of relation in terms of symmetry with respect to an associated collection. A binary relation R on a collection C is:

(i) symmetric, if for all members x, y of C that are in R it holds that if (x,y) is in R then (y,x) is in R as well;

(ii) anti-symmetric, if for all members x, y of C it holds that whenever (x,y) is in R then (y,x) is not in R;

(iii) neither, if for some but not all members x, y of C that are in R it holds that both (x,y) and (y,x) are in R.

The symmetric type is given by the controlled vocabulary {symmetric, anti-symmetric, neither, unknown}.

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