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Definition:

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

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

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

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

The transitivy type is given by the controlled vocabulary transitive, anti-transitive, neither, unknown}.

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