High Quality Content by WIKIPEDIA articles! In logic and mathematics, relation reduction and relational reducibility have to do with the extent to which a given relation is determined by an indexed family or a sequence of other relations, called the relation dataset. The relation under examination is called the reductandum. The relation dataset typically consists of a specified relation over sets of relations, called the reducer, the method of reduction, or the relational step, plus a specified set of other relations, simpler in some measure than the reductandum, called the reduciens or the relational base. A question of relation reduction or relational reducibility is sometimes posed as a question of relation reconstruction or relational reconstructibility, since a useful way of stating the question is to ask whether the reductandum can be reconstructed from the reduciens. See Humpty Dumpty. A relation that is not uniquely determined by a particular relation dataset is said to be irreducible in just that respect. A relation that is not uniquely determined by any relation dataset in a particular class of relation datasets is said to be irreducible in respect of that class.

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