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In [[logic]] and [[mathematics]], '''relation reduction''' and '''relational reducibility''' have to do with the extent to which a given [[relation (mathematics)|relation]] is determined by a set 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 set of other relations, called the ''reduciens'' or the ''relational base'', each of which is properly simpler in a specified way than the relation under examination.
In [[logic]] and [[mathematics]], '''relation reduction''' and '''relational reducibility''' have to do with the extent to which a given [[relation (mathematics)|relation]] is determined by a set 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 set of other relations, called the ''reduciens'' or the ''relational base'', each of which is properly simpler in a specified way than the relation under examination.
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 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.
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.
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.