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A normalized relation can still suffer anomalies. Going the other way, which (if any) normal forms can be violated by a relation that's free from anomalies? If such exist,

  • For each such normal form that can be violated, what is an example of an anomaly free relation that violates the normal form?
  • Are there any normal forms that an anomaly free relation is guaranteed to comply with?
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  • If "all normal forms" includes DKNF then the answer is no. A relation in 6NF does not have undesirable update, insertion or deletion anomalies in the usual sense but it still may not satisfy DKNF. On the other hand DKNF is not very important and is frequently irrelevant or unachievable.
    – nvogel
    Jan 25, 2012 at 6:47
  • @sqlvogel: hopefully the edit resolves the ambiguity. Interestingly, one of the schema that inspired this question is (as far as I can tell) valid 6NF but not DKNF. I'm not confident enough in my knowledge of normal forms to say with certainty if this is an example that fulfills parts of my question.
    – outis
    Jan 25, 2012 at 7:53
  • Consider whether the set 'update anomalies removed by normalization' is a subset of 'update anomalies'.
    – onedaywhen
    Jan 25, 2012 at 8:48
  • @onedaywhen: If A is the set of relations with anomalies (not exactly the set of update anomalies, but...) and N the set of normalized relations, then the former is A-N, which is naturally a subset of A (is that what you were getting at?). However, I'm asking about neither anomalous, non-normalized relations nor anomalous, normalized relations (A ∩ N). I'm asking about the non-anomalous, non-normalized relations (which involves the complement of update anomalies); whether A̅ ∩ N̅ is empty and, if not, what are some example elements.
    – outis
    Jan 25, 2012 at 9:31
  • If you are using the word "anomalies" to refer to anything other than "update anomalies" (where the word "update" means assignment i.e. insert, amend and delete operations) then please define it. Also, "normalized" means 1NF and is a fundamental requirement of the relational model, hence "non-normalized relations" is a contradiction. If you are referring to something that isn't a relation then, again, please define it.
    – onedaywhen
    Jan 25, 2012 at 11:43

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A relvar that is considered free of all update anomalies will satisfy 6NF and by implication 5NF and BCNF (other normal forms defined many years ago are no longer deemed useful).

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