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I believe that 2nd and 3rd normal form definitions could obviously be specified with less complexity, but they're not.

The definition found in textbooks is something like this:

2NF: No partial FD between prime and non-prime attributes.

This means there is no such situation as: A -> B -> C where A is a key, B its subset, and C a non-prime.

As A -> B always holds for every B, this could be simplified by removing A -> B to get B -> C, or:

2NF-new: No FD between a subset of a key and a non-prime.

and,

3NF: No indirect FD between a key and non-prime attributes.

This means there is no such thing as: K -> NP1 -> NP2. Again, as K -> X for every X, this could be simplified to get NP1 -> NP2 leading to:

3NF-new: No FD between two non-primes.

However, I have not seen this simplified version anywhere, except

Equivalently, a transitive dependency exists when a nonprime attribute determines another nonprime attribute.

What makes me is more doubtful is the word typically in

A nonprime attribute determines another nonprime attribute. Here we typically have a transitive dependency that violates 3NF.

By Elmasri and Navathe. So why not always?

Are my definitions wrong? If not, why are they not used?

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  • IMO, "No FD between a subset of a key and a non-prime" does not read any more concisely or simply than "No partial FD between prime and non-prime attributes.". Also, I believe "No indirect FD between prime and non-prime attributes" has a different meaning technically than "No FD between two non-primes".
    – J.D.
    Commented Oct 12, 2022 at 22:20
  • "no such situation as: A -> B -> C where A is a key, B its subset, and C a non-prime." If we insert "proper/smaller" before subset we get a definition of 2NF. But a CK determines every attribute set & attribute, so simpler is "no such situation as: B -> C where B is a subset of a CK, and C a non-prime." But "No partial FD between prime and non-prime attributes" is not clear & it seems that if it were clear it would be wrong in a way that does not "mean" either your paraphrase or the paraphrase+insertion that actually defines 2NF.
    – philipxy
    Commented Oct 13, 2022 at 1:12
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    This post meanders over many unclear claims with unclear justifications/reasoning/arguments. Almost everything is so unclear it cannot be critiqued. If they were clear it would still be unhelpful to show they are wrong when you don't clearly show why you think they are right. You don't include the context for the final quotes that you ask about or clearly relate it to the rest of the post. Each claim or rephrasing is effectively another question. You explicitly ask multiple questions. Please ask 1 clear specific question. PS FDs are directed, it's not appropriate to say "between".
    – philipxy
    Commented Oct 13, 2022 at 1:58

1 Answer 1

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All those definitions you give are wrong. Also, note that the textbook quotes are not definitions. Moreover, there are multiple definitions for things. Also, things are what they are: "Everything should be made as simple as possible, but not simpler."

The 2NF & 3NF articles (among others) at Wikipedia present some variations. Although they also give wrong ones, and almost every relational model page has errors. The web page you link to says wrong things.

See my answer at Normal forms - 2nd vs 3rd - is the difference just composite keys? non trivial dependency?.

Follow multiple (good) published textbooks. Beware that many textbook presentations of database normalization (and the relational model) give definitions for special cases, and/or are poorly written, and/or are outright wrong, including in definitions.

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  • I've made many simplifications to just deliver my point. For example, I did not mention that the subset must be a proper one. But despite these, I think still my definitions are correct. I've checked two well-known books, websites, and the post you referenced here. I think I understand your definitions but still don't understand why they cannot be simplified (especially 3NF).
    – Mehrin
    Commented Oct 13, 2022 at 4:47
  • Your edit hasn't helped. It's unfortunate that you can't see how unclear & unjustified your claims are. I hope you act on my comments. Be sure to read the Wikipedia 3NF article to see how Codd's partial/transitive definitions compare to Zaniolo's. Elmasri & Navathe is a mess.
    – philipxy
    Commented Oct 13, 2022 at 11:27

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