Re: NULLs: theoretical problems?

"paul c" <toledobythesea_at_oohay.ac> wrote in message news:vnIui.42734$_d2.2251_at_pd7urf3no...

> Hugo Kornelis wrote:

> ...

>
> I noticed in your blog you said that the table with a null-able birthday 
> column was in 2NF.  If saying that is right, I suppose we must be careful 
> to regard functional dependencies as determining values sometimes and 
> non-values other times.

But Hugo is not right. From the Alice Book, p163:

"A relation I over U satisfies X -> Y, if for each pair s, t of tuples in I, s{X} = t{X} implies s{Y} = t{Y}."

Since null = null is not true, no attribute with nulls satisfies any FD, not even the trivial one {A}->{A}!

Furthermore, no relation with nulls satisfies any join dependency since join dependency requires a natural join and a natural join involving nulls will exclude some tuples. Chris Date this time:

"Let A1, A2,., An be subsets of the heading of relvar r. Then r satisfies the join dependency (JD) *{A1,A2,.,An} if and only if every relation that's a legal value for R is equal to the join of its projections on A1, A2,., An."

Naturally enough it follows that any relation hypothetically containing null values ought to be decomposed so as to eliminate them, ie. 5NF.

-- 
David Portas