Elementary key normal form was introduced by Zaniolo in 1982.^[137] Here’s the definition:

EKNF falls strictly between 3NF and BCNF; that is, BCNF implies EKNF, EKNF implies 3NF, and the reverse implications don’t hold. The stated intent of EKNF is “to capture the salient qualities of both 3NF and BCNF” while avoiding the problems of both (namely, that 3NF is “too forgiving” and BCNF is “prone to computational complexity”). That said, I should say too that EKNF isn’t much referenced in the literature.

Recall that 5NF was originally called PJ/NF, and PJ/NF means every JD is implied by keys (speaking rather loosely). In fact, in the paper in which he introduced PJ/NF, Fagin also introduced what he called overstrong PJ/NF, which meant (again rather loosely) that every JD is implied by some specific key considered in isolation. Note that this latter is what one might intuitively have expected the definition of regular PJ/NF (i.e., 5NF) to have been—recall the remarks in Chapter 10 and Chapter 12 concerning the parallelism between the definitions of BCNF, 4NF, and 5NF. Be that as it may, here’s the definition:

Overstrong PJ/NF clearly implies 5NF (i.e., “regular” PJ/NF), but the reverse is not true. A single counterexample suffices to demonstrate this latter fact:^[138] Consider a relvar R with attributes A, B, C, and D (only) and keys {A} and {B} only. Let the only dependencies to hold in R be ones that are implied by these keys (so R is definitely in 5NF). Now consider the JD {AB,BC,AD}. Applying the membership algorithm, we see that this JD holds in R; but it’s not a consequence of either of the keys considered in isolation, as can also be seen by checking the membership algorithm. So R is in 5NF (or PJ/NF) but not in overstrong PJ/NF.

Consider the parts relvar P from the suppliers-and-parts database. Normalization theory as I’ve described it prior to this point tells us relvar P is in a “good” normal form; indeed, it’s in 5NF, and it’s therefore guaranteed to be free of anomalies that can be removed by taking projections. But why keep all parts in a single relvar? What about a design in which red parts are kept in one relvar (RP, say), blue ones in another (BP, say), and so on? In other words, what about the possibility of decomposing the original parts relvar via restriction instead of projection? Would the resulting structure be a good design or a bad one? (In fact it would almost certainly be bad unless we were very careful, as we’ll see in Part IV of this book; however, the point here is that classical normalization theory as such has absolutely nothing to say about the matter.)

Another direction for design research therefore consists of examining the implications of decomposing relvars by some operator other than projection. In the example, the decomposition operator is, as already mentioned, (disjoint) restriction; the corresponding recomposition operator is (disjoint) union. Thus, it might be possible to construct a “restriction-union” normalization theory, analogous to—but orthogonal to—the projection-join normalization theory we’ve been considering prior to this point. I don’t want to get much more specific on such matters here; suffice it to say that some initial ideas along these lines can be found (a) in Fagin’s PJ/NF paper, which additionally discusses a normal form called PJSU/NF, and (b) in a paper by Smith, which discusses a normal form called (3,3)NF.^[139] This latter paper, incidentally, shows that (3,3)NF implies BCNF, but that a (3,3)NF relvar need not be in 4NF, nor need a 4NF relvar be in (3,3)NF. As suggested above, therefore, reduction to (3,3)NF is orthogonal to reduction to 4NF (and 5NF).