*Who’s on first, What’s on second, I Don’t Know’s on third*

—Bud Abbott and Lou Costello: *Naughty Nineties*

In Chapter 10, I said that 4NF, like 2NF and 3NF, is mostly of historical interest. However, that characterization is perhaps a little unfair, because:

First of all, 4NF is

*the*normal form with respect to what are called multivalued dependencies or MVDs. Now, MVDs are really just a special kind of JD; so if you know about JDs in general, you know about MVDs already, in a sense. Nevertheless, MVDs are still worth studying in their own right (for one thing, they’re probably more common in practice than JDs that aren’t MVDs are).Second, MVDs have a more intuitive real world interpretation than JDs in general do, and therefore tend to be a little easier to understand.

Third, MVDs, unlike JDs in general, do have an axiomatization, as we’ll see.

So let’s take a closer look.

In this section and the next, I’ll examine MVDs from a comparatively informal point of view; in the section after that I’ll consider them again, but more formally, and use that more formal understanding to lead up to 4NF. I’ll begin with a definition.

**Definition:**A**multivalued dependency**(MVD) is a join dependency with exactly two components.

It follows from this definition that a nonloss decomposition on the basis of an MVD always yields exactly two projections (recall that JDs in general can be *n-*way for some *n* > 2; by contrast, MVDs are always exactly 2-way). It follows ...

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