Re: Discovering new relationships

"Marshall" <marshall.spight_at_gmail.com> wrote in message news:1172869458.132871.258340_at_h3g2000cwc.googlegroups.com...
> On Mar 2, 12:01 pm, "Walt" <wami..._at_verizon.net> wrote:

> > I think the two examples where I used SQL notation would be clearer if
they
> > were in mathematical notation, but I'm too timid to try. Can anybody
help?
>
> Ohhh! Ohhh! Pick me!
>
> -----
>
> & is used here for natural join.
>
> Consider your functions f and g. Let us imagine a "bind" operation,
> that gives names to both the parameter and return value of the
> procedural
> code f. Here is the syntax:
>
> y = f(x)
>
> So that expression (the whole thing: "y = f(x)") is interpreted as
>
> { (x, y) | y = f(x) }
>
> "The set of all x and y values where y is equal to f applied to x."
>
> Using this notation, let us rewrite your example. Assume j is a
> name that does not appear as an attribute of either R nor S.
>
> (R & (j = f(a))) & (S & (j = g(b)))
>
> This has a bunch of parens to avoid any ambiguities; we could
> also just write
>
> R & j=f(a) & S & j=g(b)
>
> Once you have bind and a complete set of relational operators,
> you can do anything SQL can do. (This also raises the question
> of what makes a good set of relational operators, which is an
> enormous topic on its own.)
>
> Darwen (and others) have an argument about the superiority of
> an algebraic relational language over one like SQL, which argument
> I find quite compelling.
>
>
> Marshall
>

Thanks for the translation. Once I looked at it in mathematical notation, it reminded me that a function is just a special case of a relation. From there, I realized that I could have presented the example I gave without having to use SQL "functions" at all.

Let's say that we have two relations S(a) and R(b) with no "natural join" between them.
All we need to do to relate the data is discover a relation T(a,b). Now there's a natural join between S and T, and one between T and R. In the abstract, such a relation always exists.

The question, in data management terms is this: Is such a relation "meaningful" in our universe of discourse? Stated in another way, is the proposition that T represents one that says anything useful in the U of D? This brings it back to data analysis.

So I'm glad to have learned something, at the cost of having launched an unnecessary discussion. Received on Sat Mar 03 2007 - 14:10:59 CET