Re: A different definition of MINUS, Part 3

[Snipped]
> So if the result of R JOIN S is {{A:3, B:6}, {A:3, B:7}}, then what are the
> operands?
> {{A:3, B:6}, {A:3, B:7}, {A:4, B:7}} and {{A:3, B:6}, {A:3, B:7}}?
> {{A:3, B:6}, {A:3, B:7}} and {{A:3, B:6}, {A:3, B:7}, {A:4,B:6}}?
> {{A:3, B:6}, {A:3, B:7}} and {{A:3, B:6}, {A:3, B:7}}?
> Which?
>
> The whole notion that there is some algebraic solution to the "problem" is
> ludicrous.
paul c and Vadim never claimed that algebric expression of the problem is the solution. They are only trying to rely on a formalism which has proven to be effective.

To qualify as *ludicrous* that motivation implies that you can offer a more credible alternative expression of the problem.

> > Why do we want to do that? Two reasons:
> > 1. Database constraints are equations, and this generalization is a
> > natural way to encompass them.
>
> That's an interesting take.  I'm assuming that these equations can be
> expressed in the algebra.  Supposing that you have relation schemata R{A, B,
> C} and S{A, D}. How would you express an interrelational constraint, such as
> the inclusion dependency,
>
> R[A] IN S[A]
Date has clarified this aspect as subtyping.

> as an equation using the algebra?  Or for that matter, how would you express
> the functional dependency,
>
> AB --> C
>
> as an equation using the algebra?
Truth tables are easy to set up to validate FD in ra and FOPC. Validating each fact can be easily formalized in ra.

> > 2. Information preservation. This one is easier to explain by the
> > familiar linear system example. If there is not enough (linearly
> > independent) equations, then there is a fundamental ambiguity of the
> > inverse map that calculates input delta vector from the output.
I believe somehow that you are missing entirely the point paul and vadim are trying to formulate. There is nothing wrong in expressing a problem in a way that can allow people to communicate to exchange ideas. That, ra is a proven effective way of expressing RL problems/ operation is a fact, not a matter of opinion.

To play devil's advocate (you'd be the devil), I would claim that ra does have its limits, but since you have not pointed any of them so far, I can only conclude that you missing the point.

Regards Received on Sat Dec 20 2008 - 13:26:47 CET