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
.

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