# Re: A different definition of MINUS, Part 3

Date: Sat, 20 Dec 2008 11:30:16 -0800 (PST)

On Dec 20, 3:09 am, "Brian Selzer" <br..._at_selzer-software.com> wrote:
> 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]
> as an equation using the algebra?

I think you'll have no problems writing it in Relational Algebra. Here is RL expression:

S v A < R v A

or equivalently

S v R v A = R v A

> Or for that matter, how would you express
> the functional dependency,
>
> AB --> C
>
> as an equation using the algebra?

Given a relation R(x,y) the x->y functional dependency holds whenever

(R1 ^ R2 ^ E') v R00 = R00

where R1=R(x,y1), that is R(x,y) with y renamed to y1, R2 = R(x,y2), E is equality relation y1=y2, and single quotation mark is negation. (Here again, much of the symbol choice is forced by the Prover9).

In anticipation of your next question: "OK, now that you formalized functional dependency algebraically, please show us how to deduce if Armstrong axioms within your system". Admittedly, I don't have any solution, because equality relation is not captured within RL axiom system yet. Received on Sat Dec 20 2008 - 20:30:16 CET

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