Re: A different definition of MINUS, Part 3

On Dec 20, 3:09 am, "Brian Selzer" <br...@xxxxxxxxxxxxxxxxxxx> 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.




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