Re: header part of the value?

On Feb 28, 1:38 pm, Jan Hidders <hidd...@xxxxxxxxx> wrote:
On 28 feb, 22:27, Tegiri Nenashi <TegiriNena...@xxxxxxxxx> wrote:



On Feb 28, 1:16 pm, Jan Hidders <hidd...@xxxxxxxxx> wrote:

On 28 feb, 21:58, Tegiri Nenashi <TegiriNena...@xxxxxxxxx> wrote:

On Feb 28, 11:35 am, Tegiri Nenashi <TegiriNena...@xxxxxxxxx> wrote:

Let me reiterate the generalized relation idea one more time, on a
level perhaps more digestable for wider audience. Consider classic
relation

"The person first name is ..."

Normally, we don't write the whole sentence in the relation header (we
focus exclusively on named perspective, of course) and abbreviate it
to just

Name
-----
Scott
Mike

The concept of domain has been introduced to resolve questions weather
this relation is allowed to be joined with something like

"The ship name is ..."

All we do when allowing generalized relations is admitting predicates
like this:

"The variable x is greater or equal than ..."

and insisting that the whole sentence matters as a relation header.

Here is little more background. The inspirational paper is Grumbach&Su
"Finitely Representable Databases". They introduced the concept of
finite representativity, for example the relation {x:x>=0} is not
finitely representable as a classic relation on infinite domain, but
is finitely representable in more general sense. However, after few
pages they lost me: I can't understand where are they heading with
this idea, why compactness theorem, Ehrenfeuht-Frausse gaimse and
PTIME matter. From practical perspective, one would think the first
thing they should discuss is an algebra to conveniently operate these
finite representations.

The complexity and computability results indicate to which extent such
an algebra is possible and/or useful. Besides, why do you think such
an algebra is necessary? What is necessary is that you can ask queries
and that there are algorithms to compute them. An algebra is just one
possible solution for that.

Anyway, returning to the example

Q:
x + 3 = y \/
x + 5 = y

Is it binary or unary relation? Sure it is a binary relation Q(x,y) in
classic sense, but it is not finitely representable!

Why do you think it is not finitely representable?

Sure, there is infinite number of tuples in

Q(x,y) = {(x,y) | exists t in N such that x = t and (y = t + 3 or y =
t + 5)}

That does not mean it is not finitely representable. Or are you using
a different definition than Grumbach and Su?

Oops, I meant "not a finite classic relation" rather than "finitely
representable" in the sense of Grumbach&Su.

.

Relevant Pages

  • Re: header part of the value?
    ... finite representativity, for example the relation is not ... is finitely representable in more general sense. ... an algebra is possible and/or useful. ... Sure it is a binary relation Qin ...
    (comp.databases.theory)
  • Re: header part of the value?
    ... finite representativity, for example the relation is not ... finitely representable as a classic relation on infinite domain, ... is finitely representable in more general sense. ... an algebra is possible and/or useful. ...
    (comp.databases.theory)
  • Re: header part of the value?
    ... finite representativity, for example the relation is not ... finitely representable as a classic relation on infinite domain, ... is finitely representable in more general sense. ... an algebra is possible and/or useful. ...
    (comp.databases.theory)