Re: header part of the value?

On 28 feb, 21:58, Tegiri Nenashi <TegiriNena..._at_gmail.com> wrote:
> On Feb 28, 11:35 am, Tegiri Nenashi <TegiriNena..._at_gmail.com> 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?

• Jan Hidders