Re: header part of the value?

On Feb 28, 1:38 pm, Jan Hidders <hidd..._at_gmail.com> wrote:
> On 28 feb, 22:27, Tegiri Nenashi <TegiriNena..._at_gmail.com> wrote:
>
>
>
> > On Feb 28, 1:16 pm, Jan Hidders <hidd..._at_gmail.com> wrote:
>
> > > 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?
>
> > 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. Received on Thu Feb 28 2008 - 22:52:55 CET