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Re: Multisets and 3VL

From: vc <boston103_at_hotmail.com>
Date: 18 Jan 2006 15:22:33 -0800
Message-ID: <1137626553.553775.3730@z14g2000cwz.googlegroups.com>


David Fetter wrote:
> vc <boston103_at_hotmail.com> wrote:
> >
> > David Fetter wrote:
> >> Folks,
> >>
> >> I've read Date, Darwen and Pascal's ideas on how their relational
> >> model is based on set theory (I assume they mean ZFC, but it's
> >> probably not important) and two-valued logic, and they've done a
> >> thorough job of writing this down.
> >>
> >> Has anybody done similar work starting from multiset theory and
> >> three-valued logic?
> >
> > See:
> >
> > Query Languages for Bags (1993) Leonid Libkin, Limsoon Wong
> >
> > Multi-sets and multi-relations in Z with an application to a
> > bill-of-materials system (1990)
>
> Thanks :)
>
> > [...]
> >> neutral geometry has sharper limits on what it can prove than
> >> Euclidean geometry does.
> >
> > That does not make any obvious sense. What "sharper limits" do you
> > have in mind ?
>
> Well, at this stage, it's just fuzzy intuition, but if I had to assign
> a reason, it would be that I've noticed that when you "know extra
> stuff" about a problem domain, for example, that every multiset has
> multiplicity one, or that truth values will only be in {T,F}, you can
> then use that knowlege to get to places you couldn't have gotten to if
> you hadn't have it.

I still do not understand your analogy. Say, in neutral geometry, one can deduce that the angle sum of any triangle is not more than 180 degrees. In Euclidian geometry, one can prove that the angle sum is exactly 180 degrees thanks to the fifth postulate. So, it's the Eucleadian geometry that "has sharper limits", not neutral, unless you redefine the word "sharper".

>
> Cheers,
> David.
> --
> David Fetter david@fetter.org http://fetter.org/
> phone: +1 510 893 6100 mobile: +1 415 235 3778
>
> Yesterday, upon the stair,
> I saw a man who wasn't there.
> He wasn't there again today.
> I think he's with the NSA.
Received on Wed Jan 18 2006 - 17:22:33 CST

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