david@fetter.org (david

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? I'd imagine that since those theories are more
general, they limit the things you can say definitively just as
neutral geometry has sharper limits on what it can prove than
Euclidean geometry does.

If such work has been done, can I get a reference to it?

Thanks in advance for your help

Cheers,
David.
--
David Fetter david@fetter.org http://fetter.org/
phone: +1 510 893 6100 mobile: +1 415 235 3778

You don't need intelligence to have luck, but you do need luck to have
intelligence.

vc

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) [...]

That does not make any obvious sense. What "sharper limits" do you have in mind ?

david@fetter.org (david

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.

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.

vc

I still do not understand your ****ogy. 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".

david@fetter.org (david

Actually, one can't. Neutral geometry includes spaces with positive
(aka spherical), negative (aka hyperbolic) and zero (aka Euclidean) curvature.

With the parallel postulate, you can prove things that you simply
can't prove without it. In this sense, when you're using neutral
geometry, you have to "stop short" in places where you could go
further with the parallel postulate in any of the above formulations.
"Sharper limits" == "Sharper limits on what particular things you can
prove using the more general theory."

Cheers,
David.
--
David Fetter david@fetter.org http://fetter.org/
phone: +1 510 893 6100 mobile: +1 415 235 3778

Whenever a theory appears to you as the only possible one, take
this as a sign that you have neither understood the theory nor
the problem which it was intended to solve.
Karl Popper

vc

That is not true. Elliptic geometry is not neutral, whereas Euclidean
and hyperbolic are.
According to the Saccheri-Legendre theorem, in neutral geometry the
sum of the three angles in any triangle is less than or equal to 180
(equal in Eucleadian geometry and less in hyperbolic).

So saying that something is less or equal 180 degrees is "sharper" (or
more precise) than saying that something is exactly 180 degrees ? A
very strange notion indeed.

By the same token you'd claim that rings are "sharper" than fields and
integers (being an example of the former) are "sharper" than rationals
that are an example of the latter ?