David@fetter.o2007-04-14 04:33:34

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 ðŸ™‚

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.

Vc2007-04-14 09:03:24

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.o2007-04-14 13:45:41

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.

Vc2007-04-14 18:36:39

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”.

David@fetter.o2007-04-16 13:10:00

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

Vc2007-04-16 13:10:05

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 ?

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