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From: Cimode <cimode@hotmail.com>
Newsgroups: comp.databases.theory
Subject: Re: A different definition of MINUS, part 4
Date: Sun, 28 Dec 2008 14:49:54 -0800 (PST)
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[Snipped]
<<One thing I don't understand about your quantifier comment; if an
algebra has a projection operator, don't we have quantification in the
algebra? =A0(ie., "Exists"?)>>
A fundamental question which is unfortunately unpractical to respond
to through this NG. So allow me to rephrase it.  What conditions must
satisfy a quantifier in RL to allow an effective formalization of
relation operations (effective =3D allow a practical and formalized
measurement of logical cost of relation operation).  So far I have
come with the three following conditions:

> Closure: A relational quantifier is euclydian.  A valid relational quanti=
fier must be expressed as the output of a function (a value) that can allow=
 permutation with other quantifiers having the same output in other algebri=
c operations.
> Stability: a quantifier with a specific value applied to a domain of tupl=
es defining a relation, necessarily has the same value for all relations th=
at are subtypes of that relation.
> Measurability: a quantifier should allow a *numeric* quantification of lo=
gical operations involved in a relational operation and provide a basis for=
 optimization of the relational operation.  How does one simplify relation =
operations and assertions without having an objective measurement for simpl=
icity.

I consider the quantifiers in traditional ra too naive to satisfy the
above conditions.

Regards.