# Re: A different definition of MINUS, part 4

Date: Wed, 31 Dec 2008 01:13:43 -0800 (PST)

Message-ID: <d99319ee-59a1-4fb1-ad27-39a8a8767815_at_n28g2000vba.googlegroups.com>

On 28 déc, 23:49, Cimode <cim..._at_hotmail.com> wrote:

> [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? (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 = 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 quantifier must be expressed as the output of a function (a value) that can allow permutation with other quantifiers having the same output in other algebric operations.
**> > Stability: a quantifier with a specific value applied to a domain of tuples defining a relation, necessarily has the same value for all relations that are subtypes of that relation.
**> > Measurability: a quantifier should allow a *numeric* quantification of logical 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 simplicity.
**>
**> I consider the quantifiers in traditional ra too naive to satisfy the
**> above conditions.
**>
**> Regards.
*

To clarify further...

The traditional quantifiers used by D&D do allow the manipulation of relations at fundamental level. They do allow to verify the soundness of a ra expression with no doubt. However, from there to establish a relational computing model, there is a missing link: numeric quantification.

How does one represent a relation operation in such a way that it not allow operation but also simplification and reduction of number of logical operations involved. I have not seen so far any consistent ruling expressed by D&D about that aspect which I believe is a prerequisite for expressing a potential relational computing model. I must insist also that a relational computing model is orthogonal to traditional relational model.

Regards... Received on Wed Dec 31 2008 - 10:13:43 CET