Re: A different definition of MINUS, part 4

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