# Re: A different definition of MINUS, part 4

From: Cimode <cimode_at_hotmail.com>
Date: Sun, 28 Dec 2008 14:49:54 -0800 (PST)

[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. Received on Sun Dec 28 2008 - 23:49:54 CET

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