# Re: A different definition of MINUS, part 4

Date: Sun, 28 Dec 2008 14:49:54 -0800 (PST)

Message-ID: <2a03d4b1-30e3-46e6-8a02-6af78cc86b42_at_i24g2000prf.googlegroups.com>

[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