Re: On formal HAS-A definition
Date: Tue, 11 May 2010 21:14:52 -0700 (PDT)
Message-ID: <42d7d235-9b92-49b1-836e-91a2473fca5c_at_h20g2000prn.googlegroups.com>
On May 11, 5:19 pm, Erwin <e.sm..._at_myonline.be> wrote:
> On 12 mei, 00:30, Tegiri Nenashi <tegirinena..._at_gmail.com> wrote:
>
>
>
> > IMO there is a benchmark formal definition for both HAS-A and IS-A
> > already. Both are set theory concepts:
> > HAS-A = "element of"
> > IS-A = "subset of"
> > ...
> > I'm not that sure about the HAS-A. Certainly, one can assert that a
> > set of attributes has an attribute, but this is quite different from
> > saying that a relation has an attribute.
>
> A relation has a body and a heading. So a relation can be viewed as a
> set of two members, after which your formalism can be made to apply.
> And a heading is a set of attribute declarations. So under the
> assumption of "has-a" being transitive, I have indeed made a relation
> "have an" attribute in the formal sense you spoke of.
Nope, if we aspire to cast HAS-A after set membership, then transitivity has to be sacrificed.
> (PS - second problem, now that I'm on it : what if you disagree with
> the body-heading view of a relation, and want to insist that a
> relation _IS_ a set of tuples, i.e. it does _NOT_ "have" a heading in
> the foregoing sense,
If you exclude heading from relation, then how do you represent an empty relation? There is only one empty set, but multiple empty relations!
> but rather the heading that it "has" is just a
> function of the body (e.g. projecting away the values from each member
> of the body to retain only the attribute names and the attribute
> types) ? Then the "having" of something (e.g. an attribute) can also
> be a consequence of a function being applied to something else (the
> body). In other words the "having" of something also applies if the
> "RHS" of your 'element-of' formal concept is in fact any arbitrary
> function applied to some set (just so long as that arbitrary function
> yields another set).).
I lost you there. The best course of actions in such circumstances to support your idea with an example. Received on Wed May 12 2010 - 06:14:52 CEST