Re: On Formal IS-A definition

On May 6, 4:12 pm, Erwin <e.sm..._at_myonline.be> wrote:
> OK.  Now I see what you meant by "that typo of mine".  It wasn't a
> typo.  I deliberately used the term "relation algebra" to denote any
> algebra that operates on relations.  I did try to follow the link you
> gave, but it produced an http 404, or some such.

Google newsgroup reader decided to break URL with a new line.

> I know an algebra is nothing more than just a set of operators, so I
> understand that anyone can define any algebra he(/she) likes (I also
> understand why it takes an extremely bright mind to define one that
> turns out to be useful), I am even aware of the consequences to the
> extent that I have written myself in several places that "there is no
> such thing as _the_ relational algebra", but I do not know how many
> relation(al) algebras have been defined, let alone that I would know
> the details of all of them.

The two similarly sounded algebras is an unfortunate artifact. Names stick, no matter how awkward they are. A better name for De Morgan's Relation Algebra is "The Algebra of Binary Relations", while Codd's Relational Algebra should be called "The Algebra of Relations with Named Attributes".

> > I was implying that relation algebras are perfect abstractions for
> > modeling graphs. Relational model? Hardly.
>
> Are you suggesting that even with generalized transitive closure being
> included in the RM, there are still certain graph things that are
> impossible to do with the RM ?

IIRC it has been demonstrated that RA amended with TC is Turing complete.

> > Again, my impression is that transitive closure doesn't fit into
> > relational model.
>
> I have seen the comment that "TC was added to the RA in an ad-hoc
> fashion after the unanswerability of some queries with Codd's algebra
> was proved.".  I think I also understand how the formulation/
> definition of the generalized version of TC was much the same kind of
> response when it was proved that even with "regular" TC, queries such
> as "how many distinct paths exist between a and b" were still
> unanswerable.  But does that warrant the conclusion that "(G)TC
> doesn't fit" ?  I'm hesitant to answer that with a "yes".

My idea is simple. If TC genesis is [De Morgan's] Relation Algebra, why not to bring *all its operations* into Codd's Relational Algebra, and not just one? Merging the two algebras together, so to speak. Received on Sat May 08 2010 - 01:00:01 CEST