# Re: On Formal IS-A definition

Date: Thu, 6 May 2010 16:12:57 -0700 (PDT)

Message-ID: <8fa2e3ed-e853-4e56-97fd-9f5d8a103326_at_j33g2000yqn.googlegroups.com>

On 6 mei, 22:02, Tegiri Nenashi <tegirinena..._at_gmail.com> wrote:

*> On May 6, 1:39 am, Erwin <e.sm..._at_myonline.be> wrote:*

*>*

*> > On 5 mei, 22:56, Tegiri Nenashi <tegirinena..._at_gmail.com> wrote:*

*>*

*> > > On May 5, 12:41 pm, Erwin <e.sm..._at_myonline.be> wrote:*

*>*

*> I was referring to deMorgan/Peirce/Tarski relation algebra, which has*

*> nothing to do with relational algebra. Kleene star is a natural*

*> operation for the former, while its reincarnation in relational model*

*> in the form of Transitive Closure looks like an afterthought. It is*

*> not even total.*

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.

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.

*> 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 ?

*> 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".

*> As far as Information principle is concerned, here is my attitude:*

*> "Relational algebras should be defined with purely equational*

*> postulates". Removing the suffix "al" in the first word, this is*

*> literally the same how Tarski put it.*

Sorry. My skills and knowledge are lacking to discuss such matters. Which I regret. Received on Thu May 06 2010 - 18:12:57 CDT