Re: Can relvars be dissymetrically decomposed? (vadim and x insight demanded on that subject)

Cimode wrote:
> No. Mathematics of ensembles (known as Ensemblist mathematics) is a
> totally independent area from set theory (they of course exist
> relationship between the two). While set theory main focus is
> operation definitions between sets of values, ensemble mathematics main
> focus is characterization and definition of ensembles of values at
> higher level of abstraction. For simplification purposes, I guess one
> could consider ensemblist math as a macro view and set theory as a
> micro view of the same problem.

Unfortunately every Google on "théorie des ensembles" returned definitions of set theory. I Amazon'd for the Bourbaki book, and the English translation is "Elements of Mathematics I : The Theory of Sets". However, from the table of contents I think I know what you're getting at. Just to check; are "ensembles of parties" the "families of sets" described in sections 3 & 4 of chapter II ? That would give me something to go searching on.

> As stated, my belief is that set theory might not be *sufficient* to
> characterize nature of relvars and that much work still needs to be
> done using math to clarify issues that are unclear in Codd's and Date's
> work.
>

As an aside, what are the issues you consider unclear in the work of Codd & Date ? (Not argumentative; I'd like to know what areas are problematic to you.)

> No. The question is not really about how are defined the constraints or
> according to *what* they are applied. The question is about the relvar
> characterization knowing how they have been already defined in Codd's
> and Date's work thanks to the use of other mathematical tools.
>

What do you mean by "relvar characterization" here ?

> I am sorry but that is really off topic. The question is not about
> constraints but about the relvar itself.
>

It's sneakily relevant in a way; if the domains are different, then the sets of values are different; if the domains are the same, then the sets of values are the same, but the restrictions occur elsewhere.

> Accepting the difference between domain and data type is not really
> relevant to this topic because such difference is not the main focus of
> trying to launch discussion about the nature of relvars.
>

> *Ensemble of parties* is a the abstract ensemble that is defined as a
> ensemble to which necessarily belong N sub ensembles. It has been
> proven mathematically that such ensemble ALWAYS exists when some sub
> ensemble of values exist. Such ensemble is also called Ensemble of
> parties (noted B(DoR1) --> read *Beta of DoR1*). As you may have
> guessed domains here are used as ensembles...
>

That's why the difference drawn between data type and domain is important; as I mentioned above, it potentially changes the sets of values available.

> That's a valid point. But be aware that we are here in unknown ground
> in RM (which in my perspective should be the purpose of
> comp.database.theory). Keep also in mind, that it may be interesting
> to get some better understanding of ensemblist math theory before
> getting any further.

We're in unknown territory for me anyway, that's for sure. However, the terrain is quite interesting ... Received on Sun Jul 16 2006 - 13:03:40 CEST