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

From: Cimode <cimode_at_hotmail.com>
Date: 9 Jul 2006 02:55:19 -0700

Jonathan Leffler wrote:
> I suspect this might be quite an interesting if only I knew what all the
> terms meant.
>
> Cimode wrote:
> > As far as I could observe, relational variables are repetitively
> > confused with their projections as tables. On the last few years, I
> > have focused some efforts into searching mathematical tools to help
> > characterize more precisely relvars.
> >
> > On such perspective, I have found ensemblist mathematics useful.
>
> Can you provide some pointers to 'ensemblist mathematics'? Google
> didn't seem to help.
Most of the sources I am aware of are French published I am not aware if they did get published inUS...Here are a few pointers you may look for "Bourbaki association"
+ a few names...
Henri Cartan, Claude Chevalley, Jean Coulomb, Jean Delsarte, Jean Dieudonné, Charles Ehresmann, René de Possel,

> > Once defined according to predicate theory requirements and RM, relvar
> > have the characteristics of constituing themselves new domain of
> > arbitrarily complex values. For instance, relvar R1{A1, A2} draws and
> > restricts values from domains Da1 and Da2 (for attributes A1 and A2).
> > As soon as defined, all occurrences of relvar R1 populate a domain of
> > value DoR1. (Such domain may be utilized for instance to define a new
> > data type DaR1).
>
> 'value DoR1'? Or of 'type DoR1' or 'domain DoR1'?
Sorry, this sentence is indeed ambiguous. The sentence should read //....all occurrences of relvar R1 populate a domain of values that constitute domain DoR1...///
meaning all occurences of the relvar R1 are the elementary elements of DoR1

> > The question that arose from that observation is whether the domain
> > DoR1 is equivalent to the ensemble consitued by the some adjonction of
>
> constituted? And 'adjunction'? (Are these typos, or some new words?)
I guess *made of * could be a synonym.

> > all attribute domains D1, D2. So far, assuming they are different
> > indeed has some advantage: it allows differentiation of domains which
> > simplifies deduction about relvar characterization. As a consequence,
> > I expressed the relvar R1 as equal to the intersection between the
> > domain of value it would constitute, and the ensemble consituted by the
> > attributes domains.
> >
> > In Zermelo-Fraenkel approach, this would be expressed as
>
> Googling 'Zermelo-Fraenkel' picks up reasonably comprehensible
> definitions at Wikipedia and Wolfram Mathworld.
Yep. Check also names above.

> > Assuming DoR1 there is an ensemble of values constituted by R1 occuring
> > values, there exists an ensemble of parties B(DoR1) that represents
> > their attributes as element of the DoR1 group.
> >
> > Considering B(DoR1) as an ensemble of values different from DoR1, R1
> > could be defined by the intersect of the 2 ensembles.
> >
> > Stated in math language...
> >
> > R1 = DoR1 INTERSECT B(DoR1)
> >
> > One observation that arises from this axiom is the dissimetrical nature
> > of relvar definition due to restriction of drawing value by data type
> > definition. One advantage would be formal expression of the difference
> > between domain and data type.
> >
> > A consequence is that the ensemble of parties made by all attributes
> > are constituted as a product of belonging and restrictions.
> >
> > For all R1{A1, A2, A3} relvars drawn from domain DoR1, there exists an
> > ensemble of parties that allows dissymetrical decomposition and
> > characterization of relvars.
>
> Google couldn't help on a definition of dissymetric, though it turned up
> a number of references to the word.
replace *dissymetric* by *non symetric*. Sorry my English speaking math is limited.

> Can you help me understand whether it is a variant of 'asymmetric',
> 'non-symmetric', 'anti-symmetric', 'unsymmetric' or some other word, or
> whether it has some specialized meaning and what that meaning is?
>
> > The admission of this axiom may have interesting consequences in
> > operation characterization.
> >
> > I would like to get some insight, advice and reading pointers from
> > vadim and x on that point but anybody else that has constructive
> > motivation is welcome as well.
> >
>
>
> --
> Jonathan Leffler #include <disclaimer.h>