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

Date: 9 Jul 2006 02:55:19 -0700

Message-ID: <1152438919.627748.157140_at_h48g2000cwc.googlegroups.com>

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>
**> Email: jleffler_at_earthlink.net, jleffler_at_us.ibm.com
**> Guardian of DBD::Informix v2005.02 -- http://dbi.perl.org/
*

Received on Sun Jul 09 2006 - 11:55:19 CEST