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

Date: Sun, 09 Jul 2006 05:20:14 GMT

Message-ID: <im0sg.5287$ye3.918_at_newsread1.news.pas.earthlink.net>

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.

> 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'?

> 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?)

> 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.

> 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.

> 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 - 07:20:14 CEST