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

From: Tony D <tonyisyourpal_at_netscape.net>
Date: 13 Jul 2006 12:26:02 -0700
Message-ID: <1152818762.262919.33650_at_b28g2000cwb.googlegroups.com>


<health warning>
OK, this thread has been sitting here for a few days with not much action, and gently intriguing me. Nobody else who really knows about this stuff, so at risk of betraying cluelesseness about some of this stuff, I'd like to kick some discussion off. I may misinterpret some terms, so if I do and go off on a tangent be gentle. Ok ? </health warning>

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.
>

I'm assuming at this point that "ensemblist" = "set theoretic" ? (One of the references to Bourbaki I found on teh intairweb made that equation; if it's wrong I'm even more off beam than I thought.)

> 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).
>
> The question that arose from that observation is whether the domain
> DoR1 is equivalent to the ensemble consitued by the some adjonction of
> 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.
>

So I suppose the question is, do the constraints on R1 that would prevent it accepting any value drawn from the product type of D1, D2, ... Dn apply to the relvar R1, or to the domain DoR1 ?

At this point, I would tend towards the constraints applying to the relvar, rather than to the domain itself, on the general view that values can't be constrained, but variables can. For example, you can't apply a constraint to the value 2, but you could apply a constraint to an integer variable so that it can only indicate even numbers.

> In Zermelo-Fraenkel approach, this would be expressed as
>
> 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.
>

As we've discussed before, this is a difference I don't readily accept; I'm willing to accept a convincing argument as to why I should accept it though. This would be the logical consequence of separating "domain" and "data type" though.

> 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.
>

I'm not sure I'm quite clear on what is meant by "ensemble of parties", so I won't comment on this section (I can take a guess, but it would be a guess and might lead to a horrible misunderstanding).

> 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.

Can we have some discussion on this ? It might be quite interesting. (More interesting than yet more blether about object oriented stuff, anyway.) Received on Thu Jul 13 2006 - 21:26:02 CEST

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