Re: Towards a definition of atomic

From: David Cressey <cressey73_at_verizon.net>
Date: Fri, 01 Feb 2008 14:13:48 GMT
Message-ID: <wOFoj.5441\$4f.724_at_trndny06>

"David BL" <davidbl_at_iinet.net.au> wrote in message news:0b742d39-2a67-4ece-ab76-f78ebe36848b_at_m34g2000hsf.googlegroups.com...
> AFAIK the conventional wisdom is that no absolute definition of atomic
> exists for domain types. Throwing caution to the wind, in this post I
> wish to conjecture a definition of atomic that, perhaps with some more
> effort at its formalisation, can provide some absolute meaning for a
> given attribute within a given RDB schema.
>
> The examples are a little contrived, but are only meant to be
> illustrative.
>
> Example 1:
> "Einstein discovered the formula E = mc^2"
> "Newton discovered the formula F = ma"
>
> Example 2:
> "Bill is a parent of { Mary, John }"
> "Mary is a parent of { Don, Alex, Sue }"
>
>
> In example 1, in Prolog we can define a predicate 'discovered' to
> represent the two facts as follows
>
> discovered(einstein, eq(var("E"), prod(var("m"),
> pow(var("c"),num(2))))).
> discovered(newton, eq(var("F),prod(var("m"),var("a")))).
>
> In previous threads I have discussed how it is not possible to
> decompose the information in nested expressions into a set of
> propositions about the nodes without the introduction of node
> identifiers.
>
> By contrast, in example 2 it is straightforward to map the two facts
> into five (by decomposing the sets of children) as follows
>
> parent(bill,mary).
> parent(bill,john).
> parent(mary,don).
> parent(mary,alex).
> parent(mary,sue).
>
>
> I think we could make the meaning of "atomic" more tangible if we can
> define what decompositions of an attribute are valid.
>

Perhaps the place to start is to define what kinds of compositions a relational system is capable of. Once you have that in place, it should be straightforward to define relational decompositions as the inverse of relational compositions. Received on Fri Feb 01 2008 - 15:13:48 CET

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