Re: atomic

From: paul c <>
Date: Mon, 05 Nov 2007 16:52:23 GMT
Message-ID: <bTHXi.179476$th2.166230_at_pd7urf3no>

David BL wrote:

>> Not to say D&D's basic definitions are the only ones that can
>> be used, but I think we'd have to have agreement on how the operators
>> apply.  For example, if I understand D&D, r1 |x| r2 above would be empty.

> Consider that we have a function I (an "interpretation") that maps a
> relation with MV attributes to an "equivalent" relation with SV
> attributes. Formally this simply takes cross products. For example,
> in the above example I(r1) is
> Name Car
> --------------------------
> bill car1
> bill car2
> bill car4
> john car3
> fred car3
> and I(r2) is
> Car Colour
> --------------------------
> car1 red
> car3 red
> car4 red
> car2 green
> I think it is straightforward to prove the following in the general
> case
> I(r1 |x| r2) = I(r1) |x| I(r2)
> where |x| on the LHS is the join operator on relations with MV
> attributes, and |x| on the RHS is the conventional inner join on
> relations with SV attributes.
> ...

Are you suggesting cross product as an additional fundamental operator? If we're instead talking about cartesian product, I take it that r1 could be written like this:

Name Car
----------- ------------
{bill} {car1,car2,car4}
{john,fred} {car3}

and r2 like this:

Car Colour

----------------  ---------
{car1,car3,car4}  {red}
{car2}            {green}

if those make sense, by the D&D definition of "cartesian product", I think r1 |x| r2 would be empty and I presume so would I(r1 |x| r2). Received on Mon Nov 05 2007 - 17:52:23 CET

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