Re: RA with MV attributes

Never mind. Partial order is not enough. It has to be total order.

Aloha Kakuikanu wrote:
> David wrote:
> > Here is a partial formalization of a relational algebra based on MV
> > attributes. The approach appears simple and intuitive. In particular
> > the join of two relations is rather elegant.
> > ...
>
> IMO, RA with MV attributes is quite easy to formalize. I suggest a
> nested relation as a formal definition for MV attribute. A critical
> step is noticing that there is a (partial) order "<" among all the
> relations. Formally:
>
> Q < R iff Q /\ R = R
>
> where "/\" is a symbol for relational join. (I don't quite like the
> "&&" symbol that Marshall uses:-)
>
> Next,
>
> Q = R iff Q < R and R < Q
>
> Now that we can compare relational valued attributes, we can define all
> the RA operations. Interestingly, set joins (and relational division)
> are easily expressed in this framework. For example, given
>
> A = { <x=1, y={<t=a>,<t=b>}> , <x=2, y={<t=b>,<t=c>} > }
>
> B = { <y={<t=a>} }
>
> Then, inequality join
>
> A /\_a.y<b.y B
>
> is the same as relational division between "flattened" A and B
> relations.
Received on Thu Jan 18 2007 - 22:02:26 CET