Re: Is relational theory irrelevant? (was Re: Dreaming About Redesigning SQL)

"Paul" <pbrazier_at_cosmos-uk.co.uk> wrote in message news:51d64140.0311130156.6c376b59_at_posting.google.com...
> "Mikito Harakiri" <mikharakiri_at_iahu.com> wrote in message
news:<DxBsb.30$1n1.179_at_news.oracle.com>...
> > > Ordered domains do have logical order. Relations have no order, but
the
> > > values in the relations have order.
> >
> > That totally depends whom you ask, of course. A person with mathematical
> > background would have no trouble defining an order relation among the
tuples
> > of the original relation induced by the order defined on each domain
> > associated with individual column.
>
> I think the answer is due to the intended "real-life" meaning of
> relations.
> Clearly in general a set can have an ordering defined on it.
> But a relation isn't just any old set, it is a set of *logical
> propositions*.
> So:
>
> 1) the grass is green.
> 2) the sky is blue.
>
> means exactly the same as:
>
> 1) the sky is blue.
> 2) the grass is green.
>
> i.e. P1 AND P2 = P2 AND P1
>
> where P1, P2 are the propositions above.
> So you could say the fact that relations can't have an order comes
> down to the commutativity of the logical AND operator.

While the meaning of the statements does not change when we reorder them, it is possible to give them meaningful orders. For instance, we can sort the statements by wavelength (defined by the color data type) or we can sort the statements by elevation, and the resulting orders do not have to match.

We can partition the statements a number of ways according to the orders defined by the data types for the attributes or according to the orders defined bny derivable data types. A quota query is one such partition. A quota query is a shorthand for other relational operations assuming summarize as an operation.

As such, a quota query is a logication operation on relations that depends on the logical order of the data in the relation. Received on Thu Nov 13 2003 - 14:57:37 CET