Re: Basic question?What 's the key if there 's no FD(Functional Dependencies)?

Jan Hidders wrote:
> NENASHI, Tegiri schreef:
>
> > Jan Hidders wrote:
> > > Do you know of any results that might be interesting for database
> > > theory and could not already be shown with good old set theory?
> >
> > The categorical sketches to use for universal view updatability:
> >
> > Michael Johnson and Robert Rosebrugh.
> > Universal view updatability
>
> That's not a result but a reformulation of the problem in new
> terminology.

It is not a reformulation but to find the universal property of updatability: let E be a sketch, V a view of the sketch, Mon(E) the category of models of the sketch E whose arrows are monic. The universal property of updatability is the functor F:Mon(V)==>Mon(E) must be left and right fibration.

I have already written to Aloha that the union updatability for SQL is not permitted but the category property permits the updatability in certain case:

• The union view is a coproduct in the category language. Generally, the
• coproduct is not updatable but if one injects an element that is not in
• the database like one of the legs of the coproduct, it will be
• updatable. The universal property of updatability that the functor
• F:Mon(V)==>Mon(E) must be left and right fibration is honored. The
• proof is easy. Like I recollect the SQL union is never updatable.

It is a new result, no ?

> What does it learn us that we didn't know already from
> work by for example Georg Gottlob or Stephen Hegner?

I do not know the works. Did they use the sketch data model ?

The sketch model permits the closure that other models that are not relational do not permit. The people in other nonrelational models are very busy to climb in the XML trees and to lose their time in the XML forest. It is sad that they do not have the time to study the category theory. It is why they can not have the closure of algebra of XML.

The sketch model has a very naturel and rich expression of constraints: the commutativity of diagrams, the finite limits and the coproducts. Did the people that you speek of develop the constraints ?

The sketch model permits to study the generic model management. You can read works of Philip Bernstein and Zinovy Diskin. You can learn that the relational algebra does not permit to study the generic model management.

The sketch model, it is also a very good instrument for semantical modelling.

Bonne chance dans tes etudes !

--
Tegi


I> 


> -- Jan Hidders