Re: Complete axiomatization of relational algebra

Neil Nelson wrote:
> "Drieux...just Drieux" wrote:
> > Jan Hidders wrote:
> > >
> > > Does anybody know if there is a complete algebraic axiomatization
> > > of the relational algebra (as used in relational database theory)
> > > or a proof that such a thing is not possible?
> >
> > There have been papers published on this, of which I'm sure you're
> > aware. You might want to have a look both at xxx.lanl.gov and at the
> > Hypatia on-line library.
> >
> > I'll look through my own files; my research area is category theory, and
> > I'm a practising consultant dealing with VLDB and VLDW problems. I've
> > seen approaches to this topic, but the actual reduction to an axiomatic
> > basis, if it was done, has eluded me.
>
> Here is one way of approaching this question.
>
> If we are just talking about a set of tables each identified as some
> sequence of properties that take values as rows and that sequence
> repeated as rows, and with some properties from table to table whose
> values are associated as keys or pointers, then this arrangement may
> be converted to a single set of elements each having a uniform set of
> properties. I.e., we should be able to `denormalize' to a single
> table. The primary operation on this table is to ask what rows have
> some set of property values that consists of set intersection and
> union. The operation identifies which rows satisfy, say, some
> conjunctive (disjunctive) normal form of monadic predicates, and
> where each predicate is on a particular property.

Ah, yes, the universal relation approach. Often used in the past in articles on database theory as a simplifying assumption. But it is not as expressive as the normal algebra. You cannot do joins on attributes with different names for instance. So it is like having the algebra without the rename operator.

-- 
  Jan Hidders