Re: Logical = relational?

Jan Hidders wrote:
[...]
> What about Wittgenstein (proof by truth
> tables),

That a common myth that Wittgenstein himself had denied. Frege is believed to be one of the first to use the truth tables.

> > The relation dimension moved from 2 to n, but remained fixed.
> > E Codd expanded the idea to manipulate relations of mixed dimensions.
>
> Mixed dimensions? I have no idea what that means. Codd also talked
> about n-ary relations so I don't see what in what sense the idea was
> expanded except that perhaps the places in the predicates now became
> labled with names.

The cylindric set algebra universe consists of fixed, but not necessarily finite, arity relations whereas Codd's relational algebra can freely mix relations of different arities. However, that is a technicality and Codd's RA algebra can be easily translated into CSA as Imielinski and Lipski showed ca. 1980. There have been numerous attempts to apply algebraic logic methods to relational databases with various degrees of success.

Generally, names of Boole, Tarski and Halmos and more recently Andreka and Nemeti are associated with the algebraic logic field. Codd's RA is not much of an innovation in this respect, although it arguably appears to be more suitable for the RM than other algebraic approaches.

>
> -- Jan Hidders
Received on Fri May 05 2006 - 05:25:24 CEST