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From: "Mikito Harakiri" <mikharakiri_nospaum@yahoo.com>
Newsgroups: comp.databases.theory
Subject: Re: Logical = relational?
Date: 4 May 2006 15:34:07 -0700
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Jan Hidders wrote:
> > 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.

I had an impression that Cylindric Algebras are "homodenous" algebras
of the relations which have the same dimension. Take the
cylindrification, for example (Van den Bussche "Applications of Tarski
Ideas in DB theory"): "The cylindrification along the dimension i of
the relation r < A^n with i in {1,...,n} we mean the operation:

y_i(r) = {(a_1, ..., a_n) in A^n | ...}

In other words cylindrification unlike projection doen't reduce
relation arity.