Re: Codd provided appropriate mathematics ... (was Re: Relational and MV (response to "foundations of relational theory"))

I of course don't know what was in Codd's head but there are a couple of reasons that he restricted his work to 1NF data. First of all, he was creating a theory of first order, extensional databases. He was showing how to implement 1st order relational algebra operations against a database. He proved the equivalence between relational algebra and the relational calculus to give himself the tools to prove theorems (in relational calculus) about the data language and its model. But his intent was to create a first order language and model. To put it simply, he did it because it was what he was trying to do. Secondly, keeping the data 1NF greatly simplified the assignment function for the model. This is the function that maps a relation in the data language to its interpretation in the model. For a first-order, function free language (with a 1NF model) the assignment function is '='. That is the interpretation of aRb is {a,b} or (a=a, b=b). But for a non-1NF language, it becomes more complex. Assignment functions for logics with the power to describe natural language for example have very complex assignment functions that map sets of properties to sets of points in space and time. This is not what Codd was trying to do...

To my knowledge Codd made no value judgments about the language and model that he created. Subsequent work in the '80's focused on non-first order languages (the so-called logical database theorists) and non-1NF languages (the ORDB folks).

"Dawn M. Wolthuis" <dwolt_at_tincat-group.com> wrote in message news:c18u0i$skr$1_at_news.netins.net...
> "mountain man" <hobbit_at_southern_seaweed.com.op> wrote in message
> news:dQRZb.70077$Wa.44456_at_news-server.bigpond.net.au...
> > "Dawn M. Wolthuis" <dwolt_at_tincat-group.com> wrote in message
> > news:c12ia2$p0l$1_at_news.netins.net...
> > > "mountain man" <hobbit_at_southern_seaweed.com.op> wrote in message
> > > news:r3%Yb.66336$Wa.13812_at_news-server.bigpond.net.au...
> > > > "Neo" <neo55592_at_hotmail.com> wrote in message
> > > > news:4b45d3ad.0402181740.42d42bc2_at_posting.google.com...
> > > > > Execute("SELECT * FROM BOB WHERE OUTPUT = FALSE");
> > > > >
> > > > > 19 Records Found:
> > > > > "Codd provided appropriate mathematical backing to all of his
> claims"
> > > >
> > > > ...[trim]...
> > > >
> > > > I'd be interested to hear about this. Empirical
> > > > evidence should either exist or not exist. The
> > > > "all" word might be troublesome.
> > >
> > > I have found at least one area where Codd takes a jump mathematically.
> > I'm
> > > not taking the time right now to get his exact wording, but a summary
is
> > > this:
> > >
> > > 1. In his 1970 paper, Codd goes through the mathematics of relations
> and
> > > indicates that elements in relations could, themselves, be relations.
> > > However, he suggests starting simply with relations that do not
contain
> > > relations.
> > > 2. In the 1974 paper and in the normal form discussions, normal forms
> are
> > > described so that "n" normal form is data that is in 1st normal form
and
> > > then ...
> > > 3. There is no mathematical foundation for putting the data into 1NF
> > except
> > > for what Codd and his followers indicate is that the model should be
as
> > > simple as possible but not simpler and they indicate that without
> > resorting
> > > to nested relations, the model is as simple as is needed. This is NOT
a
> > > mathematical conclusion.
> >
> >
> > It seems to be more of an hypothesis.
>
> Yes, but even as a hypothesis, it would not be a mathematical one. That
is
> fine with me as I have many hypotheses that would require emperical data
to
> be proven. However, it seems to me that a lot of students of relational
> database theory mistakenly think that there is some mathematical proof
that
> shows us this is the way to go in how we store and query data. While
there
> is a mathematical model involved, it is just one of many ways to model
data
> and there is no mathematical proof that it is "right" and that any other
is
> wrong. There is also, to my knowledge, no emperical data to suggest that
it
> is "right" from the perspective of yielding overall better, faster, more
> reliable, etc software applications. So, I think there is a significant
> myth about relational theory that is written in many college database
texts.

>