Re: A simple notation, again

"Bob Badour" <bbadour_at_pei.sympatico.ca> wrote in message news:469bac76$0$8868$9a566e8b_at_news.aliant.net...
> David Cressey wrote:
>
> > Using the notation [A B C] for <NOT> (A <AND> B <AND> C), etc.
> >
> > The following [ A [B]] means "A implies B" for Boolean algebra.
What is
> > the corresponding thing for Relational Algebra?
> >
> > Also, I'm trying to come up with a bracket notation for a "literal
> > relation", like literals for simple datatypes like numbers and
character
> > strings.
> >
> > I'm toying with this:
> >
> > [["David" "Cressey" 1]
> > ["Marshall" "Spight" 2]
> > ["Bob" "Badour" 3]
> > ["Jan" Hidders" 4]]
> >
> >
> >
> > This would represent a relation of order 3 and cardinality 4.
> >
> >
> > What I don't like about this is that the binding between attribute
values
> > and attribute names is
> > by position rather than by name, and in fact the attribute names don't
even
> > appear here. That's unacceptably bad. The symmetry is appealing, but
it
> > clearly needs improvement.
>
> You omitted names entirely. You would have to extend the syntax to
> something like:
> [[name="David" surname="Cressey" n=1]
> [n=2 name="Marshall" surname="Spight"]
> [surname="Badour" name="Bob" n=3]
> [name="Jan" surname="Hidders" n=4]]

Yeah, that'll do it, all right. To be consistent with the former notation, each attribute=value pair needs to be construed as a relation of order 1 and cardinality 1.

The extended <AND> of a single name, a single surname, and a single n, will be the cartesian extended product, which will be a relation of order 3 and cardinality 1.
Outside the inner bracket, what we have is the <NOT> of this, which I'll call the <NOT> of a <TUPLE>. Where <TUPLE> means a relation of cardinality one.

We have four of these <NOT> of a <TUPLE>, connected by an extended <AND> . This time the extended <AND> resolves to the intersection of the operands, bercause all the operands have the same attributes.

So inside the outer brackets we have the intersection of a collection of <NOT>s of <TUPLE>s.
This is equivalent to the <NOT> of the union of the <TUPLE>s. Outside of the outer brackets, we have the <NOT> of the <NOT> of the union of the <TUPLE>s, This is the union of the <TUPLE>s, which is the desired relation.

Does this make any sense at all, from a mathematical perspective? I am definitely in over my head, here. Received on Mon Jul 16 2007 - 21:46:53 CEST