Re: A simple notation, again
Date: Mon, 16 Jul 2007 11:58:24 -0700
On Jul 16, 8:56 am, paul c <toledobythe..._at_oohay.ac> wrote:
> 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?
> > ...
> In "TTM-A" I believe it is "(<NOT> A) <OR> B", which is on the surface,
> similar to Boolean algebra. Supposing A and B have identical headings,
> the value could have a very large number of tuples because it would
> include all possible tuples that don't match any tuple in A, and many of
> those tuples might not appear in B either.
> This "explosion" seems to be a consequence of relational domains having
> many more possible values than the two values that boolean variables have.
Boolean algebra can have more than 2 values. Is the "A imply B" construction well defined then? There are 2 possibilities:
- "A imply B" interpreted as a partial order relation A < B.
- "A imply B" interpreted as low level "material" implication, which is boolean algebra element !A \/ B. We'll keep the "A->B" notation for material implication.
There is nice connection between them
(A->B) & (B->C) < (A->C)
which is an easy theorem in the boolean algebra.
Now, moving on from boolean algebra to relations, we have obvious difficulty definting partial order relation in D&D algebra, and defining material implication in relational lattice... Received on Mon Jul 16 2007 - 20:58:24 CEST