# Re: A simple notation, again

Date: Mon, 16 Jul 2007 11:58:24 -0700

Message-ID: <1184612304.854603.221750_at_e16g2000pri.googlegroups.com>

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:

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