Re: A simple notation, again

From: paul c <>
Date: Mon, 16 Jul 2007 15:56:42 GMT
Message-ID: <_yMmi.122916$1i1.35302_at_pd7urf3no>

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.

Eg., for simplicity, assume A and B have identical headings and the possible tuples for each of them include t1, t2, t3, ..., tn. Suppose A has only the tuple t1 and B only the tuple t2. The implication (result) would include every possible tuple except t1, because t2, t3, ... tn are all true of "NOT t1". Ie., it could have many, many tuples that are not in either A or B.

p Received on Mon Jul 16 2007 - 17:56:42 CEST

Original text of this message