Re: A different definition of MINUS, Part 3
Date: Sun, 21 Dec 2008 14:49:25 -0800
> On Dec 21, 11:53 am, Bob Badour <bbad..._at_pei.sympatico.ca> wrote:
>> vadim..._at_gmail.com wrote: >>> On Dec 21, 11:36 am, vadim..._at_gmail.com wrote: >>>> x + y = ((x ^ x)' ^ (y ^ y)')'. >>>> ... is tough... >>> Actually, easy. The right side simplifies to >>> x + y = (x' ^ y')'. >>> Applying double negation (provable in RL), we get >>> (x+y)' = x' ^ y'. >>> De Morgan, which is again provable in RL. Amazing. >> Why are you amazed?
> Two reasons:
> 1. Relational Algebra is a weaker system than boolean algebra.
> Therefore there is no reason to expect BA properties to carry over.
> 2. All RA operation, not just three can be reduced to a single one.
> Here is my worksheet:
> Join, is <AND>. It is representable in terms of Sheffer stroke.
> Projection, is inner union in RL terms. Well, I don't see how to
> represent inner union in terms of other operations:-(
I like the inner union very much, as a two-operand replacement for projection/Exists, provided <OR> is retained for convenience. While it may not have any present use in the A-algebra, there might be a future use but I need to do a lot of work to show that.
However, I think something like <RENAME> is still needed, for example to
define certain constraints such as functional dependencies. Received on Sun Dec 21 2008 - 23:49:25 CET