Re: A different definition of MINUS, Part 3
Date: Tue, 23 Dec 2008 06:41:04 -0800
Walter Mitty wrote:
> "paul c" <toledobythesea_at_oohay.ac> wrote in message
>> paul c wrote: >> ... >>> >>> ... Projection and <REMOVE> are always fundamental. ... >>> >> Oops, should have said <REMOVE> (projection) and <RENAME> are always >> fundamental.
> I am sorry to be so dense, but I need further explanation...
> I asked whether <AND> <OR> &<NOT> are the three fundamental ones you
> referred to.
> I sounds, from your two answers as though the answer is "no". If I
> understand you right, the three fundamentals are:
> Either <NAND> or <NOR>, take you pick.
> <REMOVE> (projection)
> Is this right?
Yes, I think that you have said it right. This quote is from page 8 of
We do not actually need both <AND> and <OR> in order to achieve relational completeness, thanks to De Morgan's Laws. For example, A <AND> B is identically equal to <NOT>((<NOT> A) <OR> (<NOT> B)), so we could dispense with <AND> if we included both <NOT> and <OR>. We could even collapse <NOT> and <OR> into a single operator, <NOR> ("neither A nor B"; equivalently, "not A and not B"). Equally well, of course, we could dispense with <OR> and collapse <AND> and <NOT> into a single operator, <NAND> ("not A or not B"). Overall, therefore, we could if desired reduce our algebra to just three operators: <RENAME>, <REMOVE>, and either <NOR> or <NAND> (plus <TCLOSE>). (end quote)
(This quote is not part of the formal definition (pages 12 to 14), it is just part of D&D's surrounding explanation. I think that all one really needs to understand are pages 12 to 14, which seem self-contained to me.) Received on Tue Dec 23 2008 - 15:41:04 CET