Re: A Simple Notation
From: Bob Badour <bbadour_at_pei.sympatico.ca>
Date: Fri, 06 Jul 2007 12:10:11 -0300
Message-ID: <468e5b3e$0$4318$9a566e8b_at_news.aliant.net>
>
> but
>
>
> (such
>
>
> his
>
>
> of
>
>
> In reaction to Brian's responses, I'm going to reformulate the notation,
> using OR and <OR> instead of AND and <AND>
>
> Thus the starting place is:
>
>
> [A B] means <NOT> (A <OR> B) in RA.
>
> Extending to 3 or more operands.....
>
> [A B C] means <NOT> (A <OR> B <OR> C) and so on.
>
> This is a classic "inverter" which I think is the same as a NAND gate.
>
> 1 operand:
>
> [A] means <NOT> A as before.
>
> No operands:
>
> [] means TRUE
> [[]] means FALSE as before.
>
>
> One more item:
>
> [[]] =
>
> Yes, that's right, there's nothing to the right of the equal sign. At
> least at this level there is no need to introduce a third logical value to
> deal with missing items.
>
> I still haven't figured out how to make use of Bob's response regarding
> MINUS as distinct from <NOT>
>
> I guess I would want
>
> [A] to mean X MINUS A for some X that I can't figure out. Still mulling
> on this.
Date: Fri, 06 Jul 2007 12:10:11 -0300
Message-ID: <468e5b3e$0$4318$9a566e8b_at_news.aliant.net>
David Cressey wrote:
> "Brian Selzer" <brian_at_selzer-software.com> wrote in message
> news:UHlji.18386$2v1.9600_at_newssvr14.news.prodigy.net...
>
>>"paul c" <toledobythesea_at_oohay.ac> wrote in message >>news:4Ifji.90354$xq1.46042_at_pd7urf1no... >> >>>Brian Selzer wrote: >>>... >>> >>>>The symmetry is rather pleasing. >>>>... >>> >>>Not saying that the above comment by itself deserves to be criticized,
>
> but
>
>>>I would say that apparent lack of symmetry doesn't necessarily mean a >>>method doesn't have same, just that we are unable to see it in some >>>mechanical interpretation that we happen to prefer for other reasons
>
> (such
>
>>>as, "it gets the answer we want!"). >>> >> >>As far as I can tell, David's choice of [] for TRUE is arbitrary. It's
>
> his
>
>>notation, and therefore it's his perogative to do as he pleases. But what >>is contained within the brackets is a conjunction of an arbitrary number
>
> of
>
>>boolean values, so it makes sense to view [] as the negation of a nullary >>product just as it makes sense to view [A] as the negation of a unary >>product, or [A B] as the negation of a binary product, and so on. Now had >>David begun with OR and <OR>, then it would have made sense to view [] as >>the negation of a nullary sum. A nullary sum takes on the value of the >>additive identity which is 0 or FALSE, whereas a nullary product takes on >>the value of the multiplicative identity which is 1 or TRUE. So, >> >>for OR and <OR>, [] should yield TRUE, but >>for AND and <AND>, [] should yield FALSE >> >> >>>p >> >>
>
> In reaction to Brian's responses, I'm going to reformulate the notation,
> using OR and <OR> instead of AND and <AND>
>
> Thus the starting place is:
>
>
> [A B] means <NOT> (A <OR> B) in RA.
>
> Extending to 3 or more operands.....
>
> [A B C] means <NOT> (A <OR> B <OR> C) and so on.
>
> This is a classic "inverter" which I think is the same as a NAND gate.
>
> 1 operand:
>
> [A] means <NOT> A as before.
>
> No operands:
>
> [] means TRUE
> [[]] means FALSE as before.
>
>
> One more item:
>
> [[]] =
>
> Yes, that's right, there's nothing to the right of the equal sign. At
> least at this level there is no need to introduce a third logical value to
> deal with missing items.
>
> I still haven't figured out how to make use of Bob's response regarding
> MINUS as distinct from <NOT>
>
> I guess I would want
>
> [A] to mean X MINUS A for some X that I can't figure out. Still mulling
> on this.
Bob was only noting a difference. In what you have above, the X is implicit (and probably infinite) whereas using MINUS requires it become explicit.
I suggest Vadim's comments are probably much more informative (and informed.) Received on Fri Jul 06 2007 - 17:10:11 CEST