Re: A Simple Notation

From: David Cressey <cressey73_at_verizon.net>
Date: Fri, 06 Jul 2007 13:18:02 GMT
Message-ID: <eirji.2\$475.1_at_trndny04>

"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
>
>

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.

[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. Received on Fri Jul 06 2007 - 15:18:02 CEST

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