# Re: A Simple Notation

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
**>
**>
*

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.

[] means TRUE

[[]] means FALSE as before.

I still haven't figured out how to make use of Bob's response regarding MINUS as distinct from <NOT>

[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