# Re: A Simple Notation

From: David Cressey <cressey73_at_verizon.net>
Date: Thu, 05 Jul 2007 13:07:44 GMT
Message-ID: <A26ji.4526\$wu5.3127_at_trndny03>

"Brian Selzer" <brian_at_selzer-software.com> wrote in message news:wd5ji.20671\$RX.16718_at_newssvr11.news.prodigy.net...
>
> "David Cressey" <cressey73_at_verizon.net> wrote in message
> news:kv4ji.6553\$za5.2586_at_trndny09...
> > In Boolean algebra, you could, if you wanted to, express everything by
> > just
> > using brackets, as follows:
> >
> > [A B] means NOT (A AND B)
> >
> > This notation can be extended to 3 or more operands, as follows:
> >
> > [A B C] means NOT (A AND B AND C)
> >
> > "AND" is associative, so there's no confusion.
> >
> > You can reduce the notation to 1 operand as follows:
> >
> > [A] means NOT (A)
> >
> > And to zero operands as follows:
> >
> > [] means TRUE
> > [[]] means FALSE
> >
>
> I would switch these because the nullary product is 1, or TRUE, and the
> nullary Cartesian product is {()}, or DEE. I think that you would agree
> that [DEE] should be FALSE.
>

> [] should mean FALSE
> [[]] should mean TRUE

I contemplated what you suggest, and I chose to let the representation of TRUE be []. You can read it as "not nothing". Regardless, we agree that [[]] represents NOT ([]). What do you gain by going the other way?

Another choice I'm far more hesitant about is whether I should have begun with AND and <AND> or OR and <OR>. You can go either way. <AND> looks "computationally simpler" to me, and that's why I chose it. But I might regret that choice downstream, and have to come back to this point and start over. Received on Thu Jul 05 2007 - 15:07:44 CEST

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