# Re: A Simple Notation

From: Brian Selzer <brian_at_selzer-software.com>
Date: Thu, 05 Jul 2007 12:11:08 GMT
Message-ID: <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

> You can build up everything else from there. For example,
>
> [[A B]] = A AND B
> [[A] [B]] = A OR B
>
> Now my question is, can you do the corresponding thing in the RA, using
> <NOT> and <AND>? I don't see why not.
>
> So you would get (for example)
>
> [[A B]] = A <AND> B
> [[A] [B]] = A <OR> B
>
> As written text, this notation is rather unwieldy, but you can represent
> it
> fairly tightly in internal data structures. And its simplicity does make
> some things easier.
>
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Received on Thu Jul 05 2007 - 14:11:08 CEST

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