# Re: A Simple Notation

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.
**>
**>
**>
**>
**>
**>
**>
**>
**>
**>
**>
*

Received on Thu Jul 05 2007 - 14:11:08 CEST