# Re: A Simple Notation

From: Bob Badour <bbadour_at_pei.sympatico.ca>

Date: Thu, 05 Jul 2007 10:55:37 -0300

Message-ID: <468cf844$0$4318$9a566e8b_at_news.aliant.net>

> using

> represent it

> The truth is that <AND> and <OR> are new territory for me, and quite

Date: Thu, 05 Jul 2007 10:55:37 -0300

Message-ID: <468cf844$0$4318$9a566e8b_at_news.aliant.net>

> "Bob Badour" <bbadour_at_pei.sympatico.ca> wrote in message

*> news:468cef93$0$4340$9a566e8b_at_news.aliant.net...
**>
*

>>David Cressey wrote: >> >>>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 >>> >>>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. >> >>The RA generally replaces NOT with MINUS to avoid dealing with >>open-ended or infinite relations. D&D show a similar approach in the >>version of TTM that I have where they allow open-ended negation. They >>use it to show that function calls are just another sort of relation >>etc. Paul C mentions it here a lot. >> >>Then again, perhaps you refer to the same thing with <AND> and <OR> in >>which case, I simply agree that using [A B] to mean <NOT>(A <AND> B) >>achieves something similar.

*>*> The truth is that <AND> and <OR> are new territory for me, and quite

*> possibly over my head.**> But if the RA really is isomporhic to Bollean Algebra, then I'd like to**> leverage what I think I do understand in order to better understand**> something else.**>**> As far as replacing <NOT> with MINUS, something similar is done with 2s**> complement integer notation. We represent -1 in the computer as 2^X-1**> where X is some number like 32.**> My mind is not made up on this score. It's clear that, at implementation**> time, you have to settle for what's finite, as least witihn a certain**> limited time frame.*I see the problem of NOT as being more than just the infinite. Most actual uses of NOT in human communication have some implicit or explicit universe of discourse. From a computational perspective, unless one makes the universe explicit, which is basically what MINUS does, the result is indeterminate even when finite. Received on Thu Jul 05 2007 - 15:55:37 CEST