# Re: A Simple Notation

Date: Thu, 05 Jul 2007 10:55:37 -0300
Message-ID: <468cf844\$0\$4318\$9a566e8b_at_news.aliant.net>

> 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
```

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> 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
> 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

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