# Re: A Simple Notation

Date: Fri, 06 Jul 2007 12:10:11 -0300
Message-ID: <468e5b3e\$0\$4318\$9a566e8b_at_news.aliant.net>

David Cressey wrote:

> "Brian Selzer" <brian_at_selzer-software.com> wrote in message
> news:UHlji.18386\$2v1.9600_at_newssvr14.news.prodigy.net...
>

```>>"paul c" <toledobythesea_at_oohay.ac> wrote in message
>>news:4Ifji.90354\$xq1.46042_at_pd7urf1no...
>>
>>>Brian Selzer wrote:
>>>...
>>>
>>>>The symmetry is rather pleasing.
>>>>...
>>>
>>>Not saying that the above comment by itself deserves to be criticized,
```

>
> but
>
```>>>I would say that apparent lack of symmetry doesn't necessarily mean a
>>>method doesn't have same, just that we are unable to see it in some
>>>mechanical interpretation that we happen to prefer for other reasons
```

>
> (such
>
```>>>as, "it gets the answer we want!").
>>>
>>
>>As far as I can tell, David's choice of [] for TRUE is arbitrary.  It's
```

>
> his
>
```>>notation, and therefore it's his perogative to do as he pleases.  But what
>>is contained within the brackets is a conjunction of an arbitrary number
```

>
> of
>
```>>boolean values, so it makes sense to view [] as the negation of a nullary
>>product just as it makes sense to view [A] as the negation of a unary
>>product, or [A B] as the negation of a binary product, and so on.  Now had
>>David begun with OR and <OR>, then it would have made sense to view [] as
>>the negation of a nullary sum.  A nullary sum takes on the value of the
>>additive identity which is 0 or FALSE, whereas a nullary product takes on
>>the value of the multiplicative identity which is 1 or TRUE.  So,
>>
>>for OR and <OR>, [] should yield TRUE, but
>>for AND and <AND>, [] should yield FALSE
>>
>>
>>>p
>>
>>
```

>
> In reaction to Brian's responses, I'm going to reformulate the notation,
> using OR and <OR> instead of AND and <AND>
>
> Thus the starting place is:
>
>
> [A B] means <NOT> (A <OR> B) in RA.
>
> Extending to 3 or more operands.....
>
> [A B C] means <NOT> (A <OR> B <OR> C) and so on.
>
> This is a classic "inverter" which I think is the same as a NAND gate.
>
> 1 operand:
>
> [A] means <NOT> A as before.
>
> No operands:
>
> [] means TRUE
> [[]] means FALSE as before.
>
>
> One more item:
>
> [[]] =
>
> Yes, that's right, there's nothing to the right of the equal sign. At
> least at this level there is no need to introduce a third logical value to
> deal with missing items.
>
> I still haven't figured out how to make use of Bob's response regarding
> MINUS as distinct from <NOT>
>
> I guess I would want
>
> [A] to mean X MINUS A for some X that I can't figure out. Still mulling
> on this.

Bob was only noting a difference. In what you have above, the X is implicit (and probably infinite) whereas using MINUS requires it become explicit.