# Re: A Simple Notation

From: David Cressey <cressey73_at_verizon.net>
Date: Thu, 05 Jul 2007 13:35:55 GMT
Message-ID: <%s6ji.5209\$105.2576_at_trndny08>

> 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.

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. Received on Thu Jul 05 2007 - 15:35:55 CEST

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