Re: A Simple Notation

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. Received on Thu Jul 05 2007 - 15:18:33 CEST