Re: A Simple Notation

"David Cressey" <cressey73_at_verizon.net> wrote in message news:A26ji.4526$wu5.3127_at_trndny03...
>
> "Brian Selzer" <brian_at_selzer-software.com> wrote in message
> news:wd5ji.20671$RX.16718_at_newssvr11.news.prodigy.net...
>>
>> "David Cressey" <cressey73_at_verizon.net> wrote in message
>> news:kv4ji.6553$za5.2586_at_trndny09...
>> > 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
>> >
>>
>> I would switch these because the nullary product is 1, or TRUE, and the
>> nullary Cartesian product is {()}, or DEE. I think that you would agree
>> that [DEE] should be FALSE.
>>
>
>> [] should mean FALSE
>> [[]] should mean TRUE
>
> I contemplated what you suggest, and I chose to let the representation of
> TRUE be []. You can read it as "not nothing". Regardless, we agree
> that
> [[]] represents NOT ([]). What do you gain by going the other way?
>

[T T T T] = [T T T] = [T T] = [T] = F

This just makes sense to me:

[T T T T] = [T T T] = [T T] = [T] = [] = F

The symmetry is rather pleasing.

Also, if you choose to eliminate contradictions, then

[A [A]] becomes [], but [A [A] B] becomes [B]

This makes sense only if [] = [T].

> Or, in the RA world, [[]] represents <NOT> ([]).
>
> Another choice I'm far more hesitant about is whether I should have begun
> with AND and <AND> or OR and <OR>. You can go either way. <AND> looks
> "computationally simpler" to me, and that's why I chose it. But I might
> regret that choice downstream, and have to come back to this point and
> start over.
>

I think AND and <AND> make more sense for queries, but OR and <OR> might make more sense for updates.

>
>
>
Received on Thu Jul 05 2007 - 22:45:53 CEST