Re: Idempotence and "Replication Insensitivity" are equivalent ?

Chris Smith wrote:
> <pamelafluente_at_libero.it> wrote:
> > Hi Marshall :) , Hmmm,
> >
> > T T F should evaluate to F
> > T would be in contrast with NOR definition:
> >
> >
> > "A predicate in logic equivalent to the composition
> > NOT OR that yields false (F) if ANY condition is true,
> > and true (T) if ALL conditions are false. "
>
> Hmm. In that case, the aggregate you want can be defined in two ways:
>
> 1.
> x_0 = T
> g(F,x) = F
> g(T,F) = T
> g(T,T) = F
>
> So in this case, it appears that you are right, under my (most correct)
> formalism. In this case, g is not idempotent and yet f is duplication-
> insensitive.

Not quite; see my earlier post on the T,T,F case. Also you have a mistake above: g(F,F) = T. If g is NOR, the aggregate is duplication sensitive.

> 2. Define it as a non-primitive aggregate function, as follows. First,
> define OR:
>
> x_0 = F
> g(F,F) = F
> g(x,x) = T otherwise
>
> Finally, define NOR as the complement of OR.
>
> This one works. The difference is that in the latter case, x_0 is an
> identity of g. That condition is sufficient for idempotence to be
> equivalent to duplication-insensitivity. Unfortunately, not all
> aggregate functions can be converted into such a definition. For
> example, there's no clean way to define COUNT in that manner.

COUNT: x_0 = 0
g(x, y) = y+1

Marshall Received on Tue Sep 19 2006 - 22:20:44 CEST