Re: Idempotence and "Replication Insensitivity" are equivalent ?

<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 duplicationinsensitive.

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.

-- 
Chris Smith