[SCL] Functional dependencies

[Chris Menzel]

On Mon, Jun 20, 2005 at 04:11:03PM -0500, John Sowa wrote:
> A functional dependency does not *add* anything to a
> relation.  It recognizes a feature that is already present.

Sure thing. Since we don't assume in CL that relations are extensional,
it seems to me that we can't (or shouldn't) *define* functionality, as
it might just be an accident that a certain relation is functional --
though I think Pat would be inclined to think that notions of essence
and accident are part of a big philosophical fairy tale.  If one goes
with Pat, then functionality is definable (though it turns out that all
"individuals" are functions -- that may or may not be a problem):

(iff (function ?R)
     (forall (?x ?y @z)
             (implies (and (?R ?x @z) (?R ?y @z))
                      (= ?x ?y))))

If not, then "function" should be taken as a primitive and the "iff"
there should be replaced by "implies".

Note that, without seq vars, we can only define or axiomatize
functionality piecemeal for n-place relations, for each n -- and we miss
variably polyadic functionality completely.

Actually, I'm not exactly sure how all of this relates to the point you
were making, John... :-)

-chris