Re: [KIF] Re: SUO: tuples
On Sun, Jul 07, 2002 at 04:50:34PM -0700, Robert E. Kent wrote:
> > In fact, the only way I can think of to get some such approach with
> > sequences to work is to allow only unary predicates in one's
> > language and to force domains to consist of nothing but sequences of
> > objects.
> What would be the limitations or problems with this approach?
Well, now that I think of it, I'm just not sure how it would work, as
there seem to be conflicting requirements. John wants to incorporate an
object language theory of sequences. But a theory of sequences requires
a binary predicate for concatentation, at least. But then it doesn't
seem like we can do everything with just unary predicates. I dunno,
maybe I'm just confused, but I really don't see how it's supposed to
work. But even if it can, I just don't see any warrant for such a
radical departure from the conventional semantics of FOL. Granted, in
that semantics, there's a *sense* in which all relations are unary
properties that are true of n-tuples, but that's just a metatheoretic
representation of the idea of a relation holding among individuals.
Those n-tuples are not themselves things in the domain of
> I ask that because there may be a connection between this approach and
> that of the IFF-MT, where
> 1. we identify sequences with tuples, and
> 2. we identify the unary predicates above with the classification
> relation between tuples (relation instances) and relation types (R s)
> iff s |= R
> 3. relations have a fixed arity (where the arity is a
> sequence of entity types; i.e. we have sorts)
> 4. domains that consist
> of sequences of objects are Cartesian products of component domains
> (actually, the IFF-MT relaxes this a bit).
OK. But does this mean you actually quantify over sequences? Or is it
just a nice abstract packaging of the usual semantics of FOL?