# Re: Urgent! Semantic question about rdfs:domain.

From: pat hayes (phayes@ai.uwf.edu)
Date: 04/25/01

```>pat hayes wrote:
> >
> > [...]
> > It says
> >
> > <rdfs:domain,?P,?C>    means:    if <x,y> in IR(?P) then x in IC(?C)
> >
> > but if the above is correct then it ought to say:
> >
> > <rdfs:domain,?P,?C>    means:   if x in IC(?C) then for some y,
><x,y> in IR(?P)
>
>Er... yeah, the latter corresponds to what I remember
>from when I first learned about functions, domains,
>and ranges. But the former is the rule that I've used
>several times recently.
>
>The latter does imply the former, no?
>(I can't seem to work out the details in my head.)

No!  Say that the REAL domain (the one mathematicians talk about) is
the set of x such that there is some y with <x,y> in IR(?P). Then the
former says that IC(?C) is a subset of the real domain, and the
latter says that the real domain is a subset of IC(?C).  Neither
entails the other.

In a perfect world we might want to say both are true, but that would
require all our properties to be an exact fit on their domains, which
would make life very knife-edge for DAML formalizers.

> > If the semantics is correct, however, then the example in the
> > walkthrough is rather misleading, and we will need to correct against
> > any potential misunderstanding. Also, in this case, HOW does someone
> > give a 'lower' bound to the domain of a property? Eg how can one say
> > that hasParent applies to *any* animal? (If both domain and range
> > restrict from above, then it would be consistent to give all
> > properties empty domains and ranges.)
>
>Er... huh? an empty range for ?P means there are no ?y's
>for which <?x, ?y> in ?P, no?

Right. So suppose there arent any parents, for example. Then it is
trivially true that  if <x,y> in IR(hasParent) then x in IC(animal),
so the rdfs:domain would be satisfied, so DAML wouldn't complain (if
the current semantics is right.)  But I think the intention is
clearly that it ought to complain in this case.

>I think I'm lost.

OK, never mind the empty bit. The point is, how do we say that P is
defined on everything in a class, eg that every animal has a parent?
If the semantics is right as it stands, then rdfs:domain doesn't say
this, and I can't see any other way to say it.

> > I await clarification from the Semantic Gurus, and will write
> > appropriate prose for the walkthru when clarity is restored to my
> > mind.
>
>I'm no semantic Guru, but I find the latter definition
>more appealing.

So do I, but I bet its not what the description logicians will be happy with.

Peter, Ian, Deborah??

Pat

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