RE: KIF Axioms of Restriction

I guess I was confused by the statement in daml+oil-walkthru.html - an
annotated version of the example ontology, which states that:

"What happens here is that the Restriction defines an anonymous class,
namely the class of all things that satisfy the restriction. In this case:
the class of all things whose parent is a Person."

This example does not say that besides this, this class includes all things
that have nothing to do with the property "hasParent", i.e., all things for
which the restriction is trivially satisfied. If the intent is to also
include all of those things, then the example should better say this
explicitly.

Moreover, the consequence of this way of restricting properties is not only
that restrictions are infinite, but also that whenever we extend an
ontology, all restrictions expand (well, almost all).


==Mitch



> -----Original Message-----
> From: pat hayes [mailto:phayes@ai.uwf.edu]
> Sent: Thursday, March 15, 2001 9:21 PM
> To: Mitch Kokar
> Subject: RE: KIF Axioms of Restriction
>
>
> >Thank you very much for the input. I received another message
> from Peter; he
> >also agreed with my interpretation of the KIF axioms.
> >
> >The question is - is this the intent of the language specification?
>
> Yes, I believe so.
>
> As this seems very clear from the spec., may I ask why you are
> questioning it so persistently? Do you feel that it should be
> different, or that it is confused, or confusing, in some way?
>
> Pat Hayes
>
> >==Mitch
> >
> >
> >
> > > -----Original Message-----
> > > From: pat hayes [mailto:phayes@ai.uwf.edu]
> > > Sent: Friday, March 09, 2001 4:57 PM
> > > To: Mitch Kokar
> > > Cc: www-rdf-logic@w3.org
> > > Subject: Re: KIF Axioms of Restriction
> > >
> > >
> > > >I have a question regarding the notion of Restriction. In order to
> > > >understand this notion, I looked at "Annotated DAML+OIL Ontology
> > > Markup" and
> > > >at the KIF axioms.
> > > >According to Axiom 88, the restriction class ?r is defined as
> > > all those ?i's
> > > >for which the implication (PropertyValue ?p ?j) => (Type ?j
> ?c) is true.
> > > >This means that that if
> > > >(PropertyValue ?p ?i ?j) holds, (Type ?j ?c) must hold, too.
> > > This is clear.
> > > >I thought that the intent was that ?i should be in ?r whenever both
> > > >(PropertyValue ?p ?i ?j) and (Type ?j ?c) are true.
> > >
> > > That intent would be captured by a conjunction (intersection) rather
> > > than a restriction.
> > >
> > > > But the implication is
> > > >true also when (PropertyValue ?p ?i ?j) is false.
> Consequently, class ?r
> > > >contains lots of objects, not necessarily related to the
> property ?p. It
> > > >seems that in most cases it would be even infinite. To be
> sure that my
> > > >interpretation of this KIF axiom was correct I asked Richard
> > > Fikes. Here is
> > > >his statement:
> > > >
> > > >"I think you are correct.  Namely, a class of type Restriction with a
> > > >toClass restriction C and an onProperty restriction P is the class of
> > > >all objects all of whose values of property P are type C.
> That includes
> > > >all objects that have no value for property P."
> > > >
> > > >He also suggested that this question should be posted to
> this list for
> > > >discussion. The question is whether this is the intent of
> the language
> > > >designers?
> > > >
> > >
> > > That would be my understanding also.
> > >
> > > The intuitive oddity of the conclusion arises, I think, from thinking
> > > of a restriction as a category.  Restriction classes are rather
> > > peculiar if thought of as collections. For example, the set of all
> > > things such that if they have red hair then they are Irish contains
> > > everything that doesnt have red hair, which might include planets and
> > > electrons as well as non-red-haired Irishmen. The utility of a
> > > restriction class only becomes apparent when you intersect it with
> > > the kind of class it was meant to be restricting.
> > >
> > > Pat Hayes
> > >
> > > ---------------------------------------------------------------------
> > > IHMC					(850)434 8903   home
> > > 40 South Alcaniz St.			(850)202 4416   office
> > > Pensacola,  FL 32501			(850)202 4440   fax
> > > phayes@ai.uwf.edu
> > > http://www.coginst.uwf.edu/~phayes
> > >
> > >
>
> ---------------------------------------------------------------------
> IHMC					(850)434 8903   home
> 40 South Alcaniz St.			(850)202 4416   office
> Pensacola,  FL 32501			(850)202 4440   fax
> phayes@ai.uwf.edu
> http://www.coginst.uwf.edu/~phayes
>
>

Received on Friday, 30 March 2001 15:55:48 UTC