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?

==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
>
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Received on Wednesday, 14 March 2001 18:53:55 UTC