Re: KIF Axioms of Restriction

Yes, it is certainly the case that an object that has no ?p's has all its
?p's belonging to ?c, and thus belongs to the restriction mentioned below.

Peter Patel-Schneider


From: "Mitch Kokar" <kokar@coe.neu.edu>
Subject: KIF Axioms of Restriction
Date: Fri, 9 Mar 2001 10:54:45 -0500

> 
> 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. 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?
> 
> 
> ==Mitch Kokar
>   Verstatile Information Systems, Inc.
>