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 Friday, 9 March 2001 16:55:38 UTC