Re: A Problem With The Semantics of DAML+OIL Restrictions

On Tue, 3 Jul 2001, Richard Fikes wrote:

[portion omitted]

>    (Type R Restriction)
>    (onProperty R parent)
>    (toClass R person)
> 
> We can certainly conclude that the parents of all objects that are type
> R are persons.  However, how can we legitimately conclude that an object
> all of those parents are persons is type R when the very next RDF
> statement in the file may be "(hasValue R Joe)"?  Those four statements
> together mean that in order to be type R an object has to have Joe as a
> parent and all of its parents must be persons.  Thus, the first three
> RDF statements give us a different set of sufficient conditions then do
> the four RDF statements.  The problem is that if there is no way of
> indicating that the definition of a non-primitive class is closed
> ("That's all, folks"), then there is no way for that definition to
> provide a set of sufficient conditions for membership in the class.

Why not use a cardinality constraint to bound the number of toClass (or
hasValue) values?

  (type RtoClass Restriction)
  (onProperty RtoClass toClass)
  (cardinality RtoClass "1")
  (type R RtoClass)

This restricts the number of toClass values of the R resource to be
exactly 1.  Since you know one of them, it follows that you know them all.
One can similarly restrict the number of hasValue values to be 0:

  (type RhasValue Restriction)
  (onProperty RhasValue hasValue)
  (cardinality RhasValue "0")
  (type R RhasValue)

Ken Baclawski
Versatile Information Systems
Ken@Baclawski.com