Re: a problem with comprehensive entailments

cyFrom: "Jonathan Borden" <jonathan@openhealth.org>
Subject: Re: a problem with comprehensive entailments
Date: Mon, 6 May 2002 08:29:09 -0400

> Jos,
> 
> Is there a way that you can place a finite boundary on the number of times
> this back and forth will occur, that is, is there a way, using comprehensive
> entailments, that you will be absolutely certain that the entailments are
> actually comprehensive? For example, suppose we decide to go with this
> approach, and then just after CR, for example, someone demonstrates yet
> another example of a paradox for which no easy rule can be developed. What
> then?
> 
> Jonathan

Along the same lines, here are some interesting consequences of an ontology
language with reasonable comprehension principles.

These are consequences of the empty KB:

_:0 owl:onProperty rdf:type .
_:0 owl:minCardinality 0 .
_:0 rdf:type _:0 .

_:1 owl:onProperty rdf:type .
_:1 owl:minCardinality 1 .
_:1 rdf:type _:1 .

Question:  What is the minimum n such that

_:n owl:onProperty rdf:type .
_:n owl:minCardinality n .
_:n rdf:type _:n .

is not a consequence of the empty KB, or is the above a consequence of the
empty KB for all finite n?


peter