From: Peter F. Patel-Schneider <pfps@research.bell-labs.com>

Date: Fri, 03 May 2002 09:53:14 -0400

To: jjc@hplb.hpl.hp.com

Cc: www-webont-wg@w3.org

Message-Id: <20020503095314I.pfps@research.bell-labs.com>

Date: Fri, 03 May 2002 09:53:14 -0400

To: jjc@hplb.hpl.hp.com

Cc: www-webont-wg@w3.org

Message-Id: <20020503095314I.pfps@research.bell-labs.com>

From: "Jeremy Carroll" <jjc@hplb.hpl.hp.com> Subject: DTTF: another summary Date: Fri, 3 May 2002 10:45:34 +0100 > I believe we have three live proposals: > > - comprehensive entailments: Jeremy Unfortunately, this proposal is fatally flawed. In the empty KB, we can apply the kitchen sink comprehension rule (forall (?v) (=> (and (Type ?p Property) (Type ?card NonNegativeInteger) (Type ?min NonNegativeInteger) (Type ?max NonNegativeInteger) (Type ?c1 rdfs:Class) (Type ?c2 rdfs:Class)) (exists (?r) (and (Type ?r Restriction) (PropertyValue onProperty ?r ?p) (PropertyValue minCardinality ?r ?min) (PropertyValue maxCardinality ?r ?max) (PropertyValue cardinality ?r ?card) (PropertyValue hasClass ?r ?c1) (PropertyValue toClass ?r ?c2) ) ) ) ) with ?p as rdf:type ?card as 0 ?min as 0 ?max as 0 ?c1 as rdfs:Class ?c2 as rdfs:Resource ?v as rdf:type (?v is not used in the rule) to obtain the following restriction (written in n-triples notation) _:r rdf:type owl:Restriction . _:r owl:onProperty rdf:type . _:r owl:minCardinality 0 . _:r owl:maxCardinality 0 . _:r owl:cardinality 0 . _:r owl:hasClass rdfs:Class . _:r owl:toClass rdfs:Resource . Now consider whether rdfs:Class is a member of this restriction. Because _:r has both owl:onProperty and owl:toClass, an object belongs to it exactly when all its rdf:type fillers belong to rdfs:Resource. But this is true of all objects in all interpretations. Therefore rdfs:Class belongs to _:r. Because _:r has both owl:onProperty and owl:maxCardinality, an object belongs to it exactly when it has at most 0 rdf:type fillers. But this is not true of rdfs:Class, because rdfs:Class has rdfs:Class as an rdf:type. Therefore rdfs:Class does not belong to _:r. Therefore an empty knowledge base implies that some object both belongs and does not belong to some class. peterReceived on Friday, 3 May 2002 09:53:35 GMT

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