# Re: Rule-based approach to conclude owl:intersectionOf

From: <jos.deroo@agfa.com>
Date: Tue, 5 Apr 2005 22:06:20 +0200

Cc: Chris Purcell <cjp39@cam.ac.uk>, semantic-web@w3.org
Message-ID: <OF1BDD2E6A.796CACA3-ONC1256FDA.006AF2D3-C1256FDA.006E7138@agfa.com>
```
> Oh my God.. i'd not make mistake again if it's in set..

:)

> CEXT(S(#X)) = {<#A>}
> CEXT(S(#Y)) = {<#A>,<#B>}
> CEXT(S(#Z)) = {<#A>,<#C>}
> i.e.
> <#A> rdf:type <#X> , <#Y> , <#Z> .
> <#B> rdf:type <#Y> .
> <#C> rdf:type <#Z> .
> =>
> <#X> rdfs:subClassOf <#Y> , <#Z> .
> =>
> <#X> owl:intersectionOf (<#Y>,<#Z>) .
>
> I admit that this kind of inference requires a condition that the
collection
> of facts is complete. Otherwise the inference results may be ruined if a

> fact like <#B> rdf:type <#X> is asserted. However, it is not a too bad
> interpretation because the OWL interpretation still satisifies the RDF
graph
> above.

One could say
:X owl:oneOf ( :A ).
:Y owl:oneOf ( :A :B ).
:Z owl:oneOf ( :A :C ).

and then
:X rdfs:subClassOf :Y, :Z.

easily follows, using such rules as

{ ?B has owl:oneOf ?Y.
?A has owl:oneOf ?X.
?Y :includes ?X }
=>
{ ?A rdfs:subClassOf ?B }.

{ }
=>
{ ?X :includes rdf:nil }.

{ ?S rdf:first ?A.
?X :item ?E.
?E has owl:equivalentClass ?A.
?S rdf:rest ?B.
?X :includes ?B }
=>
{ ?X :includes ?S }.

{ ?S rdf:first ?X }
=>
{ ?S :item ?X }.

{ ?S rdf:rest ?B.
?B :item ?X }
=>
{ ?S :item ?X }.

At this moment, I can't find proof for
:X owl:intersectionOf ( :Y :Z ).

i.e. probably have to add some more owl-rules..

> In addition, my main concern is the use of the universal quantification
and
> the existential quantification. It is because N3 Rules cannot express
the
> inference described in the above example. My work of rules shows that N3

> Rules is very weak to model OWL restrictions, anyway. I hope to discuss
or
> to find out the use of the quantification facilities so that the
rule-based
> approach becomes more powerful as expected.

You can have look at
http://www.w3.org/2000/10/swap/doc/Rules
and convince yourself that it can be easily done :)

> :)
> Jeremy

--
Jos De Roo, AGFA http://www.agfa.com/w3c/jdroo/
```
Received on Tuesday, 5 April 2005 20:06:45 UTC

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