Reasoner in Protege not working with Restrictions/Cardinalities

Question

I am currently building/modifying a larger ontology. As I had problems to define restrictions I build a very short example: I have EuropeanCountry as a class and IslandCountry as a class:

<owl:Class rdf:about="http://www.semanticweb.org/tanktoo/ontologies/2016/10/untitled-ontology-81#EuropeanCountry">
    <rdfs:subClassOf rdf:resource="http://www.semanticweb.org/tanktoo/ontologies/2016/10/untitled-ontology-81#Country"/>
</owl:Class>



<!-- http://www.semanticweb.org/tanktoo/ontologies/2016/10/untitled-ontology-81#IslandCountry -->

<owl:Class rdf:about="http://www.semanticweb.org/tanktoo/ontologies/2016/10/untitled-ontology-81#IslandCountry">
    <rdfs:subClassOf rdf:resource="http://www.semanticweb.org/tanktoo/ontologies/2016/10/untitled-ontology-81#Country"/>
    <rdfs:subClassOf>
        <owl:Restriction>
            <owl:onProperty rdf:resource="http://www.semanticweb.org/tanktoo/ontologies/2016/10/untitled-ontology-81#borders"/>
            <owl:maxQualifiedCardinality rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger">0</owl:maxQualifiedCardinality>
            <owl:onClass rdf:resource="http://www.semanticweb.org/tanktoo/ontologies/2016/10/untitled-ontology-81#EuropeanCountry"/>
        </owl:Restriction>
    </rdfs:subClassOf>
</owl:Class>

As you can see I set a "maxQualifiedCardinality" restriction in Protege. If I create some individuals and (C1, C2 and Germany are EuropeanCountry, Island is IslandCountry) and relate them with the border property:

<owl:NamedIndividual rdf:about="http://www.semanticweb.org/tanktoo/ontologies/2016/10/untitled-ontology-81#Island">
    <rdf:type rdf:resource="http://www.semanticweb.org/tanktoo/ontologies/2016/10/untitled-ontology-81#IslandCountry"/>
    <borders rdf:resource="http://www.semanticweb.org/tanktoo/ontologies/2016/10/untitled-ontology-81#C1"/>
    <borders rdf:resource="http://www.semanticweb.org/tanktoo/ontologies/2016/10/untitled-ontology-81#C2"/>
    <borders rdf:resource="http://www.semanticweb.org/tanktoo/ontologies/2016/10/untitled-ontology-81#Germany"/>
</owl:NamedIndividual>

I get an error thrown by Hermit reasoner that it is not allowed to set 3 neighbours to Island. If I now change the line

<owl:maxQualifiedCardinality rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger">1</owl:maxQualifiedCardinality>

to cardinality 1 I don't get any error if I set three neighbours as shown in the example. Can anyone explain this and hopefully provide me a solution how I can write a restriction that one class should have x other classes (in this case how to write that Island should have 2 neighbours and a third one will throw an error by the reasoner)?

Thanks for your help and kind regards,

tanktoo

Edit: I have now added all individuals to an AllDifferent:

<rdf:Description>
    <rdf:type rdf:resource="http://www.w3.org/2002/07/owl#AllDifferent"/>
    <owl:distinctMembers rdf:parseType="Collection">
        <rdf:Description rdf:about="http://www.semanticweb.org/tanktoo/ontologies/2016/10/untitled-ontology-81#C1"/>
        <rdf:Description rdf:about="http://www.semanticweb.org/tanktoo/ontologies/2016/10/untitled-ontology-81#C2"/>
        <rdf:Description rdf:about="http://www.semanticweb.org/tanktoo/ontologies/2016/10/untitled-ontology-81#Germany"/>
    </owl:distinctMembers>
</rdf:Description>

It is now working with the restriction above and the reasoner tells me that I am not allowed to set 3 border countries as maxCardinality is 1. I have now changed my restriction to the following:

<owl:Class rdf:about="http://www.semanticweb.org/tanktoo/ontologies/2016/10/untitled-ontology-81#IslandCountry">
    <rdfs:subClassOf rdf:resource="http://www.semanticweb.org/tanktoo/ontologies/2016/10/untitled-ontology-81#Country"/>
    <rdfs:subClassOf>
        <owl:Restriction>
            <owl:onProperty rdf:resource="http://www.semanticweb.org/tanktoo/ontologies/2016/10/untitled-ontology-81#borders"/>
            <owl:minQualifiedCardinality rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger">1</owl:minQualifiedCardinality>
            <owl:onClass rdf:resource="http://www.semanticweb.org/tanktoo/ontologies/2016/10/untitled-ontology-81#EuropeanCountry"/>
        </owl:Restriction>
    </rdfs:subClassOf>
    <rdfs:subClassOf>
        <owl:Restriction>
            <owl:onProperty rdf:resource="http://www.semanticweb.org/tanktoo/ontologies/2016/10/untitled-ontology-81#borders"/>
            <owl:maxQualifiedCardinality rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger">2</owl:maxQualifiedCardinality>
            <owl:onClass rdf:resource="http://www.semanticweb.org/tanktoo/ontologies/2016/10/untitled-ontology-81#EuropeanCountry"/>
        </owl:Restriction>
    </rdfs:subClassOf>
</owl:Class>

I would now expect that the reasoner detects an error if I set less than 1 or more than 2 neighbours:

<owl:NamedIndividual rdf:about="http://www.semanticweb.org/tanktoo
/ontologies/2016/10/untitled-ontology-81#Island">
        <rdf:type rdf:resource="http://www.semanticweb.org/tanktoo/ontologies/2016/10/untitled-ontology-81#IslandCountry"/>
        <borders rdf:resource="http://www.semanticweb.org/tanktoo/ontologies/2016/10/untitled-ontology-81#C1"/>
        <borders rdf:resource="http://www.semanticweb.org/tanktoo/ontologies/2016/10/untitled-ontology-81#C2"/>
        <borders rdf:resource="http://www.semanticweb.org/tanktoo/ontologies/2016/10/untitled-ontology-81#Germany"/>
    </owl:NamedIndividual>

In this case the reasoner detects an errro because there are 3 neighbours. If I now delete all the neighbours so that Island border 0 countries the reasoner doesn't give me an error. Can someone explain me why?

Thanks for your help :)

Answer 1

I get an error thrown by Hermit reasoner that it is not allowed to set 3 neighbours to Island

If this is what the tool says, then it is a mistake. Granted, you are giving 3 names of bordering countries. But nothing says that these are names of 3 different countries. They could be several names of the same country, like "France", "Republic of France", "République française".

Since the reasoner has no way of knowing whether they are names of the same thing or not, it can't detect an inconsistency in the second case. However, in the first case, having at least a name for something means that there is strictly more than zero thing, so it makes sense that an inconsistency is detected.

If you'd like to make sure the reasoner detects when a country has more than 2 neighbours, then you'd have to explicitly say that the countries are different:

ex:C1  owl:differentFrom  ex:C2, ex:Germany .
ex:C2  owl:differentFrom  ex:Germany .

or:

[]  a  owl:AllDifferent;
    owl:members  ( ex:C1 ex:C2 ex:Germany ) .

In Protégé, in the Individual tab, you can specify from what an individual is different.