One equals two

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Test Id one=two
Description Start with 3 classes, a,b,c and relate them so instances have to be in a 1:1 relationship with each other.

The class b-and-c is the union of b and c. Therefore there have to be 2 instances of b-and-c for every instance of a.

Relate the class 2a to b-and-c so that *their* instances are in 1:1 relationship.

Now relate 2a to a so that *their* instances are in a 1:1 relationship. This should lead to a situation in which every instance of 2a is 1:1 with an instance of a, and at the same time 2:1 with an instance of a.

Unless all the classes have an infinite number of members or are empty this doesn't work. This example has a is the enumerated class {i,j,k} (i,j,k all different individuals). So it should be inconsistent.

Status Approved (2009-07-02 when passed by two or more implementations) (proposed 2009-05-26)
Author Alan Ruttenberg
Original syntax RDF-XML
Syntactic Species/Profile OWL 2 DL (not EL, not QL, not RL)
Semantics This test is applicable under both direct and RDF-based semantics.
Inconsistent ontology (download)

Convert syntax: functional, XML, Manchester      This informative conversion will be incorrect for OWL 2 Full. info.pngConversions are provided by the OWL Syntax Converter which tries to "repair" OWL 2 Full inputs to become DL.
Open in RDF Validator

<rdf:RDF xmlns="http://example.com/"
     xml:base="http://example.com/"
     xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
     xmlns:owl="http://www.w3.org/2002/07/owl#"
     xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
    <owl:Ontology rdf:about=""/>

    <owl:ObjectProperty rdf:about="2a=a">
        <rdf:type rdf:resource="http://www.w3.org/2002/07/owl#FunctionalProperty"/>
        <rdf:type rdf:resource="http://www.w3.org/2002/07/owl#InverseFunctionalProperty"/>
        <rdfs:label rdf:datatype="http://www.w3.org/2001/XMLSchema#string">2a-to-a</rdfs:label>
    </owl:ObjectProperty>

    <owl:ObjectProperty rdf:about="2a=b-and-c">
        <rdf:type rdf:resource="http://www.w3.org/2002/07/owl#FunctionalProperty"/>
        <rdf:type rdf:resource="http://www.w3.org/2002/07/owl#InverseFunctionalProperty"/>
        <rdfs:label rdf:datatype="http://www.w3.org/2001/XMLSchema#string">2a-to-b-and-c</rdfs:label>
    </owl:ObjectProperty>

    <owl:ObjectProperty rdf:about="a=2a'">
        <rdf:type rdf:resource="http://www.w3.org/2002/07/owl#FunctionalProperty"/>
        <rdf:type rdf:resource="http://www.w3.org/2002/07/owl#InverseFunctionalProperty"/>
        <rdfs:label rdf:datatype="http://www.w3.org/2001/XMLSchema#string">a-to-2a'</rdfs:label>
        <owl:inverseOf rdf:resource="2a=a"/>
    </owl:ObjectProperty>
    

    <owl:ObjectProperty rdf:about="a=b">
        <rdf:type rdf:resource="http://www.w3.org/2002/07/owl#FunctionalProperty"/>
        <rdf:type rdf:resource="http://www.w3.org/2002/07/owl#InverseFunctionalProperty"/>
        <rdfs:label rdf:datatype="http://www.w3.org/2001/XMLSchema#string">a-to-b</rdfs:label>
    </owl:ObjectProperty>
    
    <owl:ObjectProperty rdf:about="b-and-c=2a'">
        <rdf:type rdf:resource="http://www.w3.org/2002/07/owl#FunctionalProperty"/>
        <rdf:type rdf:resource="http://www.w3.org/2002/07/owl#InverseFunctionalProperty"/>
        <rdfs:label rdf:datatype="http://www.w3.org/2001/XMLSchema#string">b-and-c-to-2a'</rdfs:label>
        <owl:inverseOf rdf:resource="2a=b-and-c"/>
    </owl:ObjectProperty>

    <owl:ObjectProperty rdf:about="b=a'">
        <rdf:type rdf:resource="http://www.w3.org/2002/07/owl#FunctionalProperty"/>
        <rdf:type rdf:resource="http://www.w3.org/2002/07/owl#InverseFunctionalProperty"/>
        <rdfs:label rdf:datatype="http://www.w3.org/2001/XMLSchema#string">b-to-a'</rdfs:label>
        <owl:inverseOf rdf:resource="a=b"/>
    </owl:ObjectProperty>
    
    <owl:ObjectProperty rdf:about="b=c">
        <rdf:type rdf:resource="http://www.w3.org/2002/07/owl#FunctionalProperty"/>
        <rdf:type rdf:resource="http://www.w3.org/2002/07/owl#InverseFunctionalProperty"/>
        <rdfs:label rdf:datatype="http://www.w3.org/2001/XMLSchema#string">b-to-c</rdfs:label>
    </owl:ObjectProperty>
    
    <owl:ObjectProperty rdf:about="c=b'">
        <rdf:type rdf:resource="http://www.w3.org/2002/07/owl#FunctionalProperty"/>
        <rdf:type rdf:resource="http://www.w3.org/2002/07/owl#InverseFunctionalProperty"/>
        <rdfs:label rdf:datatype="http://www.w3.org/2001/XMLSchema#string">c-to-b'</rdfs:label>
        <owl:inverseOf rdf:resource="b=c"/>
    </owl:ObjectProperty>
    
    <owl:Class rdf:about="2a">
        <rdfs:label rdf:datatype="http://www.w3.org/2001/XMLSchema#string">2a</rdfs:label>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="2a=b-and-c"/>
                <owl:someValuesFrom rdf:resource="b-and-c"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="2a=a"/>
                <owl:someValuesFrom rdf:resource="a"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <owl:disjointWith rdf:resource="a"/>
        <owl:disjointWith rdf:resource="b"/>
        <owl:disjointWith rdf:resource="b-and-c"/>
        <owl:disjointWith rdf:resource="c"/>
    </owl:Class>

    <owl:Class rdf:about="a">
        <rdfs:label rdf:datatype="http://www.w3.org/2001/XMLSchema#string">a</rdfs:label>
        <owl:equivalentClass>
            <owl:Class>
                <owl:oneOf rdf:parseType="Collection">
                    <rdf:Description rdf:about="http://example.com/j"/>
                    <rdf:Description rdf:about="http://example.com/k"/>
                    <rdf:Description rdf:about="http://example.com/i"/>
                </owl:oneOf>
            </owl:Class>
        </owl:equivalentClass>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="a=b"/>
                <owl:someValuesFrom rdf:resource="b"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="a=2a'"/>
                <owl:someValuesFrom rdf:resource="2a"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <owl:disjointWith rdf:resource="b"/>
        <owl:disjointWith rdf:resource="c"/>
    </owl:Class>
    
    <owl:Class rdf:about="b">
        <rdfs:label rdf:datatype="http://www.w3.org/2001/XMLSchema#string">b</rdfs:label>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="b=a'"/>
                <owl:someValuesFrom rdf:resource="a"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="b=c"/>
                <owl:someValuesFrom rdf:resource="c"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <owl:disjointWith rdf:resource="c"/>
    </owl:Class>

    <owl:Class rdf:about="b-and-c">
        <rdfs:label rdf:datatype="http://www.w3.org/2001/XMLSchema#string">b-and-c</rdfs:label>
        <owl:equivalentClass>
            <owl:Class>
                <owl:unionOf rdf:parseType="Collection">
                    <rdf:Description rdf:about="b"/>
                    <rdf:Description rdf:about="c"/>
                </owl:unionOf>
            </owl:Class>
        </owl:equivalentClass>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="b-and-c=2a'"/>
                <owl:someValuesFrom rdf:resource="2a"/>
            </owl:Restriction>
        </rdfs:subClassOf>
    </owl:Class>
    
    <owl:Class rdf:about="c">
        <rdfs:label rdf:datatype="http://www.w3.org/2001/XMLSchema#string">c</rdfs:label>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="c=b'"/>
                <owl:someValuesFrom rdf:resource="b"/>
            </owl:Restriction>
        </rdfs:subClassOf>
    </owl:Class>

    <rdf:Description rdf:about="http://example.com/i">
        <rdfs:label>i</rdfs:label>
    </rdf:Description>

    <rdf:Description rdf:about="http://example.com/j">
        <rdfs:label>j</rdfs:label>
    </rdf:Description>

    <rdf:Description rdf:about="http://example.com/k">
        <rdfs:label>k</rdfs:label>
    </rdf:Description>

    <rdf:Description>
        <rdf:type rdf:resource="http://www.w3.org/2002/07/owl#AllDifferent"/>
        <owl:distinctMembers rdf:parseType="Collection">
            <rdf:Description rdf:about="http://example.com/j"/>
            <rdf:Description rdf:about="http://example.com/k"/>
            <rdf:Description rdf:about="http://example.com/i"/>
        </owl:distinctMembers>
    </rdf:Description>
</rdf:RDF>
Imported ontologies none
Retrieved from "http://owl.semanticweb.org/page/One_equals_two"
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