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    <p>Section 3.2 of the paper that you linked to says:</p> <blockquote> <p>It is indeed possible to translate this rule into OWL 2—however this involves a transformation which we call rolification: The rolification of a concept <em>A</em> is a (new) role <em>R<sub>A</sub></em> defined by the axiom <em>A &equiv; &exist;R<sub>A</sub>.Self</em>. Armed with rolification, we can now express rule (1) by the axiom …</p> </blockquote> <p>OWL2 doesn't support expressing an axiom like <em>Elephant(x) &wedge; Mouse(y) &rarr; biggerThan(x,y)</em> directly. As I understand it, you <em>manually</em> use the process of rolification that the paper describes to produce a new axiom that can be expressed in OWL2 directly.</p> <h2>Rolification</h2> <p>As to the specific process, if you want to express something like <em>Elephant(x) &wedge; Mouse(y) &rarr; biggerThan(x,y)</em>, you first rolify the classes <em>Elephant</em> and <em>Mouse</em>. This means that you introduce new roles (properties) <em>R<sub>Elephant</sub></em> and <em>R<sub>Mouse</sub></em> (but you do not delete the classes <em>Elephant</em> and <em>Mouse</em>). These new roles are such that <em>R<sub>Elephant</sub>(x,x)</em> if and only if <em>Elephant(x)</em>. This is enforced by adding the axioms</p> <p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Elephant &equiv; &exist;R<sub>Elephant</sub>.Self</p> <p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Mouse &equiv; &exist;R<sub>Mouse</sub>.Self</p> <p>each of which is expressible in OWL2. With those two axioms in hand, you finally add the subproperty chain axiom</p> <p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;R<sub>Elephant</sub> &bullet; topObjectProperty &bullet; R<sub>Mouse</sub> &sqsubseteq; biggerThan</p> <p>which is also expressible in OWL2. Since for any elephant <em>e</em> and any mouse <em>m</em>, we have that </p> <p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;R<sub>Elephant</sub>(e,e)</p> <p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;topObjectProperty(e,m)</p> <p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;R<sub>Mouse</sub>(m,m)</p> <p>then by the subproperty chain axiom, we have that </p> <p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;biggerThan(e,m)</p> <p>which is exactly what we wanted to express.</p> <h2>Axiom Syntax</h2> <p>In the input syntax accepted by Protege, these axioms are written as follows.</p> <p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Elephant <strong>EquivalentTo</strong> R_Elephant <strong>some Self</strong><br> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Mouse <strong>EquivalentTo</strong> R_Mouse <strong>some Self</strong><br> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;R_Elephant <strong>o</strong> topObjectProperty <strong>o</strong> R_mouse <strong>SubPropertyOf</strong> biggerThan </p> <p>In Protege they appear as follows.</p> <p><img src="https://i.stack.imgur.com/6f2oM.png" alt="elephant rolification axiom"> <img src="https://i.stack.imgur.com/x2DPg.png" alt="mouse rolification axiom"> <img src="https://i.stack.imgur.com/1wtqb.png" alt="subproperty chain axiom"></p> <p>In N3:</p> <pre class="lang-none prettyprint-override"><code>@prefix : &lt;http://www.example.org/rolification#&gt; . @prefix rdfs: &lt;http://www.w3.org/2000/01/rdf-schema#&gt; . @prefix owl: &lt;http://www.w3.org/2002/07/owl#&gt; . @prefix xsd: &lt;http://www.w3.org/2001/XMLSchema#&gt; . @prefix rdf: &lt;http://www.w3.org/1999/02/22-rdf-syntax-ns#&gt; . :Elephant a owl:Class ; owl:equivalentClass [ a owl:Restriction ; owl:hasSelf "true"^^xsd:boolean ; owl:onProperty :R_Elephant ] . :R_Elephant a owl:ObjectProperty . :biggerThan a owl:ObjectProperty ; owl:propertyChainAxiom (:R_Elephant owl:topObjectProperty :R_Mouse) . :Mouse a owl:Class ; owl:equivalentClass [ a owl:Restriction ; owl:hasSelf "true"^^xsd:boolean ; owl:onProperty :R_Mouse ] . &lt;http://www.example.org/rolification&gt; a owl:Ontology . :R_Mouse a owl:ObjectProperty . </code></pre> <p>In RDF/XML:</p> <pre class="lang-xml prettyprint-override"><code>&lt;rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:owl="http://www.w3.org/2002/07/owl#" xmlns="http://www.example.org/rolification#" xmlns:xsd="http://www.w3.org/2001/XMLSchema#" xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"&gt; &lt;owl:Ontology rdf:about="http://www.example.org/rolification"/&gt; &lt;owl:Class rdf:about="http://www.example.org/rolification#Elephant"&gt; &lt;owl:equivalentClass&gt; &lt;owl:Restriction&gt; &lt;owl:onProperty&gt; &lt;owl:ObjectProperty rdf:about="http://www.example.org/rolification#R_Elephant"/&gt; &lt;/owl:onProperty&gt; &lt;owl:hasSelf rdf:datatype="http://www.w3.org/2001/XMLSchema#boolean" &gt;true&lt;/owl:hasSelf&gt; &lt;/owl:Restriction&gt; &lt;/owl:equivalentClass&gt; &lt;/owl:Class&gt; &lt;owl:Class rdf:about="http://www.example.org/rolification#Mouse"&gt; &lt;owl:equivalentClass&gt; &lt;owl:Restriction&gt; &lt;owl:onProperty&gt; &lt;owl:ObjectProperty rdf:about="http://www.example.org/rolification#R_Mouse"/&gt; &lt;/owl:onProperty&gt; &lt;owl:hasSelf rdf:datatype="http://www.w3.org/2001/XMLSchema#boolean" &gt;true&lt;/owl:hasSelf&gt; &lt;/owl:Restriction&gt; &lt;/owl:equivalentClass&gt; &lt;/owl:Class&gt; &lt;owl:ObjectProperty rdf:about="http://www.example.org/rolification#biggerThan"&gt; &lt;owl:propertyChainAxiom rdf:parseType="Collection"&gt; &lt;owl:ObjectProperty rdf:about="http://www.example.org/rolification#R_Elephant"/&gt; &lt;rdf:Description rdf:about="http://www.w3.org/2002/07/owl#topObjectProperty"/&gt; &lt;owl:ObjectProperty rdf:about="http://www.example.org/rolification#R_Mouse"/&gt; &lt;/owl:propertyChainAxiom&gt; &lt;/owl:ObjectProperty&gt; &lt;/rdf:RDF&gt; </code></pre>
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    1. USJoshua Taylor
    1. USJoshua Taylor
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    1. COThanks Joshua, but my problem is if OWL 2 supports rolification. I browsed through the language specification, but it did not mention that.
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    2. COeach of which is expressible in OWL2 - so how's it expressed in OWL 2? (I know it can be expressed in description logic)
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    3. CO@Yang I've updated my answer with the Protégé input syntax and screenshots, as well as the N3 and RDF/XML serializations of an ontology containing these axioms.
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      1. USJoshua Taylor
 

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