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    <p>It's not entirely clear yet what you mean by making two properties <em>un</em>-equal. By default, two properties can be distinct, so you don't really have to do anything special to <em>let</em> them be unequal. If the question is clarified, though, perhaps more information can be added about that.</p> <p>It's not entirely trivial to say that, e.g.,</p> <blockquote> <p>&forall;a,x . A(a) &rarr; (hasFinish(a,x) &iff; hasColor(a,x))</p> </blockquote> <p>in OWL, but you can do it. If you want to say this for all classes, you can, as you pointed out, use <code>owl:equivalentProperty</code>. Now, when you say that <code>p</code> is an equivalent property to <code>r</code>, you could also say that</p> <blockquote> <p>p &sqsubseteq; r<br> r &sqsubseteq; p</p> </blockquote> <p>that is, that each of <code>p</code> and <code>r</code> are subproperties of the other. In OWL 2 (but, unfortunately, not OWL 2 <em>DL</em>, as Antoine Zimmermann pointed out in the comments), you can assert that a given property is a superproperty of a <em>chain</em> of properties, e.g., </p> <blockquote> <p>hasFather &bullet; hasBrother &sqsubseteq; hasUncle </p> </blockquote> <p>which says that if someone has a father who has a brother, then that father's brother is that person's uncle. </p> <p>There's also a concept called rolification, which has been described more in <a href="https://stackoverflow.com/q/16989042/1281433">OWL 2 rolification</a>, which is the process of creating a property corresponding to a class that relates each individual of that class to itself. For you class <em>A</em>, there would be a relation <em>R<sub>A</sub></em> that relates each <em>A</em> to itself, and only relates those instances. If you then look at a property chain like </p> <blockquote> <p>R<sub>A</sub> &bullet; hasFinish</p> </blockquote> <p>you'll notice that it's really the subproperty of hasFinish where the first argument is an <em>A</em>. This means that you can say that hasFinish and hasColor are the same <em>for the class A</em> by making two subproperty assertions:</p> <blockquote> <p>R<sub>A</sub> &bullet; hasColor &sqsubseteq; hasFinish<br> R<sub>A</sub> &bullet; hasFinish &sqsubseteq; hasColor</p> </blockquote> <p>These assume that individuals of type A are the subjects of these statements. If A is actually the range here, then you'd just use </p> <blockquote> <p>&forall;a,x . A(a) &rarr; (hasFinish(x,a) &iff; hasColor(x,a))<br> hasColor &bullet; R<sub>A</sub> &sqsubseteq; hasFinish<br> hasFinish &bullet; R<sub>A</sub> &sqsubseteq; hasColor </p> </blockquote> <p>To get the property R<sub>A</sub>, you need to add the definition</p> <blockquote> <p>A &equiv; &exist;R<sub>A</sub>.Self </p> </blockquote> <p>to your ontology. In Protégé, this would look like:</p> <p><img src="https://i.stack.imgur.com/x1rll.png" alt="enter image description here"> <img src="https://i.stack.imgur.com/4vblS.png" alt="enter image description here"> <img src="https://i.stack.imgur.com/NZVfL.png" alt="enter image description here"></p> <p>and the resulting ontology looks like (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:xsd="http://www.w3.org/2001/XMLSchema#" xmlns="http://example.org/ep#" xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"&gt; &lt;owl:Ontology rdf:about="http://example.org/ep"/&gt; &lt;owl:Class rdf:about="http://example.org/ep#A"&gt; &lt;owl:equivalentClass&gt; &lt;owl:Restriction&gt; &lt;owl:onProperty&gt; &lt;owl:ObjectProperty rdf:about="http://example.org/ep#R_A"/&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://example.org/ep#hasFinish"&gt; &lt;owl:propertyChainAxiom rdf:parseType="Collection"&gt; &lt;owl:ObjectProperty rdf:about="http://example.org/ep#R_A"/&gt; &lt;owl:ObjectProperty rdf:about="http://example.org/ep#hasColor"/&gt; &lt;/owl:propertyChainAxiom&gt; &lt;/owl:ObjectProperty&gt; &lt;owl:ObjectProperty rdf:about="http://example.org/ep#hasColor"&gt; &lt;owl:propertyChainAxiom rdf:parseType="Collection"&gt; &lt;owl:ObjectProperty rdf:about="http://example.org/ep#R_A"/&gt; &lt;owl:ObjectProperty rdf:about="http://example.org/ep#hasFinish"/&gt; &lt;/owl:propertyChainAxiom&gt; &lt;/owl:ObjectProperty&gt; &lt;/rdf:RDF&gt; </code></pre> <p>and in Turtle:</p> <pre class="lang-none prettyprint-override"><code>@prefix : &lt;http://example.org/ep#&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; . :hasFinish a owl:ObjectProperty ; owl:propertyChainAxiom ( :R_A :hasColor ) . :A a owl:Class ; owl:equivalentClass [ a owl:Restriction ; owl:hasSelf true ; owl:onProperty :R_A ] . :hasColor a owl:ObjectProperty ; owl:propertyChainAxiom ( :R_A :hasFinish ) . &lt;http://example.org/ep&gt; a owl:Ontology . :R_A a owl:ObjectProperty . </code></pre>
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    1. POEqual relationship between ontology properties
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    1. USJoshua Taylor
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    1. COHi Joshua, thanks for answer, I'm gonna study it to know more about ontologies. However I realized my question was not clear. I ment property equality (owl:sameAs construct) instead of equivalence (owl:equivalentProperty construct). So I want to say that if Instance is of Class A then properties hasColor and hasFinish are equal (owl:sameAs) - I treat them as a properties with same meaning, but if these properties are used with Individual of Class B, then I want to treat them as a different properties with different meaning. I think that this is probably not possible to do with owl syntax?
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      1. USuser3024710
    2. COJoshua, excellent answer. Note, however, than the construction you use is not in OWL 2 DL. Consequently, some reasoners may not be able to make inferences with it (e.g., Pellet, HermiT). Other reasoners may be able to deal with this construction but only by being incomplete.
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      1. USAntoine Zimmermann
    3. COuser3024710, from your comment here, I have the impression that you misunderstand the notion of owl:sameAs. A thing `x` is `owl:sameAs` a thing `y` if `x` and `y` are interchangeable names of just one thing, in all possible situations. There is no context dependent sameAs.
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      1. USAntoine Zimmermann
 

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