Re: Expressing mathematical relationships in an ontology?

I have been using OWL in this way  for all my work related to 
Ontologies. However one point where I got stuck up was when a class has 
two properties P1 and P2 and P2 = P1-1. I did not really know how to 
represent this with the OWL constructs available. Although for my 
purpose now, I am using a very crude form, however I would be interested 
in more expressive representative

Cheers

Monika

Francesco Cannistrà wrote:

>I think that OWL can be leveraged to express mathematical functions as well.
>Consider the folowing example [that tries to assert: Y=MyFunction(X1,X2)]
>
><FunctionData rdf:about="#Y">
>    <isFunctionValueOf>
>          <Function rdf:about="MyFunction">
>                <argument>
>                     <FunctionData  rdf:about="#X1">
>                         <value>x1</value>
>                </argument>
>                <argument>
>                     <FunctionData  rdf:about="#X2">
>                         <value>x2</value>
>                </argument>
>          </Function>
>    </isFunctionValueOf>
></FunctionData>
>
>The ontology is the following:
>
><owl:Class rdf:ID="FunctionData " />
>
><owl:DatatypeProperty rdf:ID="value">
>   <rdfs:domain rdf:resource="#FunctionData "/>
></owl:DatatypeProperty>
>
><owl:Class rdf:ID="Function"/>
>
><owl:ObjectProperty rdf:ID="isFunctionValueOf">
>   <rdfs:domain rdf:resource="#FunctionData" />
>   <rdfs:range rdf:resource="#Function" />
></owl:ObjectProperty>
>
><owl:ObjectProperty rdf:ID="argument">
>   <rdfs:domain rdf:resource="#Function" />
>   <rdfs:range rdf:resource="#FunctionData " />
></owl:ObjectProperty>
>
><owl:Class rdf:ID="MyFunctionClass">
>    <owl:IntersectionOf rdf:parseType="Collection">
>          <owl:Class rdf:about="#Function"/>
>            <owl:Restriction>
>                  <owl:onProperty rdf:resource="#argument"/>
>                  <owl:allValuesFrom rdf:resource="#X-Domain"/>
>                  <owl:cardinality
>rdf:datatype="&xsd;nonNegativeInteger">2</owl:cardinality>
>            </owl:Restriction>
>    </owl:IntersectionOf >
></owl:Class>
>
><MyFunctionClass rdf:ID="MyFunction"/>
>
><owl:Class rdf:ID="X-Domain">
>    <owl:IntersectionOf rdf:parseType="Collection">
>            <owl:Class rdf:about="#FunctionData "/>
>            <owl:Restriction>
>                  <owl:onProperty rdf:resource="#value"/>
>                  <owl:allValuesFrom rdf:resource="#X-Datatype"/>
>            </owl:Restriction>
>    </owl:IntersectionOf >
></owl:Class>
>
><owl:Class rdf:ID="Y-Domain">
>    <owl:IntersectionOf rdf:parseType="Collection">
>            <owl:Class rdf:about="#FunctionData "/>
>            <owl:Restriction>
>                  <owl:onProperty rdf:resource="#value"/>
>                  <owl:allValuesFrom rdf:resource="#Y-Datatype"/>
>            </owl:Restriction>
>    </owl:IntersectionOf >
></owl:Class>
>
>Note that you can also specialize the argument property so that no any
>confusion can arise with the order of arguments when these are of the same
>type.
>
>Francesco
>

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Monika Solanki
De Montfort University
Software Technology Research Laboratory
Hawthorn building, H00.18
The Gateway.
Leicester LE1 9BH, UK

phone: +44 (0)116 250 6170 intern: 6170
email: monika@dmu.ac.uk <mailto:monika@dmu.ac.uk>
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<http://www.cse.dmu.ac.uk/%7Emonika/>
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