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Re: Expressing mathematical relationships in an ontology?

From: Francesco CannistrÓ <fracan@inwind.it>
Date: Tue, 17 Jun 2003 14:46:08 +0200
Message-ID: <017501c334ce$6d56fab0$38971d97@Matrix>
To: "Monika Solanki" <monika@dmu.ac.uk>, <www-rdf-interest@w3.org>

If you do not consider P1 and P2 as properties but as functions and
distinguish functions from functions' values, then you could use my ontology
as follows:

<P-Domain  rdf:about="#Y">
    <isFunctionValueOf>
          <Function rdf:about="Sum">
                <argument>
                     <P-Domain  rdf:about="#P1"/>
                </argument>
                <argument>
                     <P-Domain  rdf:about="#P2"/>
                </argument>
          </Function>
    </isFunctionValueOf>
</P-Domain>

and you could define #P2 as the value of a single argument function (e.g.
"ChangeSign").
Your ontology would be:

<owl:Class rdf:ID="SumFunctionClass">
    <owl:IntersectionOf rdf:parseType="Collection">
          <owl:Class rdf:about="#Function"/>
            <owl:Restriction>
                  <owl:onProperty rdf:resource="#argument"/>
                  <owl:allValuesFrom rdf:resource="#P-Domain"/>
                  <owl:cardinality
rdf:datatype="&xsd;nonNegativeInteger">2</owl:cardinality>
            </owl:Restriction>
    </owl:IntersectionOf >
</owl:Class>

<MyFunctionClass rdf:ID="Sum"/>

<owl:Class rdf:ID="P-Domain">
    <owl:IntersectionOf rdf:parseType="Collection">
            <owl:Class rdf:about="#FunctionData "/>
            <owl:Restriction>
                  <owl:onProperty rdf:resource="#value"/>
                  <owl:allValuesFrom rdf:resource="#P-Datatype"/>
            </owl:Restriction>
    </owl:IntersectionOf >
</owl:Class>




----- Original Message -----
From: Monika Solanki
To: www-rdf-interest@w3.org
Cc: Francesco CannistrÓ
Sent: Tuesday, June 17, 2003 2:34 PM
Subject: 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 CannistrÓ 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:Datatyp
eProperty><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:cardinalityrdf: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 al
so specialize the argument property so that no anyconfusion can arise with
the order of arguments when these are of the sametype.Francesco


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Monika Solanki
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Received on Tuesday, 17 June 2003 08:46:40 GMT

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