Semantic MathML/0.1

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<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE rdf:RDF [
  <!ENTITY smml "http://ontoworld.org/index.php/Semantic_MathML/0.1#">
  <!ENTITY phml "http://ontoworld.org/index.php/PhysicalML/0.1#">
  <!ENTITY owl "http://www.w3.org/2002/07/owl#">
  <!ENTITY rdf "http://www.w3.org/1999/02/22-rdf-syntax-ns#">
  <!ENTITY rdfs "http://www.w3.org/2000/01/rdf-schema#">
  <!ENTITY xsd "http://www.w3.org/2001/XMLSchema#">
  <!ENTITY h "http://www.w3.org/TR/xhtml11#">
  <!ENTITY cc "http://web.resource.org/cc/">
  <!ENTITY dc "http://purl.org/dc/elements/1.1/">
>
]>
<rdf:RDF xml:base="http://ontoworld.org/index.php/Semantic_MathML/0.1"
         xmlns:smml="&smml;"
         xmlns:phml="&phml;"
         xmlns:owl="&owl;"
         xmlns:rdf="&rdf;"
         xmlns:rdfs="&rdfs;"
         xmlns:h="&h;"
         xmlns:cc="&cc;"
         xmlns:dc="&dc;">

Contents

[edit] Licence

 <cc:Work rdf:about="#Licence">
   <cc:license rdf:resource="http://creativecommons.org/licenses/by-sa/2.5/" />
   <dc:title>Semantic MathML v0.1</dc:title>
   <dc:date>2006</dc:date>
   <dc:description>An Ontology for descibing mathematical knowledge.</dc:description>
   <dc:creator>
     <Agent rdf:resource="http://ontoworld.org/index.php/User:MovGP0" />
   </dc:creator>
   <dc:type rdf:resource="http://purl.org/dc/dcmitype/InteractiveResource" />
   <dc:source rdf:resource="http://ontoworld.org/index.php/Semantic_MathML/0.1" />
 </cc:Work>
 <cc:License rdf:about="http://creativecommons.org/licenses/by-sa/2.5/">
   <cc:permits rdf:resource="http://web.resource.org/cc/Reproduction"/>
   <cc:permits rdf:resource="http://web.resource.org/cc/Distribution"/>
   <cc:permits rdf:resource="http://web.resource.org/cc/DerivativeWorks"/>
   <cc:requires rdf:resource="http://web.resource.org/cc/Notice"/>
   <cc:requires rdf:resource="http://web.resource.org/cc/Attribution"/>
   <cc:requires rdf:resource="http://web.resource.org/cc/ShareAlike"/>
 </cc:License>

[edit] Abstract

<!-- Ontology Information -->
  <owl:Ontology rdf:about=""
                rdfs:label="The Semantic MathML Ontology"
                owl:versionInfo="0.1.0">
    <rdfs:comment>

This is a first try to describe mathematical formulas in a semantic way. The information here is preliminary and subject to change. Suggestions are highly welcome.

    </rdfs:comment>
  </owl:Ontology>

[edit] Annotation Properties

  <owl:AnnotationProperty rdf:about="&rdfs;comment"/>
  <owl:AnnotationProperty rdf:about="&rdfs;seeAlso"/>
  <owl:AnnotationProperty rdf:about="&rdfs;label"/>
  <owl:AnnotationProperty rdf:about="&owl;versionInfo"/>

[edit] Basic Definitions

  <owl:Class rdf:about="#Variable"
             rdfs:label="Variable">
    <rdfs:comment>

Variables are the most basic element in Math. Variables can get every Value.

    </rdfs:comment>
  </owl:Class>
  <owl:Class rdf:about="#Function"
             rdfs:label="Function">
    <rdfs:comment>

Functions are executing mathematical Operations. They are mostly implemented within a Computer Algebra System (CAS).

</rdfs:comment>
    <rdfs:seeAlso>http://functions.wolfram.com/</rdfs:seeAlso>
    <rdfs:subClassOf rdf:resource="#Operator"/>
  </owl:Class>
  <owl:Class rdf:about="#Constant"
             rdfs:label="Constant">
    <rdfs:comment>

A Constant describes Constants and Literals. So rdfs:Literal derive from this Class too.

    </rdfs:comment>
    <rdfs:subClassOf rdf:resource="#Variable"/>
  </owl:Class>
  <owl:Class rdf:about="#Operator"
             rdfs:label="Operator">
    <rdfs:comment>

Operators are representing mathematical Operations.

    </rdfs:comment>
    <rdfs:subClassOf rdf:resource="#Variable"/>
  </owl:Class>

[edit] Transformations

  <owl:Class rdf:about="#OperatorTransformation">
    <rdfs:subClassOf rdf:resource="#Operator"/>
  </owl:Class>

[edit] Common Interfaces

  <owl:Class rdf:about="#OperatorInterface">
    <rdfs:subClassOf rdf:resource="#Operator"/>
  </owl:Class>
  <owl:Class rdf:about="#ListOfArgumentsFunction">
    <rdfs:subClassOf rdf:resource="#OperatorInterface"/>
    <rdfs:comment>
      Defines a Function which takes a List of values as argument. 
    </rdfs:comment>
  </owl:Class>
  <owl:Class rdf:about="#SingleArgumentFunction">
    <rdfs:subClassOf rdf:resource="#OperatorInterface"/>
    <rdfs:comment>
      Defines a Function which takes a single (scalar) value as argument. 
    </rdfs:comment>
  </owl:Class>


[edit] Apperance

  <owl:Class rdf:about="#OperatorApperance">
    <rdfs:subClassOf rdf:resource="#Operator"/>
  </owl:Class>
  <owl:Class rdf:about="#PostfixOperator">
    <rdfs:subClassOf rdf:resource="#OperatorApperance"/>
  </owl:Class>
  <owl:Class rdf:about="#PrefixOperator">
    <rdfs:subClassOf rdf:resource="#OperatorApperance"/>
  </owl:Class>
  <owl:Class rdf:about="#InfixOperator">
    <rdfs:subClassOf rdf:resource="#OperatorApperance"/>
  </owl:Class>
  <owl:Class rdf:about="#TreeOperator">
    <rdfs:subClassOf rdf:resource="#OperatorApperance"/>
  </owl:Class>


[edit] Object Properties

  <owl:ObjectProperty rdf:about="#hasBase"
                      rdfs:comment="Base of a Power Function"
                      rdfs:label="Base">
    <rdfs:subPropertyOf rdf:resource="#hasParameter"/>
  </owl:ObjectProperty>
  <owl:ObjectProperty rdf:about="#hasDividend">
    <rdfs:subPropertyOf rdf:resource="#hasParameter"/>
  </owl:ObjectProperty>
  <owl:ObjectProperty rdf:about="#hasDivisor">
    <rdfs:subPropertyOf rdf:resource="#hasParameter"/>
  </owl:ObjectProperty>
  <owl:ObjectProperty rdf:about="#hasExponent"
                      rdfs:comment="the Exponent of a Power-Function"
                      rdfs:label="Exponent">
    <rdfs:subPropertyOf rdf:resource="#hasParameter"/>
  </owl:ObjectProperty>
  <owl:ObjectProperty rdf:about="#hasParameter"
                      rdfs:label="has parameter">
    <owl:inverseOf rdf:resource="#isParameterOf"/>
  </owl:ObjectProperty>
  <owl:ObjectProperty rdf:about="#hasResult"
                      rdfs:label="has result">
    <owl:inverseOf rdf:resource="#isResultOf"/>
  </owl:ObjectProperty>
  <owl:ObjectProperty rdf:about="#isDividendOf"
                      rdfs:label="is dividend of">
    <rdfs:subPropertyOf rdf:resource="#isParameterOf"/>
    <owl:inverseOf rdf:resource="#hasDividend"/>
  </owl:ObjectProperty>
  <owl:ObjectProperty rdf:about="#isDivisorOf"
                      rdfs:label="is divisor of">
    <rdfs:subPropertyOf rdf:resource="#isParameterOf"/>
    <owl:inverseOf rdf:resource="#hasDivisor"/>
  </owl:ObjectProperty>
  <owl:ObjectProperty rdf:about="#isParameterOf"
                      rdfs:label="is Parameter of">
    <rdfs:comment>Applies a Parameter to a function. Some Operators may define different Subclasses from this. As Example the 
Divide-Operator may define the Subclasses "isDivisorOf" and "isDividendOf".</rdfs:comment>
  </owl:ObjectProperty>
  <owl:ObjectProperty rdf:about="#isResultOf"
                      rdfs:label="is result of">
    <rdfs:comment>Defines, that the given Value is the Result of a Operation.</rdfs:comment>
  </owl:ObjectProperty>
  <owl:ObjectProperty rdf:about="&phml;hasUnit"/>
  <owl:ObjectProperty rdf:about="&phml;hasPhysicalDimension"/>

[edit] Mathematical Constants

  <owl:Class rdf:about="#MathematicalConstant"
             rdfs:label="mathematical Constant">
    <rdfs:comment>
        This is incomplete. For more Constants see also:
        <rdfs:seeAlso>http://mathworld.wolfram.com/topics/Constants.html</rdfs:seeAlso>
    </rdfs:comment>
    <rdfs:subClassOf rdf:resource="#Constant"/>
  </owl:Class>
  <owl:Class rdf:about="#Pi-basedConstant">
    <rdfs:subClassOf rdf:resource="#MathematicalConstant"/>
  </owl:Class>
  <owl:Class rdf:about="#e-basedConstant">
    <rdfs:subClassOf rdf:resource="#MathematicalConstant"/>
  </owl:Class>
  <owl:Class rdf:about="#PrimeConstant">
    <rdfs:subClassOf rdf:resource="#MathematicalConstant"/>
  </owl:Class>
  <owl:Class rdf:about="#ContinuedFractionConstant">
    <rdfs:subClassOf rdf:resource="#MathematicalConstant"/>
  </owl:Class>
  <owl:Class rdf:about="#GeometricConstant">
    <rdfs:subClassOf rdf:resource="#MathematicalConstant"/>
  </owl:Class>
  <owl:Class rdf:about="#RecurrenceRelationConstant">
    <rdfs:subClassOf rdf:resource="#MathematicalConstant"/>
  </owl:Class>
  <smml:MathematicalConstant rdf:about="#Infinity">
    <smml:equalTo rdf:type="&xsd;float">INF</smml:equalTo>
    <smml:equalTo><smml:Negate rdf:resource="#Infinity"/></smml:equalTo>
  </smml:MathematicalConstant>
  <smml:MathematicalConstant rdf:about="#Null"/>
    <owl:equivalentClass rdf:resource="#Zero"/>
    <smml:equalTo rdf:type="&xsd;int">0</smml:equalTo>
    <smml:equalTo><smml:Negate rdf:resource="#Null"/></smml:equalTo>
  </smml:MathematicalConstant>
  <smml:MathematicalConstant rdf:about="#One">
    <smml:equalTo rdf:type="&xsd;int">1</smml:equalTo>
  </smml:MathematicalConstant>
  <smml:MathematicalConstant rdf:about="#Two">
    <smml:equalTo rdf:type="&xsd;int">2</smml:equalTo>
  </smml:MathematicalConstant>
  <smml:MathematicalConstant rdf:about="#Three">
    <smml:equalTo rdf:type="&xsd;int">3</smml:equalTo>
  </smml:MathematicalConstant>
  <smml:MathematicalConstant rdf:about="#Four">
    <smml:equalTo rdf:type="&xsd;int">4</smml:equalTo>
  </smml:MathematicalConstant>
  <smml:MathematicalConstant rdf:about="#Five">
    <smml:equalTo rdf:type="&xsd;int">5</smml:equalTo>
  </smml:MathematicalConstant>
  <smml:MathematicalConstant rdf:about="#Six">
    <smml:equalTo rdf:type="&xsd;int">6</smml:equalTo>
  </smml:MathematicalConstant>
  <smml:MathematicalConstant rdf:about="#Seven">
    <smml:equalTo rdf:type="&xsd;int">7</smml:equalTo>
  </smml:MathematicalConstant>
  <smml:MathematicalConstant rdf:about="#Eight">
    <smml:equalTo rdf:type="&xsd;int">8</smml:equalTo>
  </smml:MathematicalConstant>
  <smml:MathematicalConstant rdf:about="#Nine">
    <smml:equalTo rdf:type="&xsd;int">9</smml:equalTo>
  </smml:MathematicalConstant>
  <smml:MathematicalConstant rdf:about="#Sqrt2"/>
  <smml:MathematicalConstant rdf:about="#Sqrt3"/>
  <smml:MathematicalConstant rdf:about="#GoldenRatio"
                                        rdfs:comment="approx. 1,61803"
                                        rdfs:comment="the Golden Ratio"/>
  <smml:MathematicalConstant rdf:about="#EulersNumber"
                                        rdfs:label="e"/>
  <smml:MathematicalConstant rdf:about="#Pi"
                                        rdfs:label="π"/>
                                        rdfs:comment="3,14159"/>
  <smml:MathematicalConstant rdf:about="#BackhouseConstant"/>
  <smml:MathematicalConstant rdf:about="#ViswanathsConstant"/>
  <smml:MathematicalConstant rdf:about="#SierpinskiConstant"/>
  <smml:MathematicalConstant rdf:about="#RamanujanSoldnerConstant"/>
  <smml:MathematicalConstant rdf:about="#AlladiGrinsteadConstant"/>
  <smml:MathematicalConstant rdf:about="#AperyConstant"/>
  <smml:MathematicalConstant rdf:about="#EulerMascheroniConstant"
                                        rdfs:comment="approx. 0.57721..."
                                        rdfs:label="the Euler-Mascheroni constant"/>
  <smml:MathematicalConstant rdf:about="#FransenRobinsonConstant"/>
  <smml:MathematicalConstant rdf:about="#GaussKuzminWirsingConstant"/>
  <smml:MathematicalConstant rdf:about="#GolombDickmanConstant"/>
  <smml:MathematicalConstant rdf:about="#HafnerSarnakMcCurleyConstant"/>
  <smml:MathematicalConstant rdf:about="#KhinchinLevyConstant"/>
  <smml:MathematicalConstant rdf:about="#KhinchinsConstant"/>
  <smml:MathematicalConstant rdf:about="#LandauConstant"/>
  <smml:MathematicalConstant rdf:about="#LandauRamanujanConstant"/>
  <smml:MathematicalConstant rdf:about="#LaplaceConstant"/>
  <smml:MathematicalConstant rdf:about="#LegendresConstant"/>
  <smml:MathematicalConstant rdf:about="#LengyelsConstant"/>
  <smml:MathematicalConstant rdf:about="#LiebsIcebrickConstant"/>
  <smml:MathematicalConstant rdf:about="#MeisselMertensConstant"/>
  <smml:MathematicalConstant rdf:about="#MillsConstant"/>
  <smml:MathematicalConstant rdf:about="#NivensConstant"/>
  <smml:MathematicalConstant rdf:about="#BernsteinConstant"/>
  <smml:MathematicalConstant rdf:about="#CahensConstant"/>
  <smml:MathematicalConstant rdf:about="#CatalansConstant"/>
  <smml:MathematicalConstant rdf:about="#DeBruijnNewmanConstant"/>
  <smml:MathematicalConstant rdf:about="#EmbreeTrefethenConstant"/>
  <smml:MathematicalConstant rdf:about="#ErdosBorweinConstant"/>
  <!-- different defined Constants -->
  <owl:Class rdf:about="#FeigenbaumConstant">
    <rdfs:subClassOf rdf:resource="#MathematicalConstant"/>
  </owl:Class>
  <smml:FeigenbaumConstant rdf:about="#FirstFeigenbaumConstant"/>
  <smml:FeigenbaumConstant rdf:about="#SecondFeigenbaumConstant"/>
  <owl:Class rdf:about="#BrunsConstant">
    <rdfs:subClassOf rdf:resource="#MathematicalConstant"/>
  </owl:Class>
  <smml:BrunsConstant rdf:about="#BrunsConstant1"/>
  <smml:BrunsConstant rdf:about="#BrunsConstant2"/>
  <smml:BrunsConstant rdf:about="#BrunsConstant4"/>

[edit] Mathematical Dimensions

  <owl:Class rdf:about="#MathematicalDimension"
             rdfs:label="a mathematical Dimension">
    <rdfs:subClassOf rdf:resource="#Constant"/>
  </owl:Class>
  <smml:MathematicalDimension rdf:about="#Real">
    <smml:isEqualTo rdfs:type="&xsd;int">1</smml:isEqualTo>
  </smml:MathematicalDimension>
  <smml:MathematicalDimension rdf:about="#ImaginaryI"
                              rdfs:label="i">
    <smml:isEqualTo>
      <smml:Sqrt>
        <smml:hasParameter rdfs:type="&xsd;int">-1</smml:hasParameter>
      </smml:Sqrt>
    </smml:isEqualTo>
    <smml:isEqualTo>
      <smml:GrassmannProduct>
        <smml:hasLeftParameter rdfs:resouce="#ImaginaryJ"/>
        <smml:hasRightParameter rdfs:resouce="#ImaginaryK"/>
      </smml:GrassmannProduct>
    </smml:isEqualTo>
    <smml:isEqualTo>
      <smml:GrassmannProduct>
        <smml:hasLeftParameter rdfs:resouce="#ImaginaryL"/>
        <smml:hasRightParameter rdfs:resouce="#ImaginaryM"/>
      </smml:GrassmannProduct>
    </smml:isEqualTo>
    <smml:isEqualTo>
      <smml:GrassmannProduct>
        <smml:hasLeftParameter rdfs:resouce="#ImaginaryO"/>
        <smml:hasRightParameter rdfs:resouce="#ImaginaryN"/>
      </smml:GrassmannProduct>
    </smml:isEqualTo>
    <smml:isEqualTo>
      <smml:Negate>
        <smml:GrassmannProduct>
          <smml:hasLeftParameter rdfs:resouce="#ImaginaryK"/>
          <smml:hasRightParameter rdfs:resouce="#ImaginaryJ"/>
        </smml:GrassmannProduct>
      </smml:Negate>
    </smml:isEqualTo>
    <smml:isEqualTo>
      <smml:Negate>
        <smml:GrassmannProduct>
          <smml:hasLeftParameter rdfs:resouce="#ImaginaryM"/>
          <smml:hasRightParameter rdfs:resouce="#ImaginaryL"/>
        </smml:GrassmannProduct>
      </smml:Negate>
    </smml:isEqualTo>
    <smml:isEqualTo>
      <smml:Negate>
        <smml:GrassmannProduct>
          <smml:hasLeftParameter rdfs:resouce="#ImaginaryN"/>
          <smml:hasRightParameter rdfs:resouce="#ImaginaryO"/>
        </smml:GrassmannProduct>
      </smml:Negate>
    </smml:isEqualTo>
  </smml:MathematicalDimension>
  <smml:MathematicalDimension rdf:about="#ImaginaryJ"
                              rdfs:label="j">
    <smml:isEqualTo>
      <smml:Sqrt>
        <smml:hasParameter rdfs:type="&xsd;int">-1</smml:hasParameter>
      </smml:Sqrt>
    </smml:isEqualTo>
    <smml:isEqualTo>
      <smml:GrassmannProduct>
        <smml:hasLeftParameter rdfs:resouce="#ImaginaryK"/>
        <smml:hasRightParameter rdfs:resouce="#ImaginaryI"/>
      </smml:GrassmannProduct>
    </smml:isEqualTo>
    <smml:isEqualTo>
      <smml:GrassmannProduct>
        <smml:hasLeftParameter rdfs:resouce="#ImaginaryL"/>
        <smml:hasRightParameter rdfs:resouce="#ImaginaryN"/>
      </smml:GrassmannProduct>
    </smml:isEqualTo>
    <smml:isEqualTo>
      <smml:GrassmannProduct>
        <smml:hasLeftParameter rdfs:resouce="#ImaginaryM"/>
        <smml:hasRightParameter rdfs:resouce="#ImaginaryO"/>
      </smml:GrassmannProduct>
    </smml:isEqualTo>
    <smml:isEqualTo>
      <smml:Negate>
        <smml:GrassmannProduct>
          <smml:hasLeftParameter rdfs:resouce="#ImaginaryI"/>
          <smml:hasRightParameter rdfs:resouce="#ImaginaryK"/>
        </smml:GrassmannProduct>
      </smml:Negate>
    </smml:isEqualTo>
    <smml:isEqualTo>
      <smml:Negate>
        <smml:GrassmannProduct>
          <smml:hasLeftParameter rdfs:resouce="#ImaginaryN"/>
          <smml:hasRightParameter rdfs:resouce="#ImaginaryL"/>
        </smml:GrassmannProduct>
      </smml:Negate>
    </smml:isEqualTo>
    <smml:isEqualTo>
      <smml:Negate>
        <smml:GrassmannProduct>
          <smml:hasLeftParameter rdfs:resouce="#ImaginaryO"/>
          <smml:hasRightParameter rdfs:resouce="#ImaginaryM"/>
        </smml:GrassmannProduct>
      </smml:Negate>
    </smml:isEqualTo>
  </smml:MathematicalDimension>
  <smml:MathematicalDimension rdf:about="#ImaginaryK"
                              rdfs:label="k">
    <smml:isEqualTo>
      <smml:Sqrt>
        <smml:hasParameter rdfs:type="&xsd;int">-1</smml:hasParameter>
      </smml:Sqrt>
    </smml:isEqualTo>
    <smml:isEqualTo>
      <smml:GrassmannProduct>
        <smml:hasLeftParameter rdfs:resouce="#ImaginaryI"/>
        <smml:hasRightParameter rdfs:resouce="#ImaginaryJ"/>
      </smml:GrassmannProduct>
    </smml:isEqualTo>
    <smml:isEqualTo>
      <smml:GrassmannProduct>
        <smml:hasLeftParameter rdfs:resouce="#ImaginaryL"/>
        <smml:hasRightParameter rdfs:resouce="#ImaginaryO"/>
      </smml:GrassmannProduct>
    </smml:isEqualTo>
    <smml:isEqualTo>
      <smml:GrassmannProduct>
        <smml:hasLeftParameter rdfs:resouce="#ImaginaryN"/>
        <smml:hasRightParameter rdfs:resouce="#ImaginaryM"/>
      </smml:GrassmannProduct>
    </smml:isEqualTo>
    <smml:isEqualTo>
      <smml:Negate>
        <smml:GrassmannProduct>
          <smml:hasLeftParameter rdfs:resouce="#ImaginaryJ"/>
          <smml:hasRightParameter rdfs:resouce="#ImaginaryI"/>
        </smml:GrassmannProduct>
      </smml:Negate>
    </smml:isEqualTo>
    <smml:isEqualTo>
      <smml:Negate>
        <smml:GrassmannProduct>
          <smml:hasLeftParameter rdfs:resouce="#ImaginaryO"/>
          <smml:hasRightParameter rdfs:resouce="#ImaginaryL"/>
        </smml:GrassmannProduct>
      </smml:Negate>
    </smml:isEqualTo>
    <smml:isEqualTo>
      <smml:Negate>
        <smml:GrassmannProduct>
          <smml:hasLeftParameter rdfs:resouce="#ImaginaryM"/>
          <smml:hasRightParameter rdfs:resouce="#ImaginaryN"/>
        </smml:GrassmannProduct>
      </smml:Negate>
    </smml:isEqualTo>
  </smml:MathematicalDimension>
  <smml:MathematicalDimension rdf:about="#ImaginaryL"
                              rdfs:label="l">
    <smml:isEqualTo>
      <smml:Sqrt>
        <smml:hasParameter rdfs:type="&xsd;int">-1</smml:hasParameter>
      </smml:Sqrt>
    </smml:isEqualTo>
    <smml:isEqualTo>
      <smml:GrassmannProduct>
        <smml:hasLeftParameter rdfs:resouce="#ImaginaryM"/>
        <smml:hasRightParameter rdfs:resouce="#ImaginaryI"/>
      </smml:GrassmannProduct>
    </smml:isEqualTo>
    <smml:isEqualTo>
      <smml:GrassmannProduct>
        <smml:hasLeftParameter rdfs:resouce="#ImaginaryN"/>
        <smml:hasRightParameter rdfs:resouce="#ImaginaryJ"/>
      </smml:GrassmannProduct>
    </smml:isEqualTo>
    <smml:isEqualTo>
      <smml:GrassmannProduct>
        <smml:hasLeftParameter rdfs:resouce="#ImaginaryO"/>
        <smml:hasRightParameter rdfs:resouce="#ImaginaryK"/>
      </smml:GrassmannProduct>
    </smml:isEqualTo>
    <smml:isEqualTo>
      <smml:Negate>
        <smml:GrassmannProduct>
          <smml:hasLeftParameter rdfs:resouce="#ImaginaryI"/>
          <smml:hasRightParameter rdfs:resouce="#ImaginaryM"/>
        </smml:GrassmannProduct>
      </smml:Negate>
    </smml:isEqualTo>
    <smml:isEqualTo>
      <smml:Negate>
        <smml:GrassmannProduct>
          <smml:hasLeftParameter rdfs:resouce="#ImaginaryJ"/>
          <smml:hasRightParameter rdfs:resouce="#ImaginaryN"/>
        </smml:GrassmannProduct>
      </smml:Negate>
    </smml:isEqualTo>
    <smml:isEqualTo>
      <smml:Negate>
        <smml:GrassmannProduct>
          <smml:hasLeftParameter rdfs:resouce="#ImaginaryK"/>
          <smml:hasRightParameter rdfs:resouce="#ImaginaryO"/>
        </smml:GrassmannProduct>
      </smml:Negate>
    </smml:isEqualTo>
  </smml:MathematicalDimension>
  <smml:MathematicalDimension rdf:about="#ImaginaryM"
                              rdfs:label="m">
    <smml:isEqualTo>
      <smml:Sqrt>
        <smml:hasParameter rdfs:type="&xsd;int">-1</smml:hasParameter>
      </smml:Sqrt>
    </smml:isEqualTo>
    <smml:isEqualTo>
      <smml:GrassmannProduct>
        <smml:hasLeftParameter rdfs:resouce="#ImaginaryI"/>
        <smml:hasRightParameter rdfs:resouce="#ImaginaryL"/>
      </smml:GrassmannProduct>
    </smml:isEqualTo>
    <smml:isEqualTo>
      <smml:GrassmannProduct>
        <smml:hasLeftParameter rdfs:resouce="#ImaginaryO"/>
        <smml:hasRightParameter rdfs:resouce="#ImaginaryJ"/>
      </smml:GrassmannProduct>
    </smml:isEqualTo>
    <smml:isEqualTo>
      <smml:GrassmannProduct>
        <smml:hasLeftParameter rdfs:resouce="#ImaginaryK"/>
        <smml:hasRightParameter rdfs:resouce="#ImaginaryN"/>
      </smml:GrassmannProduct>
    </smml:isEqualTo>
    <smml:isEqualTo>
      <smml:Negate>
        <smml:GrassmannProduct>
          <smml:hasLeftParameter rdfs:resouce="#ImaginaryL"/>
          <smml:hasRightParameter rdfs:resouce="#ImaginaryI"/>
        </smml:GrassmannProduct>
      </smml:Negate>
    </smml:isEqualTo>
    <smml:isEqualTo>
      <smml:Negate>
        <smml:GrassmannProduct>
          <smml:hasLeftParameter rdfs:resouce="#ImaginaryJ"/>
          <smml:hasRightParameter rdfs:resouce="#ImaginaryO"/>
        </smml:GrassmannProduct>
      </smml:Negate>
    </smml:isEqualTo>
    <smml:isEqualTo>
      <smml:Negate>
        <smml:GrassmannProduct>
          <smml:hasLeftParameter rdfs:resouce="#ImaginaryN"/>
          <smml:hasRightParameter rdfs:resouce="#ImaginaryK"/>
        </smml:GrassmannProduct>
      </smml:Negate>
    </smml:isEqualTo>
  </smml:MathematicalDimension>
  <smml:MathematicalDimension rdf:about="#ImaginaryN"
                              rdfs:label="n">
    <smml:isEqualTo>
      <smml:Sqrt>
        <smml:hasParameter rdfs:type="&xsd;int">-1</smml:hasParameter>
      </smml:Sqrt>
    </smml:isEqualTo>
    <smml:isEqualTo>
      <smml:GrassmannProduct>
        <smml:hasLeftParameter rdfs:resouce="#ImaginaryJ"/>
        <smml:hasRightParameter rdfs:resouce="#ImaginaryL"/>
      </smml:GrassmannProduct>
    </smml:isEqualTo>
    <smml:isEqualTo>
      <smml:GrassmannProduct>
        <smml:hasLeftParameter rdfs:resouce="#ImaginaryI"/>
        <smml:hasRightParameter rdfs:resouce="#ImaginaryO"/>
      </smml:GrassmannProduct>
    </smml:isEqualTo>
    <smml:isEqualTo>
      <smml:GrassmannProduct>
        <smml:hasLeftParameter rdfs:resouce="#ImaginaryM"/>
        <smml:hasRightParameter rdfs:resouce="#ImaginaryK"/>
      </smml:GrassmannProduct>
    </smml:isEqualTo>
    <smml:isEqualTo>
      <smml:Negate>
        <smml:GrassmannProduct>
          <smml:hasLeftParameter rdfs:resouce="#ImaginaryL"/>
          <smml:hasRightParameter rdfs:resouce="#ImaginaryJ"/>
        </smml:GrassmannProduct>
      </smml:Negate>
    </smml:isEqualTo>
    <smml:isEqualTo>
      <smml:Negate>
        <smml:GrassmannProduct>
          <smml:hasLeftParameter rdfs:resouce="#ImaginaryO"/>
          <smml:hasRightParameter rdfs:resouce="#ImaginaryI"/>
        </smml:GrassmannProduct>
      </smml:Negate>
    </smml:isEqualTo>
    <smml:isEqualTo>
      <smml:Negate>
        <smml:GrassmannProduct>
          <smml:hasLeftParameter rdfs:resouce="#ImaginaryK"/>
          <smml:hasRightParameter rdfs:resouce="#ImaginaryM"/>
        </smml:GrassmannProduct>
      </smml:Negate>
    </smml:isEqualTo>
  </smml:MathematicalDimension>
  <smml:MathematicalDimension rdf:about="#ImaginaryO"
                              rdfs:label="o">
    <smml:isEqualTo>
      <smml:Sqrt>
        <smml:hasParameter rdfs:type="&xsd;int">-1</smml:hasParameter>
      </smml:Sqrt>
    </smml:isEqualTo>
    <smml:isEqualTo>
      <smml:GrassmannProduct>
        <smml:hasLeftParameter rdfs:resouce="#ImaginaryN"/>
        <smml:hasRightParameter rdfs:resouce="#ImaginaryI"/>
      </smml:GrassmannProduct>
    </smml:isEqualTo>
    <smml:isEqualTo>
      <smml:GrassmannProduct>
        <smml:hasLeftParameter rdfs:resouce="#ImaginaryJ"/>
        <smml:hasRightParameter rdfs:resouce="#ImaginaryM"/>
      </smml:GrassmannProduct>
    </smml:isEqualTo>
    <smml:isEqualTo>
      <smml:GrassmannProduct>
        <smml:hasLeftParameter rdfs:resouce="#ImaginaryK"/>
        <smml:hasRightParameter rdfs:resouce="#ImaginaryL"/>
      </smml:GrassmannProduct>
    </smml:isEqualTo>
    <smml:isEqualTo>
      <smml:Negate>
        <smml:GrassmannProduct>
          <smml:hasLeftParameter rdfs:resouce="#ImaginaryI"/>
          <smml:hasRightParameter rdfs:resouce="#ImaginaryN"/>
        </smml:GrassmannProduct>
      </smml:Negate>
    </smml:isEqualTo>
    <smml:isEqualTo>
      <smml:Negate>
        <smml:GrassmannProduct>
          <smml:hasLeftParameter rdfs:resouce="#ImaginaryM"/>
          <smml:hasRightParameter rdfs:resouce="#ImaginaryJ"/>
        </smml:GrassmannProduct>
      </smml:Negate>
    </smml:isEqualTo>
    <smml:isEqualTo>
      <smml:Negate>
        <smml:GrassmannProduct>
          <smml:hasLeftParameter rdfs:resouce="#ImaginaryL"/>
          <smml:hasRightParameter rdfs:resouce="#ImaginaryK"/>
        </smml:GrassmannProduct>
      </smml:Negate>
    </smml:isEqualTo>
  </smml:MathematicalDimension>
  <smml:MathematicalDimension rdf:about="#ImaginaryW"
                              rdfs:label="ω">
    <rdfs:comment>used for Biquaternions; but I've no Idea how it works</rdfs:comment>
    <rdfs:seeAlso>http://en.wikipedia.org/wiki/Clifford_biquaternion</rdfs:seeAlso>
  </smml:MathematicalDimension>
  <!-- 
  feel free to extend this list if you need more than 8 (using ImaginaryW 16) Dimensions 
  ie. when working with sedenions (http://en.wikipedia.org/wiki/Sedenion).
  -->

[edit] Number Types

  <owl:Class rdf:about="#NumberType">
    <rdfs:subClassOf rdf:resource="#Constant"/>
  </owl:Class>
  <smml:NumberType rdf:about="#NaturalNumber">
    <rdf:type rdf:resource="&owl;Class"/>
  </smml:NumberType>
  <smml:NumberType rdf:about="#Integer">
    <rdf:type rdf:resource="&owl;Class"/>
  </smml:NumberType>
  <smml:NumberType rdf:about="#RationalNumber">
    <rdf:type rdf:resource="&owl;Class"/>
  </smml:NumberType>
  <smml:NumberType rdf:about="#RealNumber">
    <rdf:type rdf:resource="&owl;Class"/>
  </smml:NumberType>
  <smml:NumberType rdf:about="#ComplexNumber">
    <rdf:type rdf:resource="&owl;Class"/>
  </smml:NumberType>
  <smml:NumberType rdf:about="#Quaternion">
    <rdf:type rdf:resource="&owl;Class"/>
  </smml:NumberType>
  <smml:NumberType rdf:about="#Biquaternion">
    <rdf:type rdf:resource="&owl;Class"/>
  </smml:NumberType>
  <smml:NumberType rdf:about="#Octonion">
    <rdf:type rdf:resource="&owl;Class"/>
  </smml:NumberType>
  <smml:NumberType rdf:about="#Sedenion">
    <rdf:type rdf:resource="&owl;Class"/>
  </smml:NumberType>
  <smml:NumberType rdf:about="#P-AdicNumber">
    <rdf:type rdf:resource="&owl;Class"/>
  </smml:NumberType>
  <smml:NumberType rdf:about="#Scalar">
    <rdf:type rdf:resource="&owl;Class"/>
  </smml:NumberType>
  <smml:NumberType rdf:about="#Vector">
    <rdf:type rdf:resource="&owl;Class"/>
  </smml:NumberType>
  <smml:NumberType rdf:about="#Matrix">
    <rdf:type rdf:resource="&owl;Class"/>
  </smml:NumberType>

[edit] Physical Constants

  <owl:Class rdf:about="&phml;Power">
    <rdfs:subClassOf rdf:resource="#PhysicalDimension"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;PhysicalConstant"
             rdfs:label="Physical Constant">
    <rdfs:subClassOf rdf:resource="&smml;Constant"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;ElectromagneticConstant"
             rdfs:label="Electromagnetic Constant">
    <rdfs:subClassOf rdf:resource="&smml;PhysicalConstant"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;GravitationalConstant"
             rdfs:label="Gravitational Constant">
    <rdfs:subClassOf rdf:resource="&smml;PhysicalConstant"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;ThermodynamicConstant"
             rdfs:label="Thermodynamic Constant">
    <rdfs:subClassOf rdf:resource="&smml;PhysicalConstant"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;ParticlePhysicsConstant"
             rdfs:label="Constant from Particle Physics">
    <rdfs:subClassOf rdf:resource="&smml;PhysicalConstant"/>
  </owl:Class>
  <phml:ElectromagneticConstant rdf:about="&phml;SpeedOfLight">
    <rdfs:comment>the Speed of Light in the emty space</rdfs:comment>
    <rdfs:comment>299.792.458 m s^-1</rdfs:comment>
    <rdfs:label>c</rdfs:label>
    <rdfs:label>c<h:sub>0</h:sub></rdfs:label>
  </phml:ElectromagneticConstant>
  <phml:ElectromagneticConstant rdf:about="&phml;ElementaryCharge">
    <rdfs:comment>the elementary Charge in the emty space</rdfs:comment>
    <rdfs:comment>1.60217653(14) 10^-19 C</rdfs:comment>
    <rdfs:label><h:em>e</h:em></rdfs:label>
  </phml:ElectromagneticConstant>
  <phml:ElectromagneticConstant rdf:about="&phml;Permeability">
    <rdfs:comment>the Permeability in the emty space</rdfs:comment>
    <rdfs:comment>4 pi 10^-7 H m^-1</rdfs:comment>
    <rdfs:label>µ<h:sub>0</h:sub></rdfs:label>
  </phml:ElectromagneticConstant>
  <phml:ElectromagneticConstant rdf:about="&phml;Permittivity">
    <rdfs:comment>the Permittivity in the emty space</rdfs:comment>
    <rdfs:comment>ε0 = µ0^-1 c0^-1 = 8.85418781762... 10^-12 F m^-1</rdfs:comment>
    <rdfs:label>ε<h:sub>0</h:sub></rdfs:label>
  </phml:ElectromagneticConstant>
  <phml:ElectromagneticConstant rdf:about="&phml;CurieConstant" />
  <phml:ElectromagneticConstant rdf:about="&phml;VerdetConstant" />

[edit] Physical Dimensions

  <owl:Class rdf:about="&phml;Surface">
    <rdfs:subClassOf rdf:resource="&phml;Area"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;Temperature">
    <rdfs:subClassOf rdf:resource="&phml;PhysicalDimension"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;TemperatureDifference">
    <rdfs:subClassOf rdf:resource="&phml;Temperature"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;ThermalConductivity">
    <rdfs:subClassOf rdf:resource="&phml;PhysicalDimension"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;ThermalDiffusivity">
    <rdfs:subClassOf rdf:resource="&phml;Coefficient"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;ThermalExpansionCoefficient">
    <rdfs:subClassOf rdf:resource="&phml;Coefficient"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;ThermodynamicTemperature">
    <rdfs:subClassOf rdf:resource="&phml;PhysicalDimension"/>
    <owl:equivalentClass rdf:resource="&phml;Temperature"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;Thickness">
    <rdfs:subClassOf rdf:resource="&phml;Lenght"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;Time">
    <rdfs:subClassOf rdf:resource="&phml;PhysicalDimension"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;Timeconstant">
    <rdfs:subClassOf rdf:resource="&phml;Time"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;Timespan">
    <rdfs:subClassOf rdf:resource="&phml;Time"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;Torque">
    <rdfs:subClassOf rdf:resource="&phml;Momentum"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;TorsionMomentum">
    <rdfs:subClassOf rdf:resource="&phml;Momentum"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;Volume">
    <rdfs:subClassOf rdf:resource="&phml;PhysicalDimension"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;VolumeExpansionCoefficient">
    <rdfs:subClassOf rdf:resource="&phml;ThermalExpansionCoefficient"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;WaveLenght">
    <rdfs:subClassOf rdf:resource="&phml;Lenght"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;WavePropagationCoefficient">
    <rdfs:subClassOf rdf:resource="&phml;Coefficient"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;WayLenght">
    <rdfs:subClassOf rdf:resource="&phml;Lenght"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;Weight">
    <rdfs:subClassOf rdf:resource="&phml;Force"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;WeightForce">
    <rdfs:subClassOf rdf:resource="&phml;Force"/>
    <owl:equivalentClass rdf:resource="&phml;Weight"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;Width">
    <rdfs:subClassOf rdf:resource="&phml;Lenght"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;Work">
    <rdfs:subClassOf rdf:resource="&phml;Energy"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;PlainAngle">
    <rdfs:subClassOf rdf:resource="&phml;Angle"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;YoungsModulus">
    <rdfs:subClassOf rdf:resource="&phml;Stress"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;SolidAngle">
    <rdfs:subClassOf rdf:resource="&phml;Angle"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;SpecificHeatCapacity">
    <rdfs:subClassOf rdf:resource="&phml;HeatCapacity"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;SpecificVolume">
    <rdfs:subClassOf rdf:resource="&phml;PhysicalDimension"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;Speed">
    <rdfs:subClassOf rdf:resource="&phml;PhysicalDimension"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;Strain">
    <rdfs:subClassOf rdf:resource="&phml;DimensionlessPhysicalDimension"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;Stress">
    <rdfs:subClassOf rdf:resource="&phml;PhysicalDimension"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;RotationFrequency">
    <rdfs:subClassOf rdf:resource="&phml;Frequency"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;Shear">
    <rdfs:subClassOf rdf:resource="&phml;DimensionlessPhysicalDimension"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;ShearModulus">
    <rdfs:subClassOf rdf:resource="&phml;Stress"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;ShearStress">
    <rdfs:subClassOf rdf:resource="&phml;Stress"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;Shift">
    <rdfs:subClassOf rdf:resource="&phml;DimensionlessPhysicalDimension"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;Exposure">
    <rdfs:subClassOf rdf:resource="&phml;PhysicalDimension"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;FlowSpeed"
             rdfs:label="the speed of liquidous-flow">
    <rdfs:subClassOf rdf:resource="&phml;Speed"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;FocalLength">
    <rdfs:subClassOf rdf:resource="&phml;Coefficient"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;Force">
    <rdfs:subClassOf rdf:resource="&phml;PhysicalDimension"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;ForceImpact">
    <rdfs:subClassOf rdf:resource="&phml;Impulse"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;Frequency">
    <rdfs:subClassOf rdf:resource="&phml;PhysicalDimension"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;GravitationalAcceleration">
    <rdfs:subClassOf rdf:resource="&phml;Acceleration"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;Heat">
    <rdfs:subClassOf rdf:resource="&phml;Energy"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;HeatAmmount">
    <rdfs:subClassOf rdf:resource="&phml;Energy"/>
    <owl:equivalentClass rdf:resource="&phml;Heat"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;HeatCapacity">
    <rdfs:subClassOf rdf:resource="&phml;Coefficient"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;HeatCurrent">
    <rdfs:subClassOf rdf:resource="&phml;Power"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;HeatResistance">
    <rdfs:subClassOf rdf:resource="&phml;Coefficient"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;HeatTransferCoefficient">
    <rdfs:subClassOf rdf:resource="&phml;Coefficient"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;Height">
    <rdfs:subClassOf rdf:resource="&phml;Lenght"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;HydrodynamicalPressure">
    <rdfs:subClassOf rdf:resource="&phml;Pressure"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;HypberbolicFunction">
    <rdfs:subClassOf rdf:resource="&phml;SingleArgumentFunction"/>
    <rdfs:subClassOf rdf:resource="&phml;TrigonometricFunction"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;HypergeometricFunction">
    <rdfs:subClassOf rdf:resource="&phml;Function"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;Illuminance">
    <rdfs:subClassOf rdf:resource="&phml;PhysicalDimension"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;Impulse">
    <rdfs:subClassOf rdf:resource="&phml;PhysicalDimension"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;Inductivity">
    <rdfs:subClassOf rdf:resource="&phml;PhysicalDimension"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;InertiaMomentum">
    <rdfs:subClassOf rdf:resource="&phml;PhysicalDimension"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;AbsolutePressure">
    <rdfs:subClassOf rdf:resource="&phml;Pressure"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;AbsorbedDose">
    <rdfs:subClassOf rdf:resource="&phml;PhysicalDimension"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;Acceleration">
    <rdfs:subClassOf rdf:resource="&phml;PhysicalDimension"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;Activity">
    <rdfs:subClassOf rdf:resource="&phml;Frequency"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;AmmountOfSubstance">
    <rdfs:subClassOf rdf:resource="&phml;PhysicalDimension"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;Angle">
    <rdfs:subClassOf rdf:resource="&phml;PhysicalDimension"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;AngularAcceleration">
    <rdfs:subClassOf rdf:resource="&phml;Acceleration"/>
    <rdfs:subClassOf rdf:resource="&phml;Angle"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;AngularFrequency">
    <rdfs:subClassOf rdf:resource="&phml;Angle"/>
    <rdfs:subClassOf rdf:resource="&phml;Frequency"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;AngularMomentum">
    <rdfs:subClassOf rdf:resource="&phml;PhysicalDimension"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;Area">
    <rdfs:subClassOf rdf:resource="&phml;PhysicalDimension"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;CatalyticActivity">
    <rdfs:subClassOf rdf:resource="&phml;Activity"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;Celsius-Temperature">
    <rdfs:subClassOf rdf:resource="&phml;ThermodynamicTemperature"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;ChargeNumber">
    <rdfs:subClassOf rdf:resource="&phml;DimensionlessPhysicalDimension"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;ChemicalValence">
    <rdfs:subClassOf rdf:resource="&phml;DimensionlessPhysicalDimension"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;Coefficient">
    <rdfs:subClassOf rdf:resource="&phml;PhysicalDimension"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;Conductance">
    <rdfs:subClassOf rdf:resource="&phml;Coefficient"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;CrossSectionArea"
             rdfs:label="cross section">
    <rdfs:subClassOf rdf:resource="&phml;Area"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;CurveLenght">
    <rdfs:subClassOf rdf:resource="&phml;Lenght"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;DampingCoefficient"
             rdfs:comment="1/m">
    <rdfs:subClassOf rdf:resource="&phml;Coefficient"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;Deep">
    <rdfs:subClassOf rdf:resource="&phml;Lenght"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;Density">
    <rdfs:subClassOf rdf:resource="&phml;PhysicalDimension"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;Diameter">
    <rdfs:subClassOf rdf:resource="&phml;Lenght"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;DimensionlessPhysicalDimension">
    <rdfs:subClassOf rdf:resource="&phml;PhysicalDimension"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;Distance">
    <rdfs:subClassOf rdf:resource="&phml;Lenght"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;Duration">
    <rdfs:subClassOf rdf:resource="&phml;Time"/>
    <owl:equivalentClass rdf:resource="&phml;Timespan"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;ElectricCapacity">
    <rdfs:subClassOf rdf:resource="&phml;PhysicalDimension"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;ElectricCharge">
    <rdfs:subClassOf rdf:resource="&phml;PhysicalDimension"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;ElectricFieldstrenght">
    <rdfs:subClassOf rdf:resource="&phml;PhysicalDimension"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;ElectricFlowDensity">
    <rdfs:subClassOf rdf:resource="&phml;PhysicalDimension"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;ElectricPotential">
    <rdfs:subClassOf rdf:resource="&phml;PhysicalDimension"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;ElectricVoltage">
    <rdfs:subClassOf rdf:resource="&phml;ElectricPotential"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;ElectricalCurrent">
    <rdfs:subClassOf rdf:resource="&phml;PhysicalDimension"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;ElectricalImpendance">
    <rdfs:subClassOf rdf:resource="&phml;ElectricalResistance"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;ElectricalResistance">
    <rdfs:subClassOf rdf:resource="&phml;PhysicalDimension"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;ElectromagneticPermeability">
    <rdfs:subClassOf rdf:resource="&phml;PhysicalDimension"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;ElemantaryFunction">
    <rdfs:subClassOf rdf:resource="&phml;Function"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;EllipticFunction">
    <rdfs:subClassOf rdf:resource="&phml;Function"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;EllipticIntegralFunction">
    <rdfs:subClassOf rdf:resource="&phml;Function"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;Energy">
    <rdfs:subClassOf rdf:resource="&phml;PhysicalDimension"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;EnergyCoefficient">
    <rdfs:subClassOf rdf:resource="&phml;DimensionlessPhysicalDimension"/>
    <owl:equivalentClass rdf:resource="&phml;EnergyEfficiency"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;EnergyEfficiency">
    <rdfs:subClassOf rdf:resource="&phml;DimensionlessPhysicalDimension"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;Entropy">
    <rdfs:subClassOf rdf:resource="&phml;PhysicalDimension"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;EquivalentDose">
    <rdfs:subClassOf rdf:resource="&phml;AbsorbedDose"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;InnerDiameter">
    <rdfs:subClassOf rdf:resource="&phml;Diameter"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;InnerEnergy">
    <rdfs:subClassOf rdf:resource="&phml;Energy"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;Lenght">
    <rdfs:subClassOf rdf:resource="&phml;PhysicalDimension"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;LenghtExpansionCoefficient">
    <rdfs:subClassOf rdf:resource="&phml;ThermalExpansionCoefficient"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;Luminance">
    <rdfs:subClassOf rdf:resource="&phml;PhysicalDimension"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;LuminousEfficiency">
    <rdfs:subClassOf rdf:resource="&phml;PhysicalDimension"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;LuminousEnergy">
    <rdfs:subClassOf rdf:resource="&phml;PhysicalDimension"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;LuminousFlux">
    <rdfs:subClassOf rdf:resource="&phml;PhysicalDimension"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;LuminousIntensity">
    <rdfs:subClassOf rdf:resource="&phml;PhysicalDimension"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;MagneticFieldstrenght">
    <rdfs:subClassOf rdf:resource="&phml;PhysicalDimension"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;MagneticFlow">
    <rdfs:subClassOf rdf:resource="&phml;PhysicalDimension"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;MagneticFlowDensity">
    <rdfs:subClassOf rdf:resource="&phml;PhysicalDimension"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;MagneticalPressure">
    <rdfs:subClassOf rdf:resource="&phml;Pressure"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;Mass">
    <rdfs:subClassOf rdf:resource="&phml;PhysicalDimension"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;MechanicalPressure">
    <rdfs:subClassOf rdf:resource="&phml;Pressure"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;MolarMass">
    <rdfs:subClassOf rdf:resource="&phml;PhysicalDimension"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;MolarVolume">
    <rdfs:subClassOf rdf:resource="&phml;PhysicalDimension"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;Momentum">
    <rdfs:subClassOf rdf:resource="&phml;PhysicalDimension"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;NormalStress">
    <rdfs:subClassOf rdf:resource="&phml;Stress"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;OuterDiameter">
    <rdfs:subClassOf rdf:resource="&phml;Diameter"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;PeriodFrequency">
    <rdfs:subClassOf rdf:resource="&phml;PhysicalDimension"/>
    <owl:equivalentClass rdf:resource="&phml;Frequency"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;PeriodTime">
    <rdfs:subClassOf rdf:resource="&phml;Time"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;Permittivity">
    <rdfs:subClassOf rdf:resource="&phml;PhysicalDimension"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;PhaseCoefficient">
    <rdfs:subClassOf rdf:resource="&phml;Coefficient"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;PhysicalDimension"
             rdfs:label="a physical Dimension">
    <rdfs:subClassOf rdf:resource="&phml;Constant"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;Pressure">
    <rdfs:subClassOf rdf:resource="&phml;PhysicalDimension"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;PressureStress">
    <rdfs:subClassOf rdf:resource="&phml;NormalStress"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;PullStress">
    <rdfs:subClassOf rdf:resource="&phml;NormalStress"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;Radioactivity">
    <rdfs:subClassOf rdf:resource="&phml;Activity"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;Radius">
    <rdfs:subClassOf rdf:resource="&phml;Lenght"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;Reactance">
    <rdfs:subClassOf rdf:resource="&phml;ElectricalResistance"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;RelativeAtomMass">
    <rdfs:subClassOf rdf:resource="&phml;DimensionlessPhysicalDimension"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;RelativeMoleculeMass">
    <rdfs:subClassOf rdf:resource="&phml;DimensionlessPhysicalDimension"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;RelativePressure">
    <rdfs:subClassOf rdf:resource="&phml;DimensionlessPhysicalDimension"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;RelativeStrain">
    <rdfs:subClassOf rdf:resource="&phml;DimensionlessPhysicalDimension"/>
  </owl:Class>
  <owl:Class rdf:about="&phml;Resistivity">
    <rdfs:subClassOf rdf:resource="&phml;PhysicalDimension"/>
  </owl:Class>
  <owl:Class rdf:about="#BulkModulus">
    <rdfs:subClassOf rdf:resource="#Stress"/>
  </owl:Class>

[edit] Mathematical Functions

  <owl:Class rdf:about="#ComplexFunction">
    <rdfs:subClassOf rdf:resource="#Function"/>
  </owl:Class>
  <owl:Class rdf:about="#GeneralizedFunction">
    <rdfs:subClassOf rdf:resource="#Function"/>
  </owl:Class>

[edit] Elementary Functions


  <smml:ElemantaryFunction rdf:about="#Times">
    <rdf:type rdf:resource="#ListOfArgumentsFunction"/>
  </smml:ElemantaryFunction>
  <smml:ElemantaryFunction rdf:about="#Divide"/>
  <smml:ElemantaryFunction rdf:about="#Add"
                           rdf:label="+">
    <rdf:type rdf:resource="#ListOfArgumentsFunction"/>
  </smml:ElemantaryFunction>
  <smml:ElemantaryFunction rdf:about="#Minus"
                           rdf:Label="-"/>
  <smml:ElemantaryFunction rdf:about="#Negate">
    <rdf:type rdf:resource="#SingleArgumentFunction"/>
  </smml:ElemantaryFunction>

[edit] Function generated Contants

  <owl:Class rdf:about="#AlgebraicConstant">
    <rdfs:subClassOf rdf:resource="#MathematicalConstant"/>
  </owl:Class>

[edit] Power Functions

  <owl:Class rdf:about="#PowerFunction">
    <rdfs:subClassOf rdf:resource="#ElemantaryFunction"/>
  </owl:Class>
  <smml:PowerFunction rdf:about="#Sqrt"
                                 rdfs:label="sqrt">
    <smml:define>
       <smml:Parameters>
          <smml:Parameter rdfs:type="#hasParameter" rdf:ID="&smml;Sqrt_Value"/>
       <smml:Parameters>
       <smml:to>
          <smml:Power>
             <smml:hasBase rdf:resource="&smml;Sqrt_Value">
             <smml:hasExponent rdfs:type="&xsd;float">0,5</smml:hasExponent>
          </smml:Power>
       </smml:to>
    </smml:define>
  </smml:PowerFunction>
  <smml:PowerFunction rdf:about="#Power"
                                 rdfs:label="^">
    <smml:define>
       <smml:Parameters>
          <smml:Parameter rdfs:type="#hasBase" rdf:ID="&smml;Power_Base"/>
          <smml:Parameter rdfs:type="#hasExponent" rdf:ID="&smml;Power_Exponent"/>
       <smml:Parameters>
       <smml:if>
          <smml:Condition>
             <rdf:statement>
                <rdf:subject rdf:resource="&smml;Power_Exponent"/>
                <rdf:predicate rdf:resouce="&smml;hasType"/>
                <rdf:object rdf:resource="&xsd;nonNegativeInteger"/>
             </rdf:statement>
          </smml:Condition>
          <smml:to>
             <smml:Times>
                <smml:hasParameter rdf:resource="&smml;Power_Base">
                <smml:hasParameter>
                  <smml:Power><!-- recursive Definition -->
                     <smml:hasBase rdf:resource="&smml;Power_Base">
                     <smml:hasExponent>
                        <smml:Add>
                           <smml:hasParameter rdf:resouce="&smml;Power_Exponent">
                           <smml:hasParameter>
                              <smml:Negate rdfs:type="&xsd;int">1</smml:Negate>
                           </smml:hasParameter>
                        <smml:Add>
                     <smml:hasExponent>
                  </smml:Power>
                </smml:hasParameter>
             </smml:Times>
          </smml:to>
       </smml:if>
       <smml:if>
          <smml:Condition><!-- Stopcondition for recursive Definition -->
             <rdf:statement>
                <rdf:subject rdf:resource="&smml;Power_Exponent"/>
                <rdf:predicate rdf:resouce="&smml;isEqualTo"/>
                <rdf:object rdfs:type="&xsd;int">1</rdf:object>
             </rdf:statement>
          </smml:Condition>
          <smml:to>
             <smml:Power_Base/>
          </smml:to>
       </smml:if>
       <smml:if>
          <smml:Condition><!-- Stopcondition for recursive Definition -->
             <smml:AND>
                <smml:hasParameter>
                   <rdf:statement>
                      <rdf:subject rdf:resource="&smml;Power_Exponent"/>
                      <rdf:predicate rdf:resouce="&smml;isEqualTo"/>
                      <rdf:object rdfs:type="&xsd;int">0</rdf:object>
                   </rdf:statement>
                </smml:hasParameter>
                <smml:hasParameter>
                   <rdf:statement>
                      <rdf:subject rdf:resource="&smml;Power_Base"/>
                      <rdf:predicate rdf:resouce="&smml;isNotEqualTo"/>
                      <rdf:object rdfs:type="&xsd;int">0</rdf:object>
                   </rdf:statement>
                </smml:hasParameter>
             </smml:AND>
          </smml:Condition>
          <smml:to rdfs:type="&xsd;int">1</smml:to>
       </smml:if>
    </smml:define>
  </smml:PowerFunction>

[edit] Exponential Function

  <owl:Class rdf:about="#ExponentialFunction">
    <rdfs:subClassOf rdf:resource="#PowerFunction"/>
  </owl:Class>
  <smml:ExponentialFunction rdf:about="#Exp"
                                       rdfs:label="e^"/>
  <smml:ExponentialFunction rdf:about="#EE"
                                       rdfs:label="10^"/>

[edit] Logarithmic Functions

  <owl:Class rdf:about="#LogarithmicFunction">
    <rdfs:subClassOf rdf:resource="#ExponentialFunction"/>
  </owl:Class>
  <smml:LogarithmicFunction rdf:about="#Lg"
                                       rdfs:label="lg"/>
  <smml:LogarithmicFunction rdf:about="#Ln"
                                       rdfs:label="ln"/>
  <smml:LogarithmicFunction rdf:about="#Log"
                                       rdfs:label="log"/>

[edit] Trigonometric Functions

  <owl:Class rdf:about="#TrigonometricFunction">
    <rdfs:subClassOf rdf:resource="#ElemantaryFunction"/>
  </owl:Class>
  <smml:TrigonometricFunction rdf:about="#Cot"
                                         rdfs:label="cot"/>
  <smml:TrigonometricFunction rdf:about="#Cos"
                                         rdfs:label="cos"/>
  <smml:TrigonometricFunction rdf:about="#Csc"
                                         rdfs:label="csc"/>
  <smml:TrigonometricFunction rdf:about="#Sec"
                                         rdfs:label="sec"/>
  <smml:TrigonometricFunction rdf:about="#Sin"
                                         rdfs:label="sin"/>
  <smml:TrigonometricFunction rdf:about="#Tan"
                                         rdfs:label="tan"/>

[edit] Inverse Trigonometric Functions

  <owl:Class rdf:about="#InverseTrigonometricFunction">
    <rdfs:subClassOf rdf:resource="#TrigonometricFunction"/>
  </owl:Class>
  <smml:InverseTrigonometricFunction rdf:about="#ArcSin">
    <rdfs:label>arcsin</rdfs:label>
    <rdfs:label>asin</rdfs:label>
  </smml:InverseTrigonometricFunction>
  <smml:InverseTrigonometricFunction rdf:about="#ArcTan"
                                                rdfs:label="atan"/>
  <smml:InverseTrigonometricFunction rdf:about="#ArcTan2"
                                                rdfs:label="atan"/>
  <smml:InverseTrigonometricFunction rdf:about="#ArcCos"
                                                rdfs:label="acos"/>
  <smml:InverseTrigonometricFunction rdf:about="#ArcCot"
                                                rdfs:label="acot"/>
  <smml:InverseTrigonometricFunction rdf:about="#ArcCsc"
                                                rdfs:label="acsc"/>
  <smml:InverseTrigonometricFunction rdf:about="#ArcSec"
                                                rdfs:label="asec"/>

[edit] Hyperbolic Functions

  <smml:HypberbolicFunction rdf:about="#Sech"
                                       rdfs:label="sech"/>
  <smml:HypberbolicFunction rdf:about="#Sinh"
                                       rdfs:label="sinh"/>
  <smml:HypberbolicFunction rdf:about="#Tanh"
                                       rdfs:label="tanh"/>
  <smml:HypberbolicFunction rdf:about="#Cosh"
                                       rdfs:label="cosh"/>
  <smml:HypberbolicFunction rdf:about="#Coth"
                                       rdfs:label="coth"/>
  <smml:HypberbolicFunction rdf:about="#Csch"
                                       rdfs:label="csch"/>

[edit] Inverse Hyperbolic Functions

  <owl:Class rdf:about="#InverseHyperbolicFunction">
    <rdfs:subClassOf rdf:resource="#HypberbolicFunction"/>
    <rdfs:subClassOf rdf:resource="#InverseTrigonometricFunction"/>
    <rdfs:subClassOf rdf:resource="#SingleArgumentFunction"/>
  </owl:Class>
  <smml:InverseHyperbolicFunction rdf:about="#ArcSech"
                                             rdfs:label="asech"/>
  <smml:InverseHyperbolicFunction rdf:about="#ArcSinh"
                                             rdfs:label="asinh"/>
  <smml:InverseHyperbolicFunction rdf:about="#ArcTanh"
                                             rdfs:label="atanh"/>
  <smml:InverseHyperbolicFunction rdf:about="#ArcCosh"
                                             rdfs:label="acosh"/>
  <smml:InverseHyperbolicFunction rdf:about="#ArcCoth"
                                             rdfs:label="acoth"/>
  <smml:InverseHyperbolicFunction rdf:about="#ArcCsch"
                                             rdfs:label="acsch"/>

[edit] Product Logarithms

  <owl:Class rdf:about="#ProductLogarithm">
    <rdfs:comment xml:lang="en">
      This is also known as "Lambert's W function" see also:
      <rdfs:seeAlso>http://en.wikipedia.org/wiki/Lambert_function</rdfs:seeAlso>
    </rdfs:comment>
    <rdfs:subClassOf rdf:resource="#LogarithmicFunction"/>
  </owl:Class>
  <smml:ProductLogarithm rdf:about="#ProductLog"/>
  <smml:ProductLogarithm rdf:about="#ProductLog2"/>

[edit] Roots

  <smml:ElemantaryFunction rdf:about="#Root"
                        rdfs:comment="the k-th root of a polynom"/>

[edit] Max and Min

  <owl:Class rdf:about="#MinAndMaxFunction">
    <rdfs:subClassOf rdf:resource="#ElemantaryFunction"/>
    <rdfs:subClassOf rdf:resource="#ListOfArgumentsFunction"/>
  </owl:Class>
  <smml:MinAndMaxFunction rdf:about="#Max"/>
  <smml:MinAndMaxFunction rdf:about="#Min"/>

[edit] Bessel, Airy, and Struve Functions

  <owl:Class rdf:about="#BesselAiryStruveFunction">
    <rdfs:subClassOf rdf:resource="#Function"/>
  </owl:Class>
  <smml:StirlingNumberFunction rdf:about="#StirlingS1"/>
  <smml:StirlingNumberFunction rdf:about="#StirlingS2"/>
  <smml:StruveFunction rdf:about="#StruveH"/>
  <smml:StruveFunction rdf:about="#StruveL"/>

[edit] Airy Functions

  <owl:Class rdf:about="#AiryFunction">
    <rdfs:subClassOf rdf:resource="#BesselAiryStruveFunction"/>
    <rdfs:subClassOf rdf:resource="#SingleArgumentFunction"/>
  </owl:Class>
  <smml:AiryFunction rdf:about="#AiryAi"/>
  <smml:AiryFunction rdf:about="#AiryAiPrime"/>
  <smml:AiryFunction rdf:about="#AiryBi"/>
  <smml:AiryFunction rdf:about="#AiryBiPrime"/>

[edit] Bessel Functions

  <owl:Class rdf:about="#BesselFunction">
    <rdfs:subClassOf rdf:resource="#BesselAiryStruveFunction"/>
  </owl:Class>
  <smml:BesselFunction rdf:about="#BesselI"/>
  <smml:BesselFunction rdf:about="#BesselJ"/>
  <smml:BesselFunction rdf:about="#BesselK"/>
  <smml:BesselFunction rdf:about="#BesselY"/>

[edit] Struve Functions

  <owl:Class rdf:about="#StruveFunction">
    <rdfs:subClassOf rdf:resource="#BesselAiryStruveFunction"/>
  </owl:Class>

[edit] Integer Functions

  <owl:Class rdf:about="#IntegerFunction">
    <rdfs:subClassOf rdf:resource="#Function"/>
  </owl:Class>

[edit] Rounding and Congruence Functions

  <owl:Class rdf:about="#RoundingAndCongruenceFunction">
    <rdfs:subClassOf rdf:resource="#IntegerFunction"/>
  </owl:Class>
  <smml:RoundingAndCongruenceFunction rdf:about="#Round"
                                                 rdfs:label="round"/>
  <smml:RoundingAndCongruenceFunction rdf:about="#Ceiling"
                                                 rdfs:label="ceil"/>
  <smml:RoundingAndCongruenceFunction rdf:about="#Floor"
                                                 rdfs:label="floor"/>
  <smml:RoundingAndCongruenceFunction rdf:about="#FractionalPart"/>
  <smml:RoundingAndCongruenceFunction rdf:about="#IntegerPart"/>
  <smml:RoundingAndCongruenceFunction rdf:about="#Quotient"/>
  <smml:RoundingAndCongruenceFunction rdf:about="#Mod"
                                                 rdfs:label="mod"/>

[edit] GCD and LCM

  <owl:Class rdf:about="#GCD_and_LCM">
    <rdfs:subClassOf rdf:resource="#IntegerFunction"/>
  </owl:Class>
  <smml:RoundingAndCongruenceFunction rdf:about="#GCD"/>
  <smml:RoundingAndCongruenceFunction rdf:about="#ExtendedGCD"
                                                 rdfs:label="GCD"/>
  <smml:RoundingAndCongruenceFunction rdf:about="#LCM"/>

[edit] Fibonacci Numbers

  <owl:Class rdf:about="#FibonacciNumberFunction">
    <rdfs:subClassOf rdf:resource="#IntegerFunction"/>
  </owl:Class>
  <smml:FibonacciNumberFunction rdf:about="#Fibonacci">
    <rdf:type rdf:resource="#PolynomialFunction"/>
  </smml:FibonacciNumberFunction>

[edit] Euler and Bernoulli Numbers

  <owl:Class rdf:about="#EulerAndBernoulliNumberFunction">
    <rdfs:subClassOf rdf:resource="#IntegerFunction"/>
  </owl:Class>
  <smml:EulerAndBernoulliNumberFunction rdf:about="#EulerE">
    <rdf:type rdf:resource="#PolynomialFunction"/>
  </smml:EulerAndBernoulliNumberFunction>
  <smml:EulerAndBernoulliNumberFunction rdf:about="#BernoulliB">
    <rdf:type rdf:resource="#PolynomialFunction"/>
  </smml:EulerAndBernoulliNumberFunction>

see also: #Polynomials

[edit] Stirling Numbers

  <owl:Class rdf:about="#StirlingNumberFunction">
    <rdfs:subClassOf rdf:resource="#IntegerFunction"/>
  </owl:Class>
  <smml:StirlingNumberFunction rdf:about="#PartitionsP"/>
  <smml:StirlingNumberFunction rdf:about="#PartitionsQ"/>

[edit] Partitions

  <owl:Class rdf:about="#PartitionFunction">
    <rdfs:subClassOf rdf:resource="#IntegerFunction"/>
  </owl:Class>

[edit] Tensor Functions

  <owl:Class rdf:about="#TensorFunction">
    <rdfs:subClassOf rdf:resource="#IntegerFunction"/>
  </owl:Class>
  <smml:TensorFunction rdf:about="#KroneckerDelta"/>
  <smml:TensorFunction rdf:about="#Signature"/>
  <smml:TensorFunction rdf:about="#DiscreteDelta"/>
  <smml:TensorFunction rdf:about="#DiscreteDeltaN"/>

[edit] Polynomials

  <owl:Class rdf:about="#PolynomialFunction">
    <rdfs:subClassOf rdf:resource="#Function"/>
  </owl:Class>
  <smml:PolynomialFunction rdf:about="#Cyclotomic"/>

[edit] Classical Orthogonal Polynomials

  <owl:Class rdf:about="#OrthogonalPolynominalFunction">
    <rdfs:subClassOf rdf:resource="#PolynomialFunction"/>
  </owl:Class>
  <smml:OrthogonalPolynominalFunction rdf:about="#HermiteH"/>
  <smml:OrthogonalPolynominalFunction rdf:about="#JacobiP"/>
  <smml:OrthogonalPolynominalFunction rdf:about="#LaguerreL"/>
  <smml:OrthogonalPolynominalFunction rdf:about="#LegendreP"/>
  <smml:OrthogonalPolynominalFunction rdf:about="#ChebyshevT"/>
  <smml:OrthogonalPolynominalFunction rdf:about="#ChebyshevU"/>

[edit] Associated Polynomials

  <owl:Class rdf:about="#AssociatedPolynominalFunction">
    <rdfs:subClassOf rdf:resource="#PolynomialFunction"/>
  </owl:Class>
  <smml:AssociatedPolynominalFunction rdf:about="#SphericalHarmonicY"/>
  <smml:AssociatedPolynominalFunction rdf:about="#GegenbauerC"/>
  <smml:AssociatedPolynominalFunction rdf:about="#LegrendeL"/>
  <smml:AssociatedPolynominalFunction rdf:about="#LegrendeP"/>

[edit] Gamma, Beta, and Erf Functions

  <owl:Class rdf:about="#GammaBetaErfFunction">
    <rdfs:subClassOf rdf:resource="#Function"/>
  </owl:Class>

[edit] Factorials


[edit] Binomials


[edit] Gamma Functions


[edit] Differentiated Gamma Functions


[edit] Beta Functions and Inverses


[edit] Probability Integrals and Inverses


[edit] Fresnel Integrals


[edit] Exponential Integrals


[edit] Hypergeometric Functions


[edit] Elliptic Integrals


[edit] Elliptic Functions


[edit] Zeta Functions and Polylogarithms

  <owl:Class rdf:about="#ZetaFunctionAndPolylogarithm">
    <rdfs:subClassOf rdf:resource="#Function"/>
  </owl:Class>

[edit] Mathieu Functions

  <owl:Class rdf:about="#MathieuFunction">
    <rdfs:subClassOf rdf:resource="#Function"/>
  </owl:Class>

[edit] Complex Components


[edit] Number Theory Functions

  <owl:Class rdf:about="#NumberTheoryFunction">
    <rdfs:subClassOf rdf:resource="#Function"/>
  </owl:Class>

[edit] Generalized Functions


[edit] Transformations

  <owl:Class rdf:about="#DistributiveFunction">
    <rdfs:subClassOf rdf:resource="#OperatorTransformation"/>
  </owl:Class>
  <owl:Class rdf:about="#AnticommutativeFunction">
    <rdfs:subClassOf rdf:resource="#OperatorTransformation"/>
    <owl:disjointWith rdf:resource="#CommutativeFunction"/>
  </owl:Class>
  <owl:Class rdf:about="#AssociativeFunction">
    <rdfs:subClassOf rdf:resource="#OperatorTransformation"/>
  </owl:Class>
  <owl:Class rdf:about="#CommutativeFunction">
    <rdfs:subClassOf rdf:resource="#OperatorTransformation"/>
    <owl:disjointWith rdf:resource="#AnticommutativeFunction"/>
  </owl:Class>


[edit] Functions

  <smml:MathematicalConstant rdf:about="#PortersConstant"/>

[edit] Units

  <owl:Class rdf:about="&phml;Unit">
    <rdfs:subClassOf rdf:resource="#Constant"/>
  </owl:Class>

[edit] SI Units

  <owl:Class rdf:about="&phml;SI-Unit">
    <rdfs:subClassOf rdf:resource="&phml;Unit"/>
  </owl:Class>

[edit] SI Base Units

  <owl:Class rdf:about="&phml;SI-BaseUnit">
    <rdfs:subClassOf rdf:resource="&phml;SI-Unit"/>
  </owl:Class>
  <phml:SI-BaseUnit rdf:about="&phml;Mol"
                               rdfs:label="mol"/>
  <phml:SI-BaseUnit rdf:about="&phml;Second"
                               rdfs:label="s"/>
  <phml:SI-BaseUnit rdf:about="&phml;Ampere"
                               rdfs:label="A"/>
  <phml:SI-BaseUnit rdf:about="&phml;Metre"
                               rdfs:label="m"/>
  <phml:SI-BaseUnit rdf:about="&phml;Kilogram"
                               rdfs:label="kg"/>
  <phml:SI-BaseUnit rdf:about="&phml;Kelvin"
                               rdfs:label="K"/>
  <phml:SI-BaseUnit rdf:about="&phml;Candela"
                               rdfs:label="cd"/>

[edit] SI derived Units

  <owl:Class rdf:about="&phml;SI-DerivedUnit">
    <rdfs:subClassOf rdf:resource="&phml;SI-Unit"/>
  </owl:Class>
  <phml:SI-DerivedUnit rdf:about="&phml;Hertz"
                                  rdfs:label="Hz">
    <smml:equalTo>
      <smml:Divide>
        <smml:hasDividend rdfs:type="&xsd;int">1</smml:hasDividend>
        <smml:hasDivisor rdf:resource="&phml;Second">
      </smml:Divide>
    </smml:equalTo>
    <phml:describesPhysicalSize rdf:resource="&phml;Frequency"/>
  </phml:SI-DerivedUnit>
  <phml:SI-DerivedUnit rdf:about="&phml;Newton"
                                  rdfs:label="N">
    <smml:isEqualTo>
      <smml:Divide>
        <smml:hasDividend>
          <smml:Times>
            <smml:hasParameter rdf:resource="#Kilogram"/>
            <smml:hasParameter rdf:resource="#Metre"/>
          </smml:Times>
        </smml:hasDividend>
        <smml:hasDivisor>
          <smml:Square>
            <smml:hasBase rdf:resource="#Second">
          </smml:Square>
        </smml:hasDivisor>
      </smml:Divide>
    </smml:isEqualTo>
    <phml:describesPhysicalSize rdf:resouce="&phml;Force"/>
  </phml:SI-DerivedUnit>
  <phml:SI-DerivedUnit rdf:about="&phml;Radian"
                                  rdfs:label="rad">
    <smml:equalTo rdfs:type="&xsd;int">1</smml:equalTo>
    <phml:describesPhysicalSize rdf:resouce="&phml;PlainAngle"/>
  <phml:SI-DerivedUnit>
  <phml:SI-DerivedUnit rdf:about="&phml;Steradian"
                                  rdfs:label="sr">
    <smml:equalTo rdfs:type="&xsd;int">1</smml:equalTo>
    <phml:describesPhysicalSize rdf:resouce="&phml;SolidAngle"/>
  <phml:SI-DerivedUnit>
  <phml:SI-DerivedUnit rdf:about="&phml;Pascal"
                                  rdfs:label="Pa">
    <smml:equalTo>
      <smml:Divide>
        <smml:hasDividend>
          <smml:hasParameter rdf:resource="#Kilogram"/>
        </smml:hasDividend>
        <smml:hasDivisor>
          <smml:Times>
            <smml:Square>
              <smml:hasBase rdf:resource="#Second">
            </smml:Square>
            <smml:hasParameter rdf:resource="#Metre"/>
          </smml:Times>
        </smml:hasDivisor>
      </smml:Divide>
    </smml:equalTo>
    <phml:describesPhysicalSize rdf:resouce="&phml;Pressure"/>
  <phml:SI-DerivedUnit>
  <phml:SI-DerivedUnit rdf:about="&phml;Joule"
                                  rdfs:label="J">
    <smml:equalTo>
        <smml:hasDividend>
          <smml:Times>
            <smml:hasParameter rdf:resource="#Kilogram"/>
            <smml:Square>
              <smml:hasBase rdf:resource="#Metre"/>
            </smml:Square>
          </smml:Times>
        </smml:hasDividend>
        <smml:hasDivisor>
          <smml:Square>
            <smml:hasBase rdf:resource="#Second"/>
          </smml:Square>
        </smml:hasDivisor>
      </smml:Divide>
    </smml:equalTo>
<!--
    <smml:equalTo>
      <smml:Times>
        <smml:hasParameter rdf:resouce="#Watt"/>
        <smml:hasParameter rdf:resouce="#Second"/>
      </smml:Times>
    </smml:equalTo>
    <smml:equalTo>
      <smml:Times>
        <smml:hasParameter rdf:resouce="#Newton"/>
        <smml:hasParameter rdf:resouce="#Meter"/>
      </smml:Times>
    </smml:equalTo>
-->
    <phml:describesPhysicalSize rdf:resouce="&phml;Energy"/>
    <phml:describesPhysicalSize rdf:resouce="&phml;Work"/>
  <phml:SI-DerivedUnit>
  <phml:SI-DerivedUnit rdf:about="&phml;Watt"
                                  rdfs:label="W">
    <smml:isEqualTo>
      <smml:Divide>
        <smml:hasDividend rdf:resource="&phml;Kilogram"/>
        <smml:hasDividend>
          <smml:Square>
            <smml:hasBase rdf:resource="&phml;Metre"/>
          </smml:Square>
        </smml:hasDividend>
        <smml:hasDivisor>
          <smml:Power>
            <hasExponent rdfs:type="&xsd;int">3</hasExponent>
            <hasBase rdf:resource="&phml;Second"/>
          <smml:Power>
        </smml:hasDivisor>
      </smml:Divide>
    </smml:isEqualTo>
<!--
    <smml:isEqualTo>
     <smml:Divide>
        <smml:hasDividend rdf:resource="&phml;Newton"/>
        <smml:hasDividend rdf:resource="&phml;Metre"/>
        <smml:hasDivisor rdf:resource="&phml;Second"/>
      </smml:Divide>
    </smml:isEqualTo>
    <smml:isEqualTo>
     <smml:Divide>
        <smml:hasDividend rdf:resource="&phml;Joule"/>
        <smml:hasDivisor rdf:resource="&phml;Second"/>
      </smml:Divide>
    </smml:isEqualTo>
    <smml:isEqualTo>
      <smml:Times>
        <smml:hasParameter rdf:resource="&phml;Volt"/>
        <smml:hasParameter rdf:resource="&phml;Ampere"/>
      </smml:Times>
    </smml:isEqualTo>
-->
    <phml:describesPhysicalSize rdf:resouce="&phml;Power"/>
  <phml:SI-DerivedUnit>
  <phml:SI-DerivedUnit rdf:about="&phml;Volt"
                                  rdfs:label="V">
    <smml:isEqualTo>
      <smml:Divide>
        <smml:hasDividend rdf:resource="&phml;Kilogram"/>
        <smml:hasDividend>
          <smml:Square>
            <smml:hasBase rdf:resource="&phml;Metre"/>
          <smml:Square>
        </smml:hasDividend>
        <smml:hasDivisor rdf:resource="&phml;Ampere"/>
        <smml:hasDivisor>
          <smml:Square>
            <smml:hasBase rdf:resource="&phml;Second"/>
          <smml:Square>
        </smml:hasDivisor>
      </smml:Divide>
    </smml:isEqualTo>
<!--
    <smml:isEqualTo>
      <smml:Divide>
        <smml:hasDividend rdf:resource="&phml;Watt"/>
        <smml:hasDivisor rdf:resource="&phml;Ampere"/>
      </smml:Divide>
    </smml:isEqualTo>
    <smml:isEqualTo>
      <smml:Divide>
        <smml:hasDividend rdf:resource="&phml;Joule"/>
        <smml:hasDivisor rdf:resource="&phml;Coulomb"/>
      </smml:Divide>
    </smml:isEqualTo>
-->
    <phml:describesPhysicalSize rdf:resouce="&phml;ElectricVoltage"/>
  <phml:SI-DerivedUnit rdf:about="&phml;Weber"
                                  rdfs:label="Wb">
    <smml:isEqualTo>
      <smml:Divide>
        <smml:hasDividend rdf:resource="#Kilogram"/>
        <smml:hasDividend>
          <smml:Square>
            <smml:hasBase rdf:resource="#Metre"/>
          </smml:Square>
        <smml:hasDivisor rdf:resource="#Ampere"/>
        <smml:hasDivisor>
          <smml:Square>
            <smml:hasBase rdf:resource="#Second"/>
          </smml:Square>
        </smml:hasDivisor>
      <smml:Divide>
    </smml:isEqualTo>
<!--
    <smml:isEqualTo>
      <smml:Times>
        <smml:hasParameter rdf:resource="#Volt">
        <smml:hasParameter rdf:resource="#Second">
      <smml:Times>
    <smml:isEqualTo>
-->
    <phml:describesPhysicalSize rdf:resouce="&phml;MagneticFlow"/>
  <phml:SI-DerivedUnit>
  <phml:SI-DerivedUnit rdf:about="&phml;Ohm"
                                  rdfs:label="Ω"/>
    <smml:isEqualTo>
      <smml:Divide>
        <smml:hasDividend rdf:resource="#Kilogram"/>
        <smml:hasDividend>
          <smml:Square>
            <smml:hasBase rdf:resource="#Metre"/>
          </smml:Square>
        </smml:hasDividend>
        <smml:hasDivisor>
          <smml:Square>
            <smml:hasBase rdf:resource="#Ampere"/>
          </smml:Square>
        </smml:hasDivisor>
        <smml:hasDivisor>
          <smml:Power>
            <smml:hasBase rdf:resource="#Second"/>
            <smml:hasExponent rdf:type="&xsd;int">3</hasExponent>
          </smml:Power>
        </smml:hasDivisor>
      </smml:Divide>
    </smml:isEqualTo>
<!--
    <smml:isEqualTo>
      <smml:Divide>
        <smml:hasDividend rdf:resource="#Volt"/>
        <smml:hasDivisor rdf:resource="#Ampere"/>
      <smml:Divide>
    </smml:isEqualTo>
-->
    <phml:describesPhysicalSize rdf:resouce="&phml;ElectricalResistance"/>
  </phml:SI-DerivedUnit>
  <phml:SI-DerivedUnit rdf:about="&phml;Siemens"
                                  rdfs:label="S">
    <smml:isEqualTo>
      <smml:Divide>
        <smml:hasDividend>
          <smml:Power>
            <smml:hasBase rdf:resource="#Second"/>
            <smml:hasExponent rdfs:type="&xsd;int">3</smml:hasExponent>
          </smml:Power>
        </smml:hasDividend>
        <smml:hasDividend>
          <smml:Square>
            <smml:hasBase rdf:resource="#Ampere"/>
          </smml:Square>
        </smml:hasDividend>
        <smml:hasDivisor rdf:resource="#Kilogram"/>
        <smml:hasDivisor>
          <smml:Square>
            <smml:hasBase rdf:resource="#Metre"/>
          </smml:Square>
        </smml:hasDivisor>
      <smml:Divide>
    </smml:isEqualTo>
<!--
    <smml:isEqualTo>
      <smml:Divide>
        <smml:hasDividend rdfs:type="&xsd;int">1</smml:hasDividend>
        <smml:hasDivisor rdf:resource="#Ohm"/>
      <smml:Divide>
    </smml:isEqualTo>
-->
    <phml:describesPhysicalSize rdf:resouce="&phml;Conductance"/>
  </phml:SI-DerivedUnit>
  <phml:SI-DerivedUnit rdf:about="&phml;Becquerel"
                                  rdfs:label="Bq"/>
    <smml:isEqualTo>
      <smml:Divide>
        <smml:hasDividend rdfs:type="&xsd;int">1</smml:hasDividend>
        <smml:hasDivisor rdf:resource="#Second"/>
      </smml:Divide>
    </smml:isEqualTo>
<!--
    <smml:isEqualTo rdf:resource="#Hertz">
-->
    <phml:describesPhysicalSize rdf:resouce="&phml;Radioactivity"/>
    <phml:describesPhysicalSize rdf:resouce="&phml;Activity"/>
  </phml:SI-DerivedUnit>
  <phml:SI-DerivedUnit rdf:about="&phml;Coulomb"
                                  rdfs:label="C"/>
  <phml:SI-DerivedUnit rdf:about="&phml;Farad"
                                  rdfs:label="F"/>
  <phml:SI-DerivedUnit rdf:about="&phml;Henry"
                                  rdfs:label="H"/>
  <phml:SI-DerivedUnit rdf:about="&phml;Gray"
                                  rdfs:label="Gy"/>
  <phml:SI-DerivedUnit rdf:about="&phml;Katal"
                                  rdfs:label="kat"/>
  <phml:SI-DerivedUnit rdf:about="&phml;Tesla"
                                  rdfs:label="T"/>
  <phml:SI-DerivedUnit rdf:about="&phml;Sievert"
                                  rdfs:label="Sv"/>
  <phml:SI-DerivedUnit rdf:about="&phml;Lumen"
                                  rdfs:label="lm"/>
  <phml:SI-DerivedUnit rdf:about="&phml;Lux"
                                  rdfs:label="lx"/>
  <phml:SI-DerivedUnit rdf:about="&phml;Gram"
                               rdfs:label="g"/>

Degree Celsius is very tricky and gives a good impression how Semantic MathML might work:

  <phml:SI-DerivedUnit rdf:about="&phml;DegreeCelsius"
                                  rdfs:label="°C">
    <rdfs:type rdf:resource="&smml;PostfixOperator"/>
    <smml:define>
       <smml:Parameters>
          <smml:Parameter rdfs:type="#hasParameter" rdf:ID="&phml;DegreeCelsius_Value"/>
       <smml:Parameters>
       <smml:to>
          <smml:Add>
             <phml:DegreeCelsius_Value />
             <hasParameter rdfs:type="&xsd;float">-275.15</hasParameter>
          </smml:Add>
       </smml:to>
    </smml:define>
    <phml:describesPhysicalSize rdf:resouce="&phml;Celsius-Temperature"/>
    <phml:describesPhysicalSize rdf:resouce="&phml;Temperature"/>
  <phml:SI-DerivedUnit>

[edit] Prefixes

  <owl:Class rdf:about="&phml;Prefix">
    <rdfs:subClassOf rdf:resource="#MathematicalConstant"/>
  </owl:Class>

[edit] Named Prefixes

  <owl:Class rdf:about="&phml;NamedPrefix">
    <rdfs:subClassOf rdf:resource="&phml;Prefix"/>
  </owl:Class>
  <smml:NamedPrefix rdf:about="#Ten"/>
  <smml:NamedPrefix rdf:about="#Twenty"/>
  <smml:NamedPrefix rdf:about="#Thirty"/>
  <smml:NamedPrefix rdf:about="#Fourty"/>
  <smml:NamedPrefix rdf:about="#Fivty"/>
  <smml:NamedPrefix rdf:about="#Sixty"/>
  <smml:NamedPrefix rdf:about="#Seventy"/>
  <smml:NamedPrefix rdf:about="#Eighty"/>
  <smml:NamedPrefix rdf:about="#Ninety"/>
<!-- specially names ones -->
  <smml:NamedPrefix rdf:about="#Eleven"/>
  <smml:NamedPrefix rdf:about="#Twelve"/>
  <smml:NamedPrefix rdf:about="#Thirteen"/>
  <smml:NamedPrefix rdf:about="#Fourteen"/>
  <smml:NamedPrefix rdf:about="#Fifteen"/>
  <smml:NamedPrefix rdf:about="#Sixteen"/>
  <smml:NamedPrefix rdf:about="#Seventeen"/>
  <smml:NamedPrefix rdf:about="#Eighteen"/>
  <smml:NamedPrefix rdf:about="#Nineteen"/>
  <smml:NamedPrefix rdf:about="#millionth"
                    rdfs:comment="10^-6"/>
  <smml:NamedPrefix rdf:about="#thousandth"
                    rdfs:comment="10^-3
  <smml:NamedPrefix rdf:about="#hundredth"
                    rdfs:comment="10^-2"/>
  <smml:NamedPrefix rdf:about="#tenth"
                    rdfs:comment="10^-1"/>
  <smml:NamedPrefix rdf:about="#Hundred"
                    rdfs:comment="10^2"/>
  <smml:NamedPrefix rdf:about="#Thousand"
                    rdfs:comment="10^3"/>
  <smml:NamedPrefix rdf:about="#Million"
                    rdfs:comment="10^6"/>
  <smml:NamedPrefix rdf:about="#billion"
                    rdfs:comment="10^9"/>
  <smml:NamedPrefix rdf:about="#Milliard"
                    rdfs:comment="10^9"/>
  <smml:NamedPrefix rdf:about="#Trillion"
                    rdfs:comment="10^12"/>
  <smml:NamedPrefix rdf:about="#Billion"
                    rdfs:comment="10^12"/>
  <smml:NamedPrefix rdf:about="#Quadrillion"
                    rdfs:comment="10^15"/>
  <smml:NamedPrefix rdf:about="#Billiard"
                    rdfs:comment="10^15"/>
  <smml:NamedPrefix rdf:about="#Quintillion"
                    rdfs:comment="10^18"/>
  <smml:NamedPrefix rdf:about="#Trillion"
                    rdfs:comment="10^18"/>
  <smml:NamedPrefix rdf:about="#Sextillion"
                    rdfs:comment="10^21"/>
  <smml:NamedPrefix rdf:about="#Septillion"
                    rdfs:comment="10^24"/>
  <smml:NamedPrefix rdf:about="#Quadrillion"
                    rdfs:comment="10^24"/>
  <smml:NamedPrefix rdf:about="#Octillion"
                    rdfs:comment="10^27"/>
  <smml:NamedPrefix rdf:about="#Nonillion"
                    rdfs:comment="10^30"/>
  <smml:NamedPrefix rdf:about="#quintillion"
                    rdfs:comment="10^30"/>
  <smml:NamedPrefix rdf:about="#Decillion"
                    rdfs:comment="10^33"/>
  <smml:NamedPrefix rdf:about="#Undecillion"
                    rdfs:comment="10^36"/>
  <smml:NamedPrefix rdf:about="#Sextillion"
                    rdfs:comment="10^36"/>
  <smml:NamedPrefix rdf:about="#googol"
                    rdfs:comment="10^100"/>
  <smml:NamedPrefix rdf:about="#Asankhyeya"
                    rdfs:comment="10^140"/>
  <smml:NamedPrefix rdf:about="#Googolplex"
                    rdfs:comment="10^10^100"/>

[edit] SI-Prefixes

  <owl:Class rdf:about="&phml;SI-Prefix">
    <rdfs:subClassOf rdf:resource="&phml;Prefix"/>
  </owl:Class>
  <phml:SI-Prefix rdf:about="&phml;Yotta"
                             rdfs:label="Y">
    <smml:equalTo rdfs:type="&xsd;float">10e24</smml:equalTo>
  </phml:SI-Prefix>
  <phml:SI-Prefix rdf:about="&phml;Zetta"
                             rdfs:label="Z">
    <smml:equalTo rdfs:type="&xsd;float">10e21</smml:equalTo>
  </phml:SI-Prefix>
  <phml:SI-Prefix rdf:about="&phml;Exa"
                             rdfs:label="E">
    <smml:equalTo rdfs:type="&xsd;float">10e18</smml:equalTo>
  </phml:SI-Prefix>
  <phml:SI-Prefix rdf:about="&phml;Peta"
                             rdfs:label="P">
    <smml:equalTo rdfs:type="&xsd;float">10e15</smml:equalTo>
  </phml:SI-Prefix>
  <phml:SI-Prefix rdf:about="&phml;Tera"
                             rdfs:label="T">
    <smml:equalTo rdfs:type="&xsd;float">10e12</smml:equalTo>
  </phml:SI-Prefix>
  <phml:SI-Prefix rdf:about="&phml;Giga"
                             rdfs:label="G">
    <smml:equalTo rdfs:type="&xsd;float">10e9</smml:equalTo>
  </phml:SI-Prefix>
  <phml:SI-Prefix rdf:about="&phml;Mega"
                             rdfs:label="M">
    <smml:equalTo rdfs:type="&xsd;float">10e6</smml:equalTo>
  </phml:SI-Prefix>
  <phml:SI-Prefix rdf:about="&phml;Kilo"
                             rdfs:label="k">
    <smml:equalTo rdfs:type="&xsd;float">10e3</smml:equalTo>
  </phml:SI-Prefix>
  <phml:SI-Prefix rdf:about="&phml;Hekto"
                             rdfs:label="h">
    <smml:equalTo rdfs:type="&xsd;float">10e2</smml:equalTo>
  </phml:SI-Prefix>
  <phml:SI-Prefix rdf:about="&phml;Deka"
                             rdfs:label="da">
    <smml:equalTo rdfs:type="&xsd;float">10e1</smml:equalTo>
  </phml:SI-Prefix>
  <phml:SI-Prefix rdf:about="&phml;Dezi"
                             rdfs:label="d">
    <smml:equalTo rdfs:type="&xsd;float">10e-1</smml:equalTo>
  </phml:SI-Prefix>
  <phml:SI-Prefix rdf:about="&phml;Zenti"
                             rdfs:label="c">
    <smml:equalTo rdfs:type="&xsd;float">10e-2</smml:equalTo>
  </phml:SI-Prefix>
  <phml:SI-Prefix rdf:about="&phml;Milli"
                             rdfs:label="m">
    <smml:equalTo rdfs:type="&xsd;float">10e-3</smml:equalTo>
  </phml:SI-Prefix>
  <phml:SI-Prefix rdf:about="&phml;Mikro"
                             rdfs:label="µ">
    <smml:equalTo rdfs:type="&xsd;float">10e-6</smml:equalTo>
  </phml:SI-Prefix>
  <phml:SI-Prefix rdf:about="&phml;Nano"
                             rdfs:label="n">
    <smml:equalTo rdfs:type="&xsd;float">10e-9</smml:equalTo>
  </phml:SI-Prefix>
  <phml:SI-Prefix rdf:about="&phml;Pico"
                             rdfs:label="p">
    <smml:equalTo rdfs:type="&xsd;float">10e-12</smml:equalTo>
  </phml:SI-Prefix>
  <phml:SI-Prefix rdf:about="&phml;Femto"
                             rdfs:label="f">
    <smml:equalTo rdfs:type="&xsd;float">10e-15</smml:equalTo>
  </phml:SI-Prefix>
  <phml:SI-Prefix rdf:about="&phml;Atto"
                             rdfs:label="a">
    <smml:equalTo rdfs:type="&xsd;float">10e-18</smml:equalTo>
  </phml:SI-Prefix>
  <phml:SI-Prefix rdf:about="&phml;Zepto"
                             rdfs:label="z">
    <smml:equalTo rdfs:type="&xsd;float">10e-21</smml:equalTo>
  </phml:SI-Prefix>
  <phml:SI-Prefix rdf:about="&phml;Yocto"
                             rdfs:label="y">
    <smml:equalTo rdfs:type="&xsd;float">10e-24</smml:equalTo>
  </phml:SI-Prefix>

[edit] IEC-Prefixes

  <owl:Class rdf:about="&phml;IEC-Prefix">
    <rdfs:subClassOf rdf:resource="&phml;Prefix"/>
  </owl:Class>
  <phml:IEC-Prefix rdf:about="&phml;kibi"
                              rdfs:label="Ki">
    <smml:equalTo rdfs:type="&xsd;integer">1024</smml:equalTo>
  </phml:IEC-Prefix>
  <phml:IEC-Prefix rdf:about="&phml;mebi"
                              rdfs:label="Mi">
    <smml:equalTo rdfs:type="&xsd;integer">1048576</smml:equalTo>
  </phml:IEC-Prefix>
  <phml:IEC-Prefix rdf:about="&phml;gibi"
                              rdfs:label="Gi">
    <smml:equalTo rdfs:type="&xsd;integer">1073741824</smml:equalTo>
  </phml:IEC-Prefix>
  <phml:IEC-Prefix rdf:about="&phml;tebi"
                              rdfs:label="Ti">
    <smml:equalTo rdfs:type="&xsd;integer">1099511627776</smml:equalTo>
  </phml:IEC-Prefix>
  <phml:IEC-Prefix rdf:about="&phml;pebi"
                              rdfs:label="Pi">
    <smml:equalTo rdfs:type="&xsd;integer">1125899906842624</smml:equalTo>
  </phml:IEC-Prefix>
  <phml:IEC-Prefix rdf:about="&phml;exbi"
                              rdfs:label="Ei">
    <smml:equalTo rdfs:type="&xsd;integer">1152921504606846976</smml:equalTo>
  </phml:IEC-Prefix>
  <phml:IEC-Prefix rdf:about="&phml;zebi"
                              rdfs:label="Zi">
    <smml:equalTo rdfs:type="&xsd;integer">1180591620717411303424</smml:equalTo>
  </phml:IEC-Prefix>
  <phml:IEC-Prefix rdf:about="&phml;yobi"
                              rdfs:label="Yi">
    <smml:equalTo rdfs:type="&xsd;integer">1208925819614629174706176</smml:equalTo>
  </phml:IEC-Prefix>

[edit] Mathematical Relations

  <owl:ObjectProperty rdf:about="#isEqualTo">
    <rdfs:type rdfs:resouce="&owl;SymmetricProperty"/>
    <owl:sameAs rdf:resource="&owl;sameAs"/>
  </owl:ObjectProperty>
  <owl:ObjectProperty rdf:about="#isLessThan">
    <owl:inverseOf rdf:resource="isGreaterOrEqual"/>
  </owl:ObjectProperty>
  <owl:ObjectProperty rdf:about="#isGreaterOrEqual">
    <owl:unionOf rdf:resource="isGreaterThan"/>
    <owl:unionOf rdf:resource="isEqualTo"/>
  </owl:ObjectProperty>
  <owl:ObjectProperty rdf:about="#isGreaterThan">
    <owl:inverseOf rdf:resource="isLessOrEqual"/>
  </owl:ObjectProperty>
  <owl:ObjectProperty rdf:about="#isLessOrEqual">
    <owl:unionOf rdf:resource="isLessThan"/>
    <owl:unionOf rdf:resource="isEqualTo"/>
  </owl:ObjectProperty>
  <owl:ObjectProperty rdf:about="#isProportionalTo">
    <owl:inverseOf rdf:resource="isInverseProportionalTo"/>
  </owl:ObjectProperty>
  <owl:ObjectProperty rdf:about="#isNot">
    <owl:sameAs rdf:resource="&owl;disjointWith"/>
    <owl:inverseOf rdf:resource="isEqualTo"/>
  </owl:ObjectProperty>
  <owl:ObjectProperty rdf:about="#isNegationOf">>
    <rdfs:type rdf:resource="&owl;inverseOf"/>
  </owl:ObjectProperty>
  <owl:ObjectProperty rdf:about="#isPartOf">
    <owl:inverseOf rdf:resource="&owl;unionOf"/>
  </owl:ObjectProperty>
  <owl:ObjectProperty rdf:about="#isAbsoluteOf">
    <owl:inverseOf rdf:resource="#hasAbsoluteValue"/>
  </owl:ObjectProperty>
  <owl:ObjectProperty rdf:about="#isNormOf">
    <owl:inverseOf rdf:resource="#hasNorm"/>
  </owl:ObjectProperty>
  <owl:ObjectProperty rdf:about="#isFactorialOf">
    <owl:inverseOf rdf:resource="#hasFactorial"/>
  </owl:ObjectProperty>
  <owl:ObjectProperty rdf:about="#isImplicitOf">
    <owl:inverseOf rdf:resource="#implies"/>
  </owl:ObjectProperty>
  <owl:ObjectProperty rdf:about="#isEquivalentOf">
    <rdfs:type rdfs:resouce="&owl;SymmetricProperty"/>
  </owl:ObjectProperty>
  <owl:ObjectProperty rdf:about="#isDerivateOf">
    <owl:inverseOf rdf:resource="#hasDerivate"/>
  </owl:ObjectProperty>
  <owl:ObjectProperty rdf:about="#isDefinedBy">
    <owl:inverseOf rdf:resource="#defines"/>
  </owl:ObjectProperty>
  <owl:ObjectProperty rdf:about="#inferencesWith">
    <rdfs:type rdfs:resouce="&owl;SymmetricProperty"/>
  </owl:ObjectProperty>
  <owl:ObjectProperty rdf:about="#isPictureOf">
    <owl:inverseOf rdf:resource="#hasPicture"/>
  </owl:ObjectProperty>
  <owl:ObjectProperty rdf:about="#isPerpendicularTo">
    <rdfs:type rdfs:resouce="&owl;SymmetricProperty"/>
  </owl:ObjectProperty>
</rdf:RDF>
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