Semantic MathML/0.1
From semanticweb.org
<?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;">
[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>
