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<node TEXT="Chapter 2:&#xa;Terminology&#xa;and Preliminaries" POSITION="right" ID="ID_1183405778" CREATED="1644658684270" MODIFIED="1661408973780">
<node TEXT="ontology language &lt;dv:23&gt;" ID="ID_578171169" CREATED="1644658780231" MODIFIED="1644659433033">
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<node TEXT="An ontology language defines which language constructs (i.e. which types of&#xa;axioms) can be used in an ontology in that language. The ontology language also&#xa;defines the formal semantics of that language. A big number of ontology languages&#xa;have been suggested in the last twenty years, such as Ontolingua (Farquhar et al.,&#xa;1996), F-logic (Kifer et al., 1995), or plain first order logic. &lt;dv:23&gt;" ID="ID_1089355675" CREATED="1644658799929" MODIFIED="1644659664628"/>
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      semantic web ontology language
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<node TEXT="All these languages are standardized by the&#xa;World Wide Web Consortium (W3C), a public standards body overseeing standards&#xa;relevant to the development of the Web." ID="ID_602403769" CREATED="1644659232808" MODIFIED="1644659235270"/>
<node TEXT="According to the Semantic Web ontology languages, ontologies do not include only&#xa;terminological knowledge &#x2013; definitions of the terms used to describe data, and the&#xa;formal relations between these terms &#x2013; but may also include the knowledge bases&#xa;themselves, i.e. terms describing individuals and ground facts asserting the state of&#xa;affairs between these individuals. Even though such knowledge bases are often not&#xa;regarded as being ontologies (see (Obrst et al., 2007) for an example), for the re-&#xa;mainder of this thesis we follow the OWL standard and regard ontologies as artifacts&#xa;encompassing both the terminological as well as the assertional knowledge." ID="ID_592287529" CREATED="1644659271092" MODIFIED="1644659272489"/>
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<node TEXT="RDF" ID="ID_1688541582" CREATED="1644659143870" MODIFIED="1644659149228"/>
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<node TEXT="ontology &lt;dv:23&gt;" ID="ID_1211397989" CREATED="1644658707141" MODIFIED="1644659422440">
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<node TEXT="a (possibly named) set of axioms. Axioms are stated in an ontology language. If all axioms of an ontology are stated in the same ontology language,&#xa;then the ontology as a whole is in that ontology language. &lt;dv:23&gt;" ID="ID_1969021118" CREATED="1644658727320" MODIFIED="1644659624050"/>
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<node TEXT="BY is_written SOME ontology language" ID="ID_1458790005" CREATED="1644658851131" MODIFIED="1644659049565">
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<node TEXT="DEF" ID="ID_847896634" CREATED="1644658864439" MODIFIED="1644658883397">
<node TEXT="Web ontologies are *ontologies* that are written in one of the standardized *Semantic Web ontology languages*." ID="ID_1200393811" CREATED="1644658980667" MODIFIED="1644658983166"/>
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<node TEXT="SOME semantic web ontology language" ID="ID_1733698471" CREATED="1644658994936" MODIFIED="1644659018220"/>
<node TEXT="BY SOME representation &lt;dv:24&gt;" ID="ID_83263003" CREATED="1644660251627" MODIFIED="1644660269254">
<node TEXT="" ID="ID_591900589" CREATED="1644660280859" MODIFIED="1644660280859">
<node TEXT="SOME RDF graph" ID="ID_1914831811" CREATED="1644660281778" MODIFIED="1644660287177"/>
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<node TEXT="ontology document" ID="ID_725335247" CREATED="1644659281797" MODIFIED="1644659286244">
<node TEXT="DEF" ID="ID_351420233" CREATED="1644659882378" MODIFIED="1644659883815">
<node TEXT="a particular serialization of an ontology" ID="ID_121366004" CREATED="1644659977645" MODIFIED="1644659983181"/>
<node TEXT="As such, it&#xa;is an information resource, usually a file, and thus an artifact that can be processed by&#xa;a machine." ID="ID_621735785" CREATED="1644660001839" MODIFIED="1644660003178"/>
<node TEXT="An infinite number&#xa;of different ontology documents can describe the same ontology." ID="ID_1981366460" CREATED="1644660128769" MODIFIED="1644660129682"/>
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<node TEXT="BY SOME serialization &lt;dv:24&gt;" ID="ID_749708956" CREATED="1644660012456" MODIFIED="1644660205100">
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<node TEXT="" ID="ID_1918115891" CREATED="1644660065743" MODIFIED="1644660065743">
<node TEXT="SOME OWL XML presentation syntax" ID="ID_385210202" CREATED="1644660035336" MODIFIED="1644660045777"/>
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<node TEXT="" ID="ID_725802425" CREATED="1644660056726" MODIFIED="1644660056726">
<node TEXT="SOME OWL Functional Syntax" ID="ID_1565487546" CREATED="1644660051758" MODIFIED="1644660147551"/>
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<node TEXT="" ID="ID_325529758" CREATED="1644660096985" MODIFIED="1644660096985">
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<node TEXT="axiom" ID="ID_1073626064" CREATED="1644660755038" MODIFIED="1644660757934">
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<node TEXT="An axiom is the smallest unit of knowledge within an ontology. It can be either a terminological axiom, a fact, or an annotation. Terminological axioms are either class axioms or property axioms. &lt;dv:25&gt;" ID="ID_495396782" CREATED="1644758959989" MODIFIED="1661409256670"/>
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<node TEXT="fact &lt;dv:25&gt;" ID="ID_371775989" CREATED="1644660900083" MODIFIED="1644660960966">
<node TEXT="SYN" ID="ID_59269298" CREATED="1644660963798" MODIFIED="1644660965262">
<node TEXT="individual axiom" ID="ID_1689160887" CREATED="1644660970615" MODIFIED="1644660971747"/>
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<node TEXT="BY SOME form" ID="ID_1232391804" CREATED="1644661010754" MODIFIED="1644661059497">
<node TEXT="instantiation" ID="ID_1393257862" CREATED="1644661013230" MODIFIED="1644661013230">
<node TEXT="SYN" ID="ID_2352486" CREATED="1644661025196" MODIFIED="1644661026682">
<node TEXT="class instantiation" ID="ID_109642815" CREATED="1644661036190" MODIFIED="1644661037565"/>
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<node TEXT="SOME ClassAssertion" ID="ID_180717966" CREATED="1644661064237" MODIFIED="1644663471801"/>
<node TEXT="DEF" ID="ID_1852634385" CREATED="1644661105253" MODIFIED="1644661106481">
<node TEXT="has the form&#xa;`ClassAssertion(C a)`&#xa;with C being a class expression and a being an individual name. &lt;dv:25&gt;" ID="ID_1942111493" CREATED="1644661122538" MODIFIED="1644661407993"/>
<node TEXT="This is the&#xa;same as stating that a has the type C. Semantically that means that the individual&#xa;that has the name a is in the extension of the set described by C. &lt;dv:25&gt;" ID="ID_65871108" CREATED="1644661158902" MODIFIED="1644661411225"/>
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<node TEXT="relation" ID="ID_448286040" CREATED="1644661013230" MODIFIED="1644661013230">
<node TEXT="SYN" ID="ID_667271882" CREATED="1644661327754" MODIFIED="1644661329674">
<node TEXT="object property instance" ID="ID_1064394474" CREATED="1644661337377" MODIFIED="1644661338658"/>
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<node TEXT="SOME PropertyAssertion(R a b)" ID="ID_868100891" CREATED="1644661347163" MODIFIED="1644661365411"/>
<node TEXT="DEF" ID="ID_851389729" CREATED="1644661368791" MODIFIED="1644661369718">
<node TEXT="has the form&#xa;PropertyAssertion(R a b)&#xa;with a and b being individual names and R being an object property expression. &lt;dv:25&gt;" ID="ID_884581111" CREATED="1644661387924" MODIFIED="1644663456218"/>
<node TEXT="Informally it means that the property R pointing from a to b holds &#x2013; e.g. saying&#xa;that Germany has the capital Berlin. In the example, Germany and Berlin are indi-&#xa;vidual names, and capital is the name of the property that holds between them. The&#xa;actual instantiation of this property is thus called the relation. Semantically it means&#xa;that the tuple (a, b) is in the extension of the set R. &lt;dv:25&gt;" ID="ID_760262355" CREATED="1644661414807" MODIFIED="1644661437339"/>
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<node TEXT="negative relation" ID="ID_688605881" CREATED="1644661576944" MODIFIED="1644661584307">
<node TEXT="SOME NegativePropertyAssertion(R a b)" ID="ID_719842474" CREATED="1644661611816" MODIFIED="1644661623870"/>
<node TEXT="DEF" ID="ID_11847130" CREATED="1644661624176" MODIFIED="1644661625481">
<node TEXT="This means that the tuple (a, b) is not in the extension of the set R. Semantically,&#xa;this was already possible to be indirectly stated in OWL DL by using the following&#xa;statement:&#xa;SubClassOf(OneOf(a) AllValuesFrom(R ComplementOf(OneOf(b))))&#xa;It is easy to see that the new syntax is far easier to understand" ID="ID_1979308488" CREATED="1644661639439" MODIFIED="1644661641049"/>
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<node TEXT="attribute" ID="ID_361494263" CREATED="1644661013231" MODIFIED="1644661013231">
<node TEXT="SYN" ID="ID_1198418689" CREATED="1644661656071" MODIFIED="1644661658487">
<node TEXT="datatype property instance" ID="ID_1006299374" CREATED="1644661669094" MODIFIED="1644661670272"/>
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<node TEXT="SOME PropertyAssertion(R a v)" ID="ID_1741188439" CREATED="1644661671626" MODIFIED="1644661681857"/>
<node TEXT="DEF" ID="ID_108017910" CREATED="1644661699685" MODIFIED="1644661702072">
<node TEXT="uses almost the same form as a relation:&#xa;PropertyAssertion(R a v)&#xa;with a being an individual name, R being a datatype property expression and v being a literal. &lt;dv:26&gt;" ID="ID_445115694" CREATED="1644661702411" MODIFIED="1661408938948"/>
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<node TEXT="negative attribute" ID="ID_99156138" CREATED="1644663282107" MODIFIED="1644663286456">
<node TEXT="SOME NegativePropertyAssertion(R a v)" ID="ID_1780000116" CREATED="1644661995562" MODIFIED="1644663422037"/>
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<node TEXT="Individual equality" ID="ID_748209934" CREATED="1644662024433" MODIFIED="1644662025400">
<node TEXT="SOME SameIndividual" ID="ID_1220245582" CREATED="1644662027515" MODIFIED="1644663222164"/>
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<node TEXT="individual inequality" ID="ID_359123306" CREATED="1644662061401" MODIFIED="1644662092376">
<node TEXT="SOME DifferentIndividuals" ID="ID_322778196" CREATED="1644662064171" MODIFIED="1644663218326"/>
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<node TEXT="terminological axiom &lt;dv:26&gt;" ID="ID_1608620516" CREATED="1644660900083" MODIFIED="1644662126164">
<node TEXT="ISA" ID="ID_1534969953" CREATED="1644660914298" MODIFIED="1644660915677">
<node TEXT="class axiom" ID="ID_1277131204" CREATED="1644660916457" MODIFIED="1644660916457">
<node TEXT="BY SOME form" ID="ID_553779861" CREATED="1644662155405" MODIFIED="1644662208106">
<node TEXT="subsumption" ID="ID_1332551177" CREATED="1644662197399" MODIFIED="1644662197399">
<node TEXT="SOME SubClassOf" ID="ID_1894352003" CREATED="1644662211435" MODIFIED="1644663193587"/>
<node TEXT="DEF" ID="ID_1316198216" CREATED="1644662223834" MODIFIED="1644662225134">
<node TEXT="A subsumption has the following form:&#xa;SubClassOf(C D)&#xa;with C (the subclass) and D (the superclass) being class expressions. &lt;dv:26&gt;" ID="ID_1467644939" CREATED="1644662253408" MODIFIED="1644662262891"/>
<node TEXT="This axiom&#xa;states that every individual in the extension of C also has to be in the extension of&#xa;D. This means that individuals in C are described as being individuals in D. For&#xa;example,&#xa;SubClassOf(Square P olygon)&#xa;describes squares as polygons." ID="ID_385917904" CREATED="1644662269342" MODIFIED="1644662286200"/>
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<node TEXT="ISA" ID="ID_438219228" CREATED="1644662294193" MODIFIED="1644662675190">
<node TEXT="simple subsumption" ID="ID_610704099" CREATED="1644662321661" MODIFIED="1644662321661">
<node TEXT="DEF" ID="ID_1084104399" CREATED="1644662346697" MODIFIED="1644662347924">
<node TEXT="In a simple subsumption both the subclass and the superclass are class names&#xa;instead of more complex class expressions. Simple subsumptions form the backbone&#xa;of class hierarchies." ID="ID_562352787" CREATED="1644662348326" MODIFIED="1644662349299"/>
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<node TEXT="complex subsumption" ID="ID_659971201" CREATED="1644662321661" MODIFIED="1644662321661">
<node TEXT="DEF" ID="ID_659235682" CREATED="1644662361629" MODIFIED="1644662362884">
<node TEXT="In a complex subsumption both the subclass and the superclass are complex&#xa;class expressions. A complex subsumption thus sets an intricate restriction on the&#xa;possible models of the ontology. Such restrictions may be rather hard to understand&#xa;by users of the ontology." ID="ID_2169683" CREATED="1644662363188" MODIFIED="1644662364795"/>
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<node TEXT="description" ID="ID_1286234408" CREATED="1644662321662" MODIFIED="1644662321662">
<node TEXT="DEF" ID="ID_847212561" CREATED="1644662410993" MODIFIED="1644662413952">
<node TEXT="In a description, either the subclass is a class name and the superclass a complex&#xa;class expression, or the other way around. This describes the named class, i.e. the&#xa;complex class expression is a condition of the named class." ID="ID_1797754279" CREATED="1644662414235" MODIFIED="1644662415436"/>
<node TEXT="Descriptions&#xa;are among the most interesting axioms in an ontology, and they are the namesake of&#xa;description logics. &lt;dv: 27&gt;" ID="ID_152164225" CREATED="1644662562127" MODIFIED="1644662588402"/>
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<node TEXT="ISA" ID="ID_1546079052" CREATED="1644662436074" MODIFIED="1644662686090">
<node TEXT="named class is subclass" ID="ID_391452683" CREATED="1644662504323" MODIFIED="1644662505830">
<node TEXT="DEF" ID="ID_938686327" CREATED="1644662519073" MODIFIED="1644662520392">
<node TEXT="If the named class is&#xa;the subclass, then the complex class expression offers a necessary condition of the&#xa;named class, i.e. each individual in the named class must also fit to the complex class&#xa;expression. &lt;dv: 27&gt;" ID="ID_744059911" CREATED="1644662521109" MODIFIED="1644662592091"/>
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<node TEXT="named class is superclass" ID="ID_476584626" CREATED="1644662534894" MODIFIED="1644662543684">
<node TEXT="DEF" ID="ID_763699398" CREATED="1644662545352" MODIFIED="1644662546446">
<node TEXT="If the named class is the superclass, then the complex class expression&#xa;offers a sufficient condition of the named class, i.e. each individual fitting to the&#xa;complex class expression will also be an individual of the named class. &lt;dv: 27&gt;" ID="ID_314955292" CREATED="1644662557825" MODIFIED="1644662594675"/>
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<node TEXT="class equivalence" ID="ID_243322140" CREATED="1644662197399" MODIFIED="1644662197399">
<node TEXT="ISA" ID="ID_1369627853" CREATED="1644662752720" MODIFIED="1644662759259">
<node TEXT="simple class equivalence" ID="ID_1650192865" CREATED="1644662765556" MODIFIED="1644662766985">
<node TEXT="DEF" ID="ID_1789520092" CREATED="1644662786544" MODIFIED="1644662787723">
<node TEXT="In a simple class equivalence, both class expressions of the class equivalence axiom are class names. This is similar to a synonym, since it states that two names mean the same class, i.e. that they have the same extension. &lt;dv:27&gt;" ID="ID_1614091425" CREATED="1644662796619" MODIFIED="1644662870136"/>
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<node TEXT="complex class equivalence" ID="ID_693023899" CREATED="1644662772032" MODIFIED="1644662773285">
<node TEXT="DEF" ID="ID_1226484294" CREATED="1644662803115" MODIFIED="1644662804189">
<node TEXT="In a complex class equivalence both classes are complex class expressions,&#xa;and thus the axiom defines an intricate condition on the possible models. Just like&#xa;complex subsumptions such axioms and their implications may be hard to under-&#xa;stand. &lt;dv:27&gt;" ID="ID_966039231" CREATED="1644662890642" MODIFIED="1644662895310"/>
</node>
<node TEXT="ISA" ID="ID_1380898422" CREATED="1644662906423" MODIFIED="1644662908055">
<node TEXT="definition" ID="ID_1284391590" CREATED="1644662916933" MODIFIED="1644662918493">
<node TEXT="DEF" ID="ID_1378798726" CREATED="1644662918889" MODIFIED="1644662920052">
<node TEXT="If any of the two classes in a class equivalence is a class name and the other a&#xa;complex class expression, then the axiom is a definition of the class name." ID="ID_1335747835" CREATED="1644662928450" MODIFIED="1644662929668"/>
<node TEXT="A&#xa;definition is the strongest statement about a class name, offering both a sufficient and&#xa;necessary condition by means of the complex class description. Thus, a definition&#xa;offers the complete meaning of a name by building on the meaning of the names used&#xa;in the defining class expression" ID="ID_1475807156" CREATED="1644662947985" MODIFIED="1644662949202"/>
<node TEXT="As an example, a mother can be completely described&#xa;by the following axiom:&#xa;EquivalentClasses(Mother IntersectionOf(Woman&#xa;SomeValuesFrom(child Thing)))&#xa;defining a Mother as a Woman with a child." ID="ID_1031162693" CREATED="1644662967975" MODIFIED="1644662973648"/>
</node>
</node>
</node>
</node>
</node>
<node TEXT="SOME EquivalentClasses" ID="ID_1665928090" CREATED="1644663148814" MODIFIED="1644663151994"/>
</node>
<node TEXT="disjoint" ID="ID_653301460" CREATED="1644662197400" MODIFIED="1644662197400">
<node TEXT="DEF" ID="ID_904224101" CREATED="1644662994360" MODIFIED="1644662995633">
<node TEXT="A disjoint is an axiom of the form (for i &#x2265; 2):&#xa;DisjointClasses(C 1 C 2 ... C i )&#xa;with C n , 1 &#x2264; n &#x2264; i, being class expressions. The axiom states that two classes&#xa;have no common individuals." ID="ID_1473180917" CREATED="1644663023008" MODIFIED="1644663024611"/>
</node>
<node TEXT="SOME DisjointClasses" ID="ID_1432256835" CREATED="1644663116361" MODIFIED="1644663119485"/>
</node>
<node TEXT="disjoint union" ID="ID_1808460400" CREATED="1644662197400" MODIFIED="1644662197400">
<node TEXT="SYN" ID="ID_687593002" CREATED="1644663053691" MODIFIED="1644663055431">
<node TEXT="complete partition" ID="ID_1320168818" CREATED="1644663061434" MODIFIED="1644663062444"/>
<node TEXT="covering axiom" ID="ID_1048786110" CREATED="1644663068256" MODIFIED="1644663069240"/>
</node>
<node TEXT="DEF" ID="ID_1048551316" CREATED="1644663049717" MODIFIED="1644663051307">
<node TEXT="A disjoint union has the form (for i &#x2265; 2):&#xa;DisjointUnion(C D 1 D 2 ... D i )&#xa;stating that the class C is a union of all classes D n , 1 &#x2264; n &#x2264; i, and at the same time&#xa;the classes D n , 1 &#x2264; n &#x2264; i are all mutually disjoint. A disjoint union is also called a&#xa;complete partition or a covering axiom." ID="ID_1425142357" CREATED="1644663051728" MODIFIED="1644663052839"/>
</node>
<node TEXT="SOME DisjointUnion" ID="ID_1295647124" CREATED="1644663082441" MODIFIED="1644663102428"/>
</node>
</node>
</node>
<node TEXT="property axiom" ID="ID_1412487387" CREATED="1644660916457" MODIFIED="1644660916457">
<node TEXT="DEF" ID="ID_163900802" CREATED="1644663649064" MODIFIED="1644663650409">
<node TEXT="A property axiom describes formal semantics of properties." ID="ID_1080831895" CREATED="1644663690848" MODIFIED="1644663692281"/>
<node TEXT="the only property expressions are inverse property&#xa;and property chains." ID="ID_805159833" CREATED="1644663705068" MODIFIED="1644663711342"/>
</node>
</node>
</node>
</node>
<node TEXT="annotation &lt;dv:29&gt;" ID="ID_1260304559" CREATED="1644660900084" MODIFIED="1644758693674">
<node TEXT="DEF" ID="ID_821139224" CREATED="1644663888949" MODIFIED="1644663890285">
<node TEXT="An annotation connects an element by an annotation property with an annotation value. Elements can be either entities, ontologies, or axioms. An&#xa;annotation has no impact on the DL semantics, but adds further information about&#xa;the elements. &lt;dv:29&gt;" ID="ID_41839552" CREATED="1644663890521" MODIFIED="1644758716157"/>
<node TEXT="The most widely deployed annotation is rdf:label. It connects an element with a&#xa;human-readable label. &lt;dv:29&gt;" ID="ID_1243423718" CREATED="1644663907216" MODIFIED="1644758718898"/>
</node>
</node>
</node>
</node>
<node TEXT="ontology element &lt;dv:29&gt;" ID="ID_512633355" CREATED="1644759025557" MODIFIED="1644761019778">
<node TEXT="DEF" ID="ID_1694475259" CREATED="1644759108425" MODIFIED="1644759110092">
<node TEXT="Ontology elements are both axioms and ontology entities. &lt;dv:25&gt;" ID="ID_6209943" CREATED="1644761022319" MODIFIED="1644761037128"/>
</node>
<node TEXT="SUP &lt;dv:25&gt;" ID="ID_11374584" CREATED="1644761129273" MODIFIED="1644761260096">
<node TEXT="axiom" ID="ID_1753281469" CREATED="1644761168181" MODIFIED="1644761193617"/>
<node TEXT="ontology entity" ID="ID_1327419519" CREATED="1644761194225" MODIFIED="1644761201346"/>
</node>
</node>
<node TEXT="ontology entity &lt;dv:29&gt;" ID="ID_1704999669" CREATED="1644759167665" MODIFIED="1644759196502">
<node TEXT="ISA" ID="ID_1062402577" CREATED="1644759204014" MODIFIED="1644759205793">
<node TEXT="individual" ID="ID_1079474693" CREATED="1644759206247" MODIFIED="1644759210131">
<node TEXT="DEF" ID="ID_1613488345" CREATED="1644759280067" MODIFIED="1644759281944">
<node TEXT="Individuals can be given by their name or as an anonymous individual. An&#xa;individual can be any entity with an identity (otherwise it would not be possible to&#xa;identify that entity with an identifier)." ID="ID_1776410630" CREATED="1644759328904" MODIFIED="1644759331581"/>
</node>
<node TEXT="ISA" ID="ID_1667081903" CREATED="1644759334425" MODIFIED="1644759336731">
<node TEXT="anonymous individual" ID="ID_1757736459" CREATED="1644759348168" MODIFIED="1644759349380">
<node TEXT="DEF" ID="ID_1326364826" CREATED="1644759349622" MODIFIED="1644759351196">
<node TEXT="An anonymous individual does not have a URI but provides only a local name&#xa;instead. This means that the individual can not be identified directly from outside of&#xa;the given ontology, but only through indirect means like inverse functional prop-&#xa;erties, keys, or nominals." ID="ID_1336415246" CREATED="1644759373371" MODIFIED="1644759374719"/>
</node>
</node>
</node>
</node>
<node TEXT="class" ID="ID_292321374" CREATED="1644759211574" MODIFIED="1644759212798">
<node TEXT="DEF" ID="ID_1255253114" CREATED="1644759380218" MODIFIED="1644759381431">
<node TEXT="A class is a set of individuals. &lt;dv: 30&gt;" ID="ID_1068162249" CREATED="1644759390036" MODIFIED="1644759398298"/>
<node TEXT="A class is given by a class expression." ID="ID_867244875" CREATED="1644759410889" MODIFIED="1644759412504"/>
</node>
<node TEXT="REL is given by" ID="ID_871217461" CREATED="1644759430774" MODIFIED="1644759928750">
<node TEXT="class expression &lt;dv:30&gt;" ID="ID_1410331113" CREATED="1644759433584" MODIFIED="1644759459301">
<node TEXT="ISA" ID="ID_1216993937" CREATED="1644759464171" MODIFIED="1644759465456">
<node TEXT="class name" ID="ID_447699763" CREATED="1644759472718" MODIFIED="1644759473900">
<node TEXT="DEF" ID="ID_248498465" CREATED="1644759522043" MODIFIED="1644759523051">
<node TEXT="A class name is simply the name, i.e. a URI, of a class." ID="ID_659231775" CREATED="1644759533204" MODIFIED="1644759536359"/>
<node TEXT="Class names do not carry any&#xa;further formal information about the class." ID="ID_712408004" CREATED="1644759543865" MODIFIED="1644759544995"/>
</node>
</node>
<node TEXT="complex class description" ID="ID_562284205" CREATED="1644759478919" MODIFIED="1644759479838">
<node TEXT="DEF" ID="ID_933146275" CREATED="1644759548288" MODIFIED="1644759549438">
<node TEXT="A complex class expression defines a class with the help of other entities of the ontology. In order to create these expressions, a number of constructs can be used." ID="ID_1941492487" CREATED="1644759557454" MODIFIED="1644759587112"/>
<node TEXT="The constructs are set operations or restrictions." ID="ID_1148110742" CREATED="1644759605204" MODIFIED="1644759607309"/>
</node>
<node TEXT="ISA" ID="ID_790777693" CREATED="1644759641078" MODIFIED="1644759641802">
<node TEXT="set operation" ID="ID_1264514526" CREATED="1644759646619" MODIFIED="1644759650953">
<node TEXT="ISA" ID="ID_1805135470" CREATED="1644759666236" MODIFIED="1644759667271">
<node TEXT="intersection" ID="ID_825407280" CREATED="1644759693541" MODIFIED="1644759693541"/>
<node TEXT="union" ID="ID_37077139" CREATED="1644759693541" MODIFIED="1644759693541"/>
<node TEXT="complement" ID="ID_1615391505" CREATED="1644759693541" MODIFIED="1644759693541"/>
<node TEXT="nominal" ID="ID_1709006977" CREATED="1644759693542" MODIFIED="1644759693542">
<node TEXT="DEF" ID="ID_526678586" CREATED="1644759697298" MODIFIED="1644759698700">
<node TEXT="A nominal defines the extension of a class by listing all instances explicitly." ID="ID_889672004" CREATED="1644759716323" MODIFIED="1644759720930"/>
</node>
</node>
</node>
</node>
<node TEXT="restriction" ID="ID_1735179485" CREATED="1644759657070" MODIFIED="1644759659929">
<node TEXT="ISA" ID="ID_1628395543" CREATED="1644759744060" MODIFIED="1644759745068">
<node TEXT="existential restriction" ID="ID_565099727" CREATED="1644759838974" MODIFIED="1644759838974">
<node TEXT="DEF" ID="ID_616808095" CREATED="1644759838974" MODIFIED="1644759838974">
<node TEXT="a class of all instances where the property exists" ID="ID_1414650355" CREATED="1644759838974" MODIFIED="1644759838974"/>
</node>
</node>
<node TEXT="universal restriction" ID="ID_575731571" CREATED="1644759838974" MODIFIED="1644759838974">
<node TEXT="DEF" ID="ID_1382751461" CREATED="1644759838975" MODIFIED="1644759838975">
<node TEXT="on a property P and a class C, constructing a class where the instances have all their P property values be instances of C" ID="ID_502152501" CREATED="1644759838975" MODIFIED="1644759838975"/>
</node>
</node>
<node TEXT="unqualifed number restriction" ID="ID_288266218" CREATED="1644759838975" MODIFIED="1644759838975"/>
<node TEXT="qualified number restriction" ID="ID_1192593849" CREATED="1644759838975" MODIFIED="1644759838975"/>
<node TEXT="self-restriction" ID="ID_1224810225" CREATED="1644759838975" MODIFIED="1644759838975">
<node TEXT="DEF" ID="ID_1618060817" CREATED="1644759838975" MODIFIED="1644759838975">
<node TEXT="on a property P , stating that an instance has to be connected to itself via P" ID="ID_1521272222" CREATED="1644759838975" MODIFIED="1644759838975"/>
</node>
</node>
</node>
</node>
</node>
<node TEXT="REL uses" ID="ID_24318721" CREATED="1644759608241" MODIFIED="1645171085917">
<icon BUILTIN="button_cancel"/>
<node TEXT="construct" ID="ID_1388420422" CREATED="1644759614063" MODIFIED="1644759639984"/>
</node>
</node>
</node>
</node>
</node>
</node>
<node TEXT="property" ID="ID_280118452" CREATED="1644759214652" MODIFIED="1644759216991">
<node TEXT="DEF" ID="ID_1525150618" CREATED="1644760124905" MODIFIED="1644760126076">
<node TEXT="Properties are given by a property expression. Most often, a property expression is just a property name. The only complex property expressions are&#xa;inverse properties and property chains." ID="ID_1966822477" CREATED="1644760126332" MODIFIED="1644760130965"/>
</node>
<node TEXT="REL ist given by" ID="ID_1746917498" CREATED="1644760144922" MODIFIED="1644760149228">
<node TEXT="property expression &lt;dv:30&gt;" ID="ID_470861881" CREATED="1644760149626" MODIFIED="1644760175076">
<node TEXT="ISA" ID="ID_326112941" CREATED="1644760187758" MODIFIED="1644760188741">
<node TEXT="property name" ID="ID_1811697774" CREATED="1644760189321" MODIFIED="1644760194892"/>
<node TEXT="complex property expression" ID="ID_118773376" CREATED="1644760208448" MODIFIED="1644760209802">
<node TEXT="ISA" ID="ID_1944091294" CREATED="1644760214998" MODIFIED="1644760215927">
<node TEXT="inverse property" ID="ID_1203803442" CREATED="1644760222747" MODIFIED="1644760226933">
<node TEXT="DEF" ID="ID_650642609" CREATED="1644760239124" MODIFIED="1644760240074">
<node TEXT="An inverse property is the property expression that is used when the subject&#xa;and the object exchange their place in a property instantiation." ID="ID_1315897667" CREATED="1644760252916" MODIFIED="1644760254297"/>
<node TEXT="For an example, child&#xa;is the inverse property of parent. Instead of giving the inverse property the property&#xa;name parent, we could have used the property expression InverseOf(child)&#xa;instead." ID="ID_1805107564" CREATED="1644760270381" MODIFIED="1644760271521"/>
</node>
</node>
<node TEXT="property chain" ID="ID_1328140857" CREATED="1644760233600" MODIFIED="1644760234807">
<node TEXT="DEF" ID="ID_1544522014" CREATED="1644760235473" MODIFIED="1644760236787">
<node TEXT="A property chain is the property expression that connects several property expressions in a chain" ID="ID_1371890194" CREATED="1644760288675" MODIFIED="1644760291876"/>
<node TEXT="e.g. the property uncle can be described as a superproperty&#xa;of the chaining of the properties parent and brother by using the following axiom:&#xa;SubPropertyOf(PropertyChain(parent brother) uncle)" ID="ID_1778880933" CREATED="1644760319827" MODIFIED="1644760320921"/>
<node TEXT="Note that this is not a definition of uncle (since uncle may also be the chaining of the properties parent, sister, and husband). Since there are no boolean operators on properties (i.e. property unions, intersections, and complements) we cannot actually define uncle." ID="ID_482643327" CREATED="1644760354109" MODIFIED="1644760362707"/>
</node>
</node>
</node>
</node>
</node>
</node>
</node>
<node TEXT="ISA" ID="ID_1795387076" CREATED="1644760383480" MODIFIED="1644760387930">
<node TEXT="object property" ID="ID_585575246" CREATED="1644760394341" MODIFIED="1644760395895">
<node TEXT="DEF" ID="ID_319912107" CREATED="1644760410571" MODIFIED="1644760412015">
<node TEXT="Object properties connect two individuals with each other." ID="ID_1452303707" CREATED="1644760412301" MODIFIED="1644760415197"/>
</node>
</node>
<node TEXT="data property" ID="ID_1147652968" CREATED="1644760396505" MODIFIED="1644760402971">
<node TEXT="DEF" ID="ID_748222082" CREATED="1644760425509" MODIFIED="1644760426689">
<node TEXT="Data properties connect an&#xa;individual with a data value." ID="ID_1427630244" CREATED="1644760426977" MODIFIED="1644760427890"/>
</node>
<node TEXT="REL connects with" ID="ID_517525337" CREATED="1644760439967" MODIFIED="1644760450388">
<node TEXT="literal &lt;dv:31&gt;" ID="ID_1618919679" CREATED="1644760542976" MODIFIED="1644760599489">
<node TEXT="DEF" ID="ID_785361428" CREATED="1644760506945" MODIFIED="1644760508103">
<node TEXT="The mapping between the literal and the data&#xa;value is given by a datatype map. For example, the typed literal &quot;4&quot;^^xsd:int is&#xa;mapped to the number 4. &lt;dv:31&gt;" ID="ID_1327533607" CREATED="1644760509042" MODIFIED="1644760608030"/>
</node>
<node TEXT="REL represents" ID="ID_654280132" CREATED="1644760557037" MODIFIED="1644760564544">
<node TEXT="data value" ID="ID_398143867" CREATED="1644760450777" MODIFIED="1644760461031">
<node TEXT="DEF" ID="ID_524272267" CREATED="1644760461252" MODIFIED="1644760464820">
<node TEXT="A data value is not represented by a URI but rather by a literal, the syntactic&#xa;representation of a concrete value. &lt;dv:31&gt;" ID="ID_584714244" CREATED="1644760477819" MODIFIED="1644760622921"/>
</node>
</node>
</node>
</node>
</node>
</node>
</node>
</node>
<node TEXT="ontology" ID="ID_736179011" CREATED="1644759217376" MODIFIED="1644759219451">
<node TEXT="DEF" ID="ID_1205298523" CREATED="1644760710703" MODIFIED="1644760711972">
<node TEXT="An ontology can be either a named or an unnamed ontology. Ontologies&#xa;can also be regarded as ontology entities and can have axioms to describe them,&#xa;especially with annotation axioms (e.g. to state the authoring institution or version&#xa;information)." ID="ID_884568901" CREATED="1644760771812" MODIFIED="1644760773256"/>
</node>
</node>
</node>
</node>
</node>
</node>
</map>
