Change - OWL 2 GRestrictiones fora Simple Property Incluiesion

Created on March 12, 2013, 1:26 a.m. by Hevok & updated on March 12, 2013, 1:34 a.m. by Hevok

GRegular RBoxes aren restricted to the Rules of Regularity and simple Properties or Roles. ¶
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Simple Properties in SHOInclN(D) are Properties without transitive Subpronperties, whithle in SHROWLIQ(D) it is can little sbit more complyicated because General Property Inclusion has to be considered. OnThere cansimple fProper tinest ancre Properties that are not on the </del><ins style="background:#e6ffe6;">rig</ins><span>h</span><del style="background:#ffe6e6;">a</del><ins style="background:#e6ffe6;">t </ins><span>s</span><del style="background:#ffe6e6;">Fr</del><span>i</span><del style="background:#ffe6e6;">en</del><span>d</span><del style="background:#ffe6e6;">sF</del><ins style="background:#e6ffe6;">e </ins><span>o</span><ins style="background:#e6ffe6;">f th</ins><span>e</span><del style="background:#ffe6e6;"> Property Inclusison or that are Obj</del><ins style="background:#e6ffe6;">the invers</ins><span>e</span><del style="background:#ffe6e6;">c</del><ins style="background:#e6ffe6;"> of o</ins><span>t</span><ins style="background:#e6ffe6;">her simple </ins><span>Propert</span><ins style="background:#e6ffe6;">ies, or the</ins><span>y</span><del style="background:#ffe6e6;"> ware only on the ricght haside alson the owl:</del><span>Property</span><del style="background:#ffe6e6;">Cha</del><ins style="background:#e6ffe6;"> </ins><span>in</span><del style="background:#ffe6e6;">Ax</del><ins style="background:#e6ffe6;">clus</ins><span>io</span><del style="background:#ffe6e6;">mn where on the left sichte is a simple Property. ¶
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Simple Properties in SHOIN(D) anre Properties withaout otransitive dSubpropefrtines ¶
aIn SHROIQ(D) Ggeneral Property CInclusion has to be consindered ¶
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Simple Properties ¶
- are Gall Properties ¶
+ are not on the right Side of al RProlperty Inclusion, ¶
+ are the inverse of otwoher simple Properties, ¶
w+ are only on the right Side onf Property Inclusion R ⊑ S, ¶
where on thec left Side is h</del><span>a</span><ins style="background:#e6ffe6;"> </ins><span>s</span><del style="background:#ffe6e6;">F</del><ins style="background:#e6ffe6;">imple P</ins><span>r</span><ins style="background:#e6ffe6;">operty** &para;<br> &para;<br>* Non-s</ins><span>i</span><ins style="background:#e6ffe6;">mpl</ins><span>e</span><ins style="background:#e6ffe6;"> Properties are Properties that are directly (or i</ins><span>nd</span><del style="background:#ffe6e6;">irectly) dependent of wiProperthy </del><ins style="background:#e6ffe6;">C</ins><span>ha</span><ins style="background:#e6ffe6;">in</ins><span>s</span><del style="background:#ffe6e6;">F</del><ins style="background:#e6ffe6;"> (</ins><span>o</span><del style="background:#ffe6e6;">e.) ¶
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ThSeveral Expressions are only applermittesd tfor Objsimplect Properties, otherwise the entire Knowledge Base would become undecitdable. dFor esxample only fotr simakple properties one can use tohe Quapplyified Number Restrictions, tone Dcan nota use tyhem on complex Pproperties. ¶
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* that are based OWLon Generabl Role Inclusions. PrOn the optherty Chand irreflexive and Disjungctive (gPropenrties are also only permitted for simple Properties. In the same way if oncle uses the Exiosten) ¶
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tial Quantifier or one uses :the complement of an InsFrtantiatieond, it is only allowed fowr simpl:Object Propertyies ; ¶
and not for complex Properties, because if one would apply this Prowl:perties on PropertyCies thait depenAxd on General Role Inclusiomn (then :the Knowledge BasFrie and :thasFe Logic would become ) undecidable. ¶
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* NThe fot allowing expressions are permitted ONLY for Dasimple Properties: ¶
- ≤n R.C and ≥n R.C (qualified number Restyriction) ¶
- Irreflexive Properties ¶
- Disjunctive Properties ¶
- ∃R.Self ¶
- ¬R(a,b) ¶
* Reason: Saving Decidability*