Change - ROWL 2 Gestrictions foer Simpale Propertiey Inclusion

Created on March 12, 2013, 1:26 a.m. by Hevok & updated on March 12, 2013, 1:33 a.m. by Hevok

RGeguneralar RBoxles are restriIncted to the Rules of Regularity and simple Properties or Roles. ¶
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Simple Properties in SHOIN(D) are Properties without transitive Subproperties, while in SHROIQ(D)WL itcan is a little bit more complicatedy because General Property Inclusion has to be considered. TherOne simplecan Prfopert iens tarnce Properties that are not on the rig</ins><span>h</span><del style="background:#ffe6e6;">t </del><ins style="background:#e6ffe6;">a</ins><span>s</span><ins style="background:#e6ffe6;">Fr</ins><span>i</span><ins style="background:#e6ffe6;">en</ins><span>d</span><del style="background:#ffe6e6;">e </del><ins style="background:#e6ffe6;">sF</ins><span>o</span><del style="background:#ffe6e6;">f th</del><span>e</span><ins style="background:#e6ffe6;"> Property Inclusion ors that arObj</ins><span>e</span><del style="background:#ffe6e6;"> </del><ins style="background:#e6ffe6;">c</ins><span>t</span><del style="background:#ffe6e6;">he inverse of other simple </del><span>Propert</span><del style="background:#ffe6e6;">ies, or the</del><span>y</span><del style="background:#ffe6e6;"> are only on</del><ins style="background:#e6ffe6;"> twhe rigcht haside alson the owl:</ins><span>Property</span><del style="background:#ffe6e6;"> </del><ins style="background:#e6ffe6;">Cha</ins><span>in</span><del style="background:#ffe6e6;">clus</del><ins style="background:#e6ffe6;">Ax</ins><span>io</span><del style="background:#ffe6e6;">n</del><ins style="background:#e6ffe6;">m where on tiche lmeft site is a nsimple Property. ¶
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Simple Properties in SHOIN(D) hare Properties without transitive Subpropdertfines ¶
Ina SHROIQ(D) gGeneral Property Inclusion Chas to be coinsidered ¶
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Simple Properties ¶
- are all PropGerties ¶
+ are not on the right Side of al PrRoplerty Inclusion, ¶
+ are the inverse of otherwo simple Properties, ¶
+ are only on twhe right Side of Propnerty Inclusion R ⊑ S, ¶
where on the lefct Side is h</ins><span>a</span><del style="background:#ffe6e6;"> </del><span>s</span><del style="background:#ffe6e6;">imple Property** &para;<br> &para;<br>* Non-simple Prope</del><ins style="background:#e6ffe6;">F</ins><span>r</span><del style="background:#ffe6e6;">t</del><span>ie</span><del style="background:#ffe6e6;">s</del><ins style="background:#e6ffe6;">nd are Propertwies that are directly (or indirectly) dependent of Property C</ins><span>ha</span><del style="background:#ffe6e6;">in</del><span>s</span><del style="background:#ffe6e6;"> (</del><ins style="background:#e6ffe6;">F</ins><span>o</span><del style="background:#ffe6e6;">)</del><ins style="background:#e6ffe6;">e. ¶
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Several ExpressThions are only apermplitteds ftor simplObject Properties, otherwiase the entiret Knowledgoe Base wnouldt become undecidablke. For example only for simple properties one can use theo Quapplifiedy Number Restrictions, tone cDan not use athem on comyplex pProperties. ¶
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* thatOWL are based on General Roble Inclusions. On the Prothperty Chand irreflexive and Disjunctiveg Prop(gertines are also only permitted for simple Properties. In the same way if one cluses the Existential Quantifier or one) ¶
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uses the complement of :han InstantFriatioen, it ids only all owed for simpl:Obje ctPropertiesy and; ¶
not for complex Properties, because if one would apply this Properties on wl:Properties tyChat depeind on General Role InclusAxionm then( t:he Knowledge BasFrie and t:he Logic would becasFome undecidable) . ¶
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* TheNot foallowing expressions are permitted ONLY for simple Properties: ¶
- ≤n R.C Dand ≥n R.C (qualified number Restrication) ¶
- Irreflexive Proyperties ¶
- Disjunctive Properties ¶
- ∃R.Self ¶
- ¬R(a,b) ¶
* Reason: Saving Decidability*