A-Description-Logic-Primer描述逻辑

arXiv:1201.4089v3[cs.AI]3Jun2013ADescriptionLogicPrimer∗MarkusKrötzsch,FrantišekSimanˇcík,IanHorrocksDepartmentofComputerScience,UniversityofOxford,UKAbstract.Thispaperprovidesaself-containedfirstintroductiontodescriptionlog-ics(DLs).Themainconceptsandfeaturesareexplainedwithexamplesbeforesyn-taxandsemanticsoftheDLSROIQaredefinedindetail.Additionalsectionsre-viewlightweightDLlanguages,discusstherelationshiptotheOWLWebOntologyLanguageandgivepointerstofurtherreading.IntroductionDescriptionlogics(DLs)areafamilyofknowledgerepresentationlanguagesthatarewidelyusedinontologicalmodelling.AnimportantpracticalreasonforthisisthattheyprovideoneofthemainunderpinningsfortheOWLWebOntologyLanguageasstan-dardisedbytheWorldWideWebConsortium(W3C).However,DLshavebeenusedinknowledgerepresentationlongbeforetheadventofontologicalmodellinginthecontextoftheSemanticWeb,tracingbacktofirstDLmodellinglanguagesinthemid1980s.Astheirnamesuggests,DLsarelogics(infactmostDLsaredecidablefragmentsoffirst-orderlogic),andassuchtheyareequippedwithaformalsemantics:aprecisespecificationofthemeaningofDLontologies.ThisformalsemanticsallowshumansandcomputersystemstoexchangeDLontologieswithoutambiguityastotheirmeaning,andalsomakesitpossibletouselogicaldeductiontoinferadditionalinformationfromthefactsstatedexplicitlyinanontology–animportantfeaturethatdistinguishesDLsfromothermodellinglanguagessuchasUML.ThecapabilityofinferringadditionalknowledgeincreasesthemodellingpowerofDLsbutitalsorequiressomeunderstandingonthesideofthemodellerand,aboveall,goodtoolsupportforcomputingtheconclusions.ThecomputationofinferencesiscalledreasoningandanimportantgoalofDLlanguagedesignhasbeentoensurethatreasoningalgorithmsofgoodperformanceareavailable.Thisisoneofthereasonswhythereisnotjustasingledescriptionlogic:thebestbalancebetweenexpressivityofthelanguageandcomplexityofreasoningdependsontheintendedapplication.Inthispaperweprovideaself-containedfirstintroductiontodescriptionlogics.WestartbyexplainingthebasicwayinwhichknowledgeismodelledinDLsinSection1andcontinuewithanintuitiveintroductiontothemostimportantDLmodellingfeaturesinSection2.ThisleadsustotheratherexpressiveDLcalledSROIQ,thesyntaxofwhichwesummariseinSection3.InSection4,weexplaintheunderlyingideasofDL∗Version1.2of3June2013.CommentsandsuggestionscanbesenttoMarkusKrö[e-mail]sedanddistributedunderthetermsofCCBy-SA-NC3.0.Pleasecontacttheauthorsifyouwouldliketoreproducethisdocumentunderanotherlicense.1semanticsanduseittodefinethemeaningofSROIQontologies.ManyDLscanbeobtainedbyomittingsomefeaturesofSROIQandinSection5wereviewsomeofthemostimportantDLsobtainedinthisway.Inparticular,thisincludesvariouslightweightdescriptionlogicsthatallowforparticularlyefficientreasoning.InSection6wediscusstherelationshipofDLstotheOWLWebOntologyLanguage.WeconcludewithpointerstofurtherreadinginSection7.1.BasicBuildingBlocksofDLOntologiesDescriptionlogics(DLs)providemeanstomodeltherelationshipsbetweenentitiesinadomainofinterest.InDLstherearethreekindsofentities:concepts,rolesandindividualnames.1Conceptsrepresentsetsofindividuals,rolesrepresentbinaryrelationsbetweentheindividuals,andindividualnamesrepresentsingleindividualsinthedomain.Readersfamiliarwithfirst-orderlogicwillrecognisetheseasunarypredicates,binarypredicatesandconstants.Forexample,anontologymodellingthedomainofpeopleandtheirfamilyrelation-shipsmightuseconceptssuchParenttorepresentthesetofallparentsandFemaletorepresentthesetofallfemaleindividuals,rolessuchasparentOftorepresentthe(bi-nary)relationshipbetweenparentsandtheirchildren,andindividualnamessuchasjuliaandjohntorepresenttheindividualsJuliaandJohn.Unlikeadatabase,aDLontologydoesnotfullydescribeaparticularsituationor“stateoftheworld”;ratheritconsistsofasetofstatements,calledaxioms,eachofwhichmustbetrueinthesituationdescribed.Theseaxiomstypicallycaptureonlypartialknowledgeaboutthesituationthattheontologyisdescribing,andtheremaybemanydif-ferentstatesoftheworldthatareconsistentwiththeontology.Although,fromthepointofviewoflogic,thereisnoprincipaldifferencebetweendifferenttypesofaxioms,itiscustomarytoseparatethemintothreegroups:assertional(ABox)axioms,terminological(TBox)axiomsandrelational(RBox)axioms.1.1.AssertingFactswithABoxAxiomsABoxaxiomscaptureknowledgeaboutnamedindividuals,i.e.,theconceptstowhichtheybelongandhowtheyarerelatedtoeachother.ThemostcommonABoxaxiomsareconceptassertionssuchasMother(julia),(1)whichassertsthatJuliaisamotheror,moreprecisely,thattheindividualnamedjuliaisaninstanceoftheconceptMother.Roleassertionsdescriberelationsbetweennamedindividuals.TheassertionparentOf(julia,john),(2)forexample,statesthatJuliaisaparentofJohnor,moreprecisely,thattheindividualnamedjuliaisintherelationthatisrepresentedbyparentOftotheindividualnamedjohn.1InOWLconceptsandrolesarerespectivelyknownasclassesandproperties;seeSection6.2Theprevioussentenceshowsthatitcanberathercumbersometoexplicitlypointoutthattherelationshipsexpressedbyanaxiomarereallyrelationshipsbetweentheindividuals,setsandrelationsthat