AN OVERVIEW OF UNCERTAINTY AND VAGUENESS IN DESCRI

INFSYSRESEARCHREPORTInstitutf¨urInformationssystemeABWissensbasierteSystemeTechnischeUniversit¨atWienFavoritenstraße9-11A-1040Wien,AustriaTel:[phone]Fax:[e-mail]¨URINFORMATIONSSYSTEMEARBEITSBEREICHWISSENSBASIERTESYSTEMEANOVERVIEWOFUNCERTAINTYANDVAGUENESSINDESCRIPTIONLOGICSFORTHESEMANTICWEBTHOMASLUKASIEWICZandUMBERTOSTRACCIAINFSYSRESEARCHREPORT1843-06-07OCTOBER2006INFSYSRESEARCHREPORTINFSYSRESEARCHREPORT1843-06-07,OCTOBER2006ANOVERVIEWOFUNCERTAINTYANDVAGUENESSINDESCRIPTIONLOGICSFORTHESEMANTICWEBOCTOBER25,2006ThomasLukasiewicz1UmbertoStraccia2Abstract.OntologiesplayacrucialroleinthedevelopmentoftheSemanticWebasameansfordefiningsharedtermsinWebresources.Theyareformulatedinwebontologylanguages,whicharebasedonexpressivedescriptionlogics.SignificantresearcheffortsarerecentlydirectedtowardsrepresentingandreasoningwithuncertaintyandvaguenessinontologiesfortheSemanticWeb.Inthispaper,wegiveanoverviewofprobabilisticuncertainty,possibilisticuncertainty,andvaguenessinexpressivedescriptionlogicsfortheSemanticWeb.1DipartimentodiInformaticaeSistemistica,Universit`adiRoma“LaSapienza”,ViaSalaria113,I-00198Rome,Italy;e-mail:[e-mail]¨urInformationssysteme,TechnischeUniversit¨atWien,Favoriten-straße9-11,A-1040Vienna,Austria;e-mail:[e-mail].2ISTI-CNR,ViaG.Moruzzi1,I-56124Pisa,Italy;e-mail:[e-mail]:ThisworkhasbeenpartiallysupportedbyaHeisenbergProfessorshipoftheGermanResearchFoundation(DFG).Copyrightc2006bytheauthorsINFSYSRR1843-06-07IContents1Introduction12UncertaintyandVagueness22.1ProbabilisticLogic.......................................22.2PossibilisticLogic........................................32.3Many-ValuedLogics......................................43ClassicalDescriptionLogics73.1Syntax..............................................73.2Semantics............................................84ProbabilisticUncertaintyandDescriptionLogics94.1Syntax..............................................104.2Semantics............................................114.2.1Preliminaries......................................114.2.2Consistency.......................................124.2.3LexicographicEntailment...............................134.3RelatedWork..........................................144.3.1ProbabilisticDescriptionLogics............................144.3.2ProbabilisticWebOntologyLanguages........................154.3.3ApplicationsinInformationRetrieval.........................155PossibilisticUncertaintyandDescriptionLogics165.1Syntax..............................................165.2Semantics............................................166VaguenessandDescriptionLogics176.1Syntax..............................................176.1.1FuzzyDatatypeTheories................................176.1.2FuzzyModifiers....................................186.1.3FuzzyKnowledgeBases................................186.2Semantics............................................196.2.1FuzzyInterpretations..................................196.2.2BestTruthValueBound................................226.3RelatedWork..........................................237Conclusions25INFSYSRR1843-06-0711IntroductionTheSemanticWeb[3,4,25,49]hasrecentlyattractedmuchattention,bothfromacademiaandindustry,andiswidelyregardedasthenextstepintheevolutionoftheWorldWideWeb.ItaimsatanextensionofthecurrentWebbystandardsandtechnologiesthathelpmachinestounderstandtheinformationontheWebsothattheycansupportricherdiscovery,dataintegration,navigation,andautomationoftasks.Themainideasbehinditaretoaddamachine-readablemeaningtowebpages,touseontologiesforaprecisedefinitionofsharedtermsinwebresources,touseKRtechnologyforautomatedreasoningfromwebresources,andtoapplycooperativeagenttechnologyforprocessingtheinformationoftheWeb.ThedevelopmentoftheSemanticWebproceedsinseveralhierarchicallayers,wheretheOntologylayer,informoftheOWLWebOntologyLanguage[49,120](recommendedbytheW3C),iscurrentlythehighestlayerofsufficientmaturity.OWLconsistsofthreeincreasinglyexpressivesublanguages,namelyOWLLite,OWLDL,andOWLFull.Hence,ontologies[29]playakeyroleintheSemanticWeb,andamajorefforthasbeenputbytheSemanticWebcommunityintothisissue.Informally,anontologyconsistsofahierarchicaldescriptionofimportantandpreciselydefinedconceptsinaparticulardomain,alongwiththedescriptionoftheproperties(oftheinstances)ofeachconcept.Webcontentisthenannotatedbyrelyingontheconceptsdefinedinaspecificdomainontology.OWLLiteandOWLDLareessentiallyveryexpressivedescriptionlogicswithanRDFsyntax[49].Asshownin[48],ontologyentailmentinOWLLiteandOWLDLreducestoknowledgebase(un)satisfiabilityintheexpressivedescriptionlogicsSHIF(D)andSHOIN(D),respectively.Hence,theseexpressivedescriptionlogicsplayanimportantroleintheSemanticWeb,sincetheyareessentiallythetheoreticalcounterpartsofOWLLiteandOWLDL,respectively.Moregenerally,descriptionlogicsarealogicalreconstructionofframe-basedknowledgerepresentationlanguages,withtheaimofprovidi