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China2011,1,语义万维网的逻辑基础LogicalFoundationoftheSemanticWeb,主讲：黄智生ZhishengHuangVrijeUniversityAmsterdam，TheNetherlandshuangcs.vu.nl助教：胡青QingHuWuhanUniversityofScienceandTechnologyhuqing,China2011,2,课程时间表Schedule,China2011,3,描述逻辑是什么？描述逻辑基本系统描述逻辑种类描述逻辑实例,讲座2：描述逻辑导论Lecture2:IntroductiontoDescriptionLogics,China2011,4,描述逻辑是一类知识表示语言表达应用领域的概念定义（有可以被看作为专业术语知识）Descriptionlogics(DL)areafamilyofknowledgerepresentationlanguageswhichcanbeusedtorepresenttheconceptdefinitionsofanapplicationdomain(knownasterminologicalknowledge),描述逻辑是什么？WhatareDescriptionLogics?,China2011,5,描述逻辑简史ABriefHistoryofDescriptionLogics,MajorfocusofKRresearchinthe80sLedbyRonBrachman(AT&TLabs)Grewoutofearlynetwork-basedKRsystemslikesemanticnetworksandframes.Majorsystemsandlanguages80s:KL-ONE,NIKL,KANDOR,BACK,CLASSIC,LOOM90s:FACT,RACER,00s:DAML+OIL,OWLUsedasthebasisfortheSemanticweblanguagesDAML+OILandOWLSome(one)commercialsystems,China2011,6,概念与本体ConceptsandOntologies,Philosophicaldiscipline,branchofphilosophythatdealswiththenatureandtheorganisationofreality.ScienceofBeing(Aristotle,Metaphysics,IV,1)Whatisbeing?Whatarethefeaturescommontoallbeings?,China2011,7,VocabularyandOntology,Controlledvocabulary(Jernst2003):alistofcontrolledtermsunambiguousnon-redundantdefinitionOntology:acontrolledvocabularyexpressedinanontologyrepresentationlanguage(Jernst2003),China2011,8,Incomputerscience,Anontologyisanexplicitspecificationofaconceptualization.Gruber93Anontologyisasharedunderstandingofsomedomainofinterest.Uschold,Gruninger96TherearemanydefinitionsaformalspecificationEXECUTABLEofaconceptualizationofadomainCOMMUNITYofsomepartofworldthatisofinterestAPPLICATIONDefinesAcommonvocabularyoftermsSomespecificationofthemeaningofthetermsAsharedunderstandingforpeopleandmachines,China2011,9,Whydevelopanontology?,TomakedomainassumptionsexplicitEasiertochangedomainassumptionsEasiertounderstandandupdatelegacydataToseparatedomainknowledgefromoperationalknowledgeRe-usedomainandoperationalknowledgeseparatelyAcommunityreferenceforapplicationsToshareaconsistentunderstandingofwhatinformationmeans.,China2011,10,本体的主要特征KeyfeaturesofanOntology,概念层次性Concepthierarchy,概念包含关系conceptsubsumption,特殊与一般关系InstanceOfRelation(Instances),部分与整体关系PartOfRelation(property),China2011,11,Whynototheralternatives,一阶谓词逻辑thefirst-orderpredicatelogic集合论settheory程序语言programminglanguages,China2011,12,概念与分类,设定存在一个所有个体（Individual）的集合一个概念被看成是一个个体的集合（Setofindividuals）定义一个概念就是确定一个分类概念集合与个体集合是不相交的个体上的一个二元关系集合被称为一个性质（Property/Role),China2011,13,复合概念,概念的否定，交与并,C,D,CD,China2011,14,描述逻辑DescriptionLogic,KnowledgeBase,Tbox(schema)术语部分,Abox(data)断言部分,ManHumanMaleHappy-FatherManhas-childFemale,John:Happy-Father:has-child,InferenceSystem,Interface,China2011,15,描述逻辑DescriptionLogic,KnowledgeBase,Tbox(schema)术语部分,Abox(data)断言部分,InferenceSystem,Interface,Rbox(data)关系部分,Has-daughterhas-child,China2011,16,BasicDescriptionLogic:AL（AttributiveLanguage）,ConceptExpressions:A(原子概念atomicconcept)(全概念，universalconcept)(空概念，bottomconcept)A(原子否定，atomicnegation)CD(并，intersection)R.C(值限制，valuerestriction)R.T(有限存在量化limitedexistentialquantification)whereAisaconceptname,CandDareconceptexpressions,andRisaroleexpression,China2011,17,FamilyofAL-Language,U:CD(交union)E:R.C(完全存在量化fullexistentialquantification)N:(数量限制Numberrestrictions)(nR)(至少限制atleastrestriction)(nR)(最多限制atmostrestriction)C:(Negation):CALEN=AL+E+NSmallestpropositionallyclosedDLisALC(equivmodalK(m)=AL+CConceptsconstructedusing,and,China2011,18,Examples,womanpersonfemalemanpersonwomanmotherwomanhasChild.personfathermanhasChild.person,China2011,19,一个实例Example,whitehorsehorsewhite.,color(white).,whitehorsehorsehasColor.white.这里white是一个列名（nominal）,whitehorsehorsehasColor.whitehasColor.white.,China2011,20,AL句法规则,，ALpAtomicConcept=pAL，pAtomicConcept=pAL，C，DAL=CDAL，CAL,RRole=R.CAL,RRole=R.TAL,China2011,21,描述逻辑的语义模型,一个描述逻辑语言DL上的一个语义模型M=(S,R1,R2,Rn,V)这里S是所有可能个体（Individual)的集合RiSXS是一个S上的二元关系V：P-PowerSet(S)是一个赋值函数，它给一个原子概念赋予S的一个子集。,China2011,22,对照：模态逻辑的语义模型,命题模态逻辑语言L上的一个语义模型M=(S,A,V)这里S是可能世界的集合ASXS是一个可达世界的关系V：P-PowerSet(S)是一个赋值函数，它给一个原始命题赋予一个可能世界子集。所以说，一个描述逻辑实质上就是一个多模态逻辑,China2011,23,描述逻辑AL的真值条件,M，s|=pifsV(p)M，s|=piffM,s|=pM，s|=CDiffM,s|=CandM,s|=DM，s|=R.CiffM,s|=CforallssuchthatR想想看：，R.T对应的真值条件是什么,China2011,24,DLSemantics,SemanticsdefinedbyinterpretationsAninterpretationI=(DI,.I),whereDIisthedomain(anon-emptyset).Iisaninterpretationfunctionthatmaps:Concept(class)nameAsubsetAIofDIRole(property)nameRbinaryrelationRIoverDIIndividualnameiiIelementofDI,China2011,25,DLSemantics(cont.),InterpretationfunctionIextendstoconcept(androle)expressionsintheobviousway,e.g.:,China2011,26,规范的AL语义,xI=xIpI=S/pICDI=CIDIR.CI=x|y(RI=yCI这里I被称作一个解释（Interpretation），实质上就是一个模型。,China2011,27,Axiomsdefinerelationsbetweenconcepts,概念包含（Subsumption）:CDiffCIDI定义：概念相等(Equivalence):CDiffCD而且DC概念不相交（Disjointness）:CD,China2011,28,GeneralConceptInclusion,ExpressivitywithGCIsDisjointness:,CD,Identity:,ab,Distinctiveness:,ab,China2011,29,DLKnowledgeBase,ADLKnowledgebaseKisapairwhereTisasetof“terminological”axioms(theTbox)Aisasetof“assertional”axioms(theAbox)Tboxaxiomsareoftheform:CD,CD,RS,RSandR+RwhereC,Dconcepts,R,Sroles,andR+setoftransitiverolesAboxaxiomsareoftheform:x:D,:Rwherex,yareindividualnames,DaconceptandRarole,China2011,30,MoreaboutFamilyofALLanguage,Additionallettersindicateotherextension,e.g.:Hforroleinclusionaxioms(rolehierarchy)Ofornominals(singletonclasses,writtenx)IforinverserolesQforqualifiednumberrestrictions(offormnR.C,nR.C)SoftenusedforALCwithtransitiveroles(R+)SHIQ:ALC+R+rolehierarchy+inverseroles+Q,China2011,31,SHOIN,SHION:S:ALC+roletransitivityH:rolehierarchiesO:nominalsI:InverserolesN:cardinalityrestrictionSHOIN(D)=OWL-DLD:datatypes,China2011,32,KnowledgeBaseSemantics,AninterpretationIsatisfies(models)aTboxaxiomA,(IA):ICDiffCIDIICDiffCI=DIIRSiffRISIIRSiffRI=SIIR+Riff(RI)+RI,China2011,33,IsatisfiesaTboxT(IT)iffIsatisfieseveryaxiomAinTAninterpretationIsatisfies(models)anAboxaxiomA(IA):Ix:DiffxIDII:RiffRIIsatisfiesanAboxA(IA)iffIsatisfieseveryaxiomAinAIsatisfiesanKBK(IK)iffIsatisfiesbothTandA,China2011,34,ReasoningTasksforConcept,China2011,35,ReductiontoSubsumption,China2011,36,ReductiontoUnsatisfiability,China2011,37,ReducingUnsatisfiability,Thefollowingsareequivalent:,China2011,38,描述逻辑系统命名规则DLNaming,BasicdescriptionlogicisALC(equivmodalK(m)Conceptsconstructedusing,andSoftenusedforALCwithtransitiverolesAdditionallettersindicateotherextension,e.g.:Hforroleinclusionaxioms(rolehierarchy)Ofornominals(singletonclasses,writtenx)IforinverserolesNfornumberrestrictions(offormnR,nR)Qforqualifiednumberrestrictions(offormnR.C,nR.C),China2011,39,DL-Lite:A“Scalable”DLFamily,RAtomicRole=R,R-BasicRoleAAtomicConcept=ABasicConcept,RAtomicRole=RBasicConceptCBasicConcept=C,CGeneralConceptRBasicRole=R,RGeneralRole,China2011,40,SimplifiedDL-LiteSyntaxRules,R-P|P-B-A|RC-B|BE-R|RWhereRisbasicrole,Pisatomicrole,Aisatomicconcept,Bisbasicconcept,Cisgeneralconcept,Eisgeneralrole,China2011,41,DL-LiteFamily,DL-LitecoreTboxisasetofinclusionaxiomsofthefromBCDL-LiteR=DL-Lite