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China20111语义万维网的逻辑基础LogicalFoundationoftheSemanticWeb主讲：黄智生ZhishengHuangVrijeUniversityAmsterdam，[e-mail]助教：胡青[e-mail]20112课程时间表Schedule时间上午9:30-11:30下午2:30-4:302011.8.22报到第一讲：现代逻辑导论2011.8.23第二讲：描述逻辑导论专题讨论：描述逻辑与知识表示2011.8.24第三讲：语义Web与逻辑I集体活动：远足或专题研讨会I2011.8.25第四讲：语义Web与逻辑II第五讲：本体推理与管理2011.8.26第六讲：语义技术与应用开发专题研讨会II2011.8.27CCFYOCSEF论坛：Large-ScaleandScalableSemanticComputing2011.8.28首届“语义技术与与生命科学”高峰论坛China20113•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:IntroductiontoDescriptionLogicsChina20114•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?China20115描述逻辑简史ABriefHistoryofDescriptionLogics•MajorfocusofKRresearchinthe80’s•LedbyRonBrachman–(AT&TLabs)•Grewoutofearlynetwork-basedKRsystemslikesemanticnetworksandframes.•Majorsystemsandlanguages–•80s:KL-ONE,NIKL,KANDOR,BACK,CLASSIC,LOOM•90s:FACT,RACER,•00s:DAML+OIL,OWL•UsedasthebasisfortheSemanticweblanguagesDAML+OILandOWL•Some(one)commercialsystemsChina20116概念与本体ConceptsandOntologies•Philosophicaldiscipline,branchofphilosophythatdealswiththenatureandtheorganisationofreality.•ScienceofBeing(Aristotle,Metaphysics,IV,1)•Whatisbeing?•Whatarethefeaturescommontoallbeings?China20117VocabularyandOntology•Controlledvocabulary(Jernst2003):•alistofcontrolledterms•unambiguous•non-redundantdefinition•Ontology:acontrolledvocabularyexpressedinanontologyrepresentationlanguage(Jernst2003)China20118Incomputerscience…•Anontologyisanexplicitspecificationofaconceptualization.[Gruber93]•Anontologyisasharedunderstandingofsomedomainofinterest.[Uschold,Gruninger96]•Therearemanydefinitions•aformalspecificationEXECUTABLE•ofaconceptualizationofadomainCOMMUNITY•ofsomepartofworldthatisofinterestAPPLICATION•Defines•Acommonvocabularyofterms•Somespecificationofthemeaningoftheterms•AsharedunderstandingforpeopleandmachinesChina20119Whydevelopanontology?•Tomakedomainassumptionsexplicit•Easiertochangedomainassumptions•Easiertounderstandandupdatelegacydata•Toseparatedomainknowledgefromoperationalknowledge•Re-usedomainandoperationalknowledgeseparately•Acommunityreferenceforapplications•Toshareaconsistentunderstandingofwhatinformationmeans.China201110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)China201111Whynototheralternatives•一阶谓词逻辑thefirst-orderpredicatelogic•集合论settheory•程序语言programminglanguagesChina201112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)China201113复合概念概念的否定，交与并CDCDChina201114描述逻辑DescriptionLogicKnowledgeBaseTbox(schema)术语部分Abox(data)断言部分ManHuman⊓MaleHappy-FatherMan⊓has-childFemale⊓…John:Happy-FatherJohn,Mary:has-childInferenceSystemInterfaceChina201115描述逻辑DescriptionLogicKnowledgeBaseTbox(schema)术语部分Abox(data)断言部分InferenceSystemInterfaceRbox(data)关系部分Has-daughter⊑has-childChina201116BasicDescriptionLogic:AL（AttributiveLanguage）•ConceptExpressions:•A(原子概念atomicconcept)•(全概念，universalconcept)•(空概念，bottomconcept)•A(原子否定，atomicnegation)•C⊓D(并，intersection)•R.C(值限制，valuerestriction)•R.T(有限存在量化limitedexistentialquantification)whereAisaconceptname,CandDareconceptexpressions,andRisaroleexpressionChina201117FamilyofAL-Language•U:C⊔D(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):C•ALEN=AL+[E]+[N]•SmallestpropositionallyclosedDLisALC(equivmodalK(m))=AL+C•Conceptsconstructedusing⊓,⊔,,andChina201118Exampleswoman≡person⊓femaleman≡person⊓womanmother≡woman⊓hasChild.personfather≡man⊓hasChild.personChina201119一个实例Example•whitehorse≡horse⊓white.•color(white).•whitehorse≡horse⊓hasColor.{white}.这里white是一个列名（nominal）•whitehorse≡horse⊓hasColor.{white}⊓hasColor.{white}.China201120AL句法规则•，AL•pAtomicConcept=pAL，•pAtomicConcept=pAL，•C，DAL=C⊓DAL，•CAL,RRole=R.CAL,•RRole=R.TALChina201121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RiSXS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。China201122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ASXS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China201123描述逻辑AL的真值条件•M，s|=pifsV(p)•M，s|=piffM,s|=\=p•M，s|=C⊓DiffM,s|=CandM,s|=D•M，s|=R.CiffM,s’|=Cforalls’suchthats,s’R想想看：，，R.T对应的真值条件是什么China201124DLSemantics•Semanticsdefinedbyinterpretations•AninterpretationI=(DI,.I),where•DIisthedomain(anon-emptyset)•.Iisaninterpretationfunctionthatmaps:•Concept(class)nameAsubsetAIofDI•Role(property)nameRbinaryrelationRIoverDI•IndividualnameiiIelementofDIChina201125DLSemantics(cont.)•Interpretationfunction¢Iextendstoconcept(androle)expressionsintheobviousway,e.g.:China201126规范的AL语义•{x}I={xI}•{p}I=S/pI•{C⊓D}I={C}I{D}I•{