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China20111语义万维网的逻辑基础

LogicalFoundationoftheSemanticWeb主讲：黄智生ZhishengHuangVrijeUniversityAmsterdam，TheNetherlands助教：胡青QingHuWuhanUniversityofScienceandTechnologyhuqing@China20112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:IntroductiontoDescriptionLogics

China20114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ABriefHistoryofDescriptionLogicsMajorfocusofKRresearchinthe80’sLedbyRonBrachman–(AT&TLabs)Grewoutofearlynetwork-basedKRsystemslikesemanticnetworksandframes.Majorsystemsandlanguages–80s:KL-ONE,NIKL,KANDOR,BACK,CLASSIC,LOOM90s:FACT,RACER,00s:DAML+OIL,OWLUsedasthebasisfortheSemanticweblanguagesDAML+OILandOWLSome(one)commercialsystemsChina20116概念与本体

ConceptsandOntologiesPhilosophicaldiscipline,branchofphilosophythatdealswiththenatureandtheorganisationofreality.ScienceofBeing(Aristotle,Metaphysics,IV,1)Whatisbeing?Whatarethefeaturescommontoallbeings?China20117VocabularyandOntology

Controlledvocabulary(Jernst2003):alistofcontrolledtermsunambiguousnon-redundantdefinitionOntology:acontrolledvocabularyexpressedinanontologyrepresentationlanguage(Jernst2003)China20118Incomputerscience…Anontologyisanexplicitspecificationofaconceptualization.[Gruber93]Anontologyisasharedunderstandingofsomedomainofinterest.[Uschold,Gruninger96]TherearemanydefinitionsaformalspecificationEXECUTABLEofaconceptualizationofadomainCOMMUNITYofsomepartofworldthatisofinterestAPPLICATIONDefinesAcommonvocabularyoftermsSomespecificationofthemeaningofthetermsAsharedunderstandingforpeopleandmachinesChina20119Whydevelopanontology?TomakedomainassumptionsexplicitEasiertochangedomainassumptionsEasiertounderstandandupdatelegacydataToseparatedomainknowledgefromoperationalknowledgeRe-usedomainandoperationalknowledgeseparatelyAcommunityreferenceforapplicationsToshareaconsistentunderstandingofwhatinformationmeans.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一阶谓词逻辑辑thefirst-orderpredicatelogic集合论settheory程序语言programminglanguagesChina201112概念与分类设定存在一个个所有个体（（Individual））的集集合合一个个概概念念被被看看成成是是一一个个个个体体的的集集合合（（Setofindividuals）定义义一一个个概概念念就就是是确确定定一一个个分分类类概念念集集合合与与个个体体集集合合是是不不相相交交的的个体体上上的的一一个个二二元元关关系系集集合合被被称称为为一一个个性性质质（（Property/Role)China201113复合合概概念念概念念的的否否定定，，交与与并并CDCDChina201114描述述逻逻辑辑DescriptionLogicKnowledgeBaseTbox(schema)术语部分Abox(data)断言部分ManHuman⊓MaleHappy-FatherMan⊓has-childFemale⊓…John:Happy-Father<John,Mary>:has-childInferenceSystemInterfaceChina201115描述逻辑DescriptionLogicKnowledgeBaseTbox(schema)术语部分Abox(data)断言部分InferenceSystemInterfaceRbox(data)关系部部分Has-daughter⊑has-childChina201116BasicDescriptionLogic:AL（（AttributiveLanguage））ConceptExpressions:A(原子概概念atomicconcept)(全概念念，universalconcept)(空概念念，bottomconcept)A(原子否否定，，atomicnegation)C⊓D(并，intersection)R.C(值限制制，valuerestriction)R.T(有限存存在量量化limitedexistentialquantification)whereAisaconceptname,CandDareconceptexpressions,andRisaroleexpressionChina201117FamilyofAL-LanguageU:C⊔D(交union)E:R.C(完全存存在量量化fullexistentialquantification)N:(数量限限制Numberrestrictions)(nR)(至少限限制atleastrestriction)(nR)(最多限限制atmostrestriction)C:(Negation):CALEN=AL+[E]+[N]SmallestpropositionallyclosedDLisALC(equivmodalK(m))=AL+CConceptsconstructedusing⊓,⊔⊔,,andChina201118Exampleswoman≡person⊓femaleman≡person⊓womanmother≡woman⊓hasChild.personfather≡man⊓hasChild.personChina201119一个实例例Examplewhitehorse≡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，ALpAtomicConcept=>pAL，，pAtomicConcept=>pAL，C，DAL=>C⊓DAL，CAL,RRole=>R.CAL,RRole=>R.TALChina201121描述逻辑的语义模型一个描述逻辑辑语言DL上的一个语义义模型M=(S,{R1,R2,…Rn},V)这里S是所有可能个个体（Individual)的集合RiSXS是一个S上的二元关系系V：P->PowerSet(S)是一个赋值函函数，它给一一个原子概念念赋予S的一个子集。。China201122对照：模态逻逻辑的语义模型命题模态逻辑辑语言L上的一个语义义模型M=(S,A,V)这里S是可能世界的的集合ASXS是一个可达世世界的关系V：P->PowerSet(S)是一个赋值函函数，它给一一个原始命题题赋予一个可可能世界子集集。所以说，一个个描述逻辑实实质上就是一一个多模态逻逻辑China201123描述逻辑AL的真值条件M，s|=pifsV(p)M，s|=piffM,s|=\=pM，s|=C⊓DiffM,s|=CandM,s|=DM，s|=R.CiffM,s’’|=Cforalls’suchthat<s,s’>R想想看看：，，，R.T对应的的真值值条件件是什什么China201124DLSemanticsSemanticsdefinedbyinterpretationsAninterpretationI=(DI,.I),whereDIisthedomain(anon-emptyset).Iisaninterpretationfunctionthatmaps:Concept(class)nameAsubsetAIofDIRole(property)nameRbinaryrelationRIoverDIIndividualnameiiIelementofDIChina201125DLSemantics(cont.)Interpretationfunction¢Iextendstoconcept(androle)expressionsintheobviousway,e.g.:China201126规范范的的AL语义义{x}I={xI}{p}I=S/pI{C⊓D}I={C}I{D}I{R.C}I={x|y(<x,y>RI=>yCI}这里里I被称称作作一一个个解解释释（（Interpretation），，实质质上上就就是是一一个个模模型型。。China201127Axiomsdefinerelationsbetweenconcepts概念念包包含含（（Subsumption）:C⊑DiffCIDI定义义：：概念念相相等等(Equivalence):CDiffC⊑D而且且D⊑C概念念不不相相交交（（Disjointness）:C⊓DChina201128GeneralConceptInclusionExpressivitywithGCIsDisjointness:C⊓D⊑Identity:{a}⊑{b}Distinctiveness:{a}⊓{b}⊑China201129DLKnowledgeBaseADLKnowledgebaseKisapair<T,A>whereTisasetof““terminological””axioms(theTbox)Aisasetof““assertional””axioms(theAbox)Tboxaxiomsareoftheform:C⊑D,CD,R⊑S,RSandR+⊑RwhereC,Dconcepts,R,Sroles,andR+setoftransitiverolesAboxaxiomsareoftheform:x:D,<x,y>:Rwherex,yareindividualnames,DaconceptandRaroleChina201130MoreaboutFamilyofALLanguageAdditionallettersindicateotherextension,e.g.:Hforroleinclusionaxioms(rolehierarchy)Ofornominals(singletonclasses,written{x})IforinverserolesQforqualifiednumberrestrictions(offormnR.C,≥nR.C)SoftenusedforALCwithtransitiveroles(R+)SHIQ:ALC+R++rolehierarchy+inverseroles+QChina201131SHOINSHION:S:ALC+roletransitivityH:rolehierarchiesO:nominalsI:InverserolesN:cardinalityrestrictionSHOIN(D)=OWL-DLD:datatypesChina201132KnowledgeBaseSemanticsAninterpretationIsatisfies(models)aTboxaxiomA,(I⊨A):I⊨C⊑DiffCIDII⊨CDiffCI=DII⊨R⊑SiffRISII⊨RSiffRI=SII⊨R+⊑Riff(RI)+RIChina201133IsatisfiesaTboxT(I⊨T)iffIsatisfieseveryaxiomAinTAninterpretationIsatisfies(models)anAboxaxiomA(I⊨A):I⊨x:DiffxIDII⊨<x,y>:Riff<xI,yI>RIIsatisfiesanAboxA(I⊨A)iffIsatisfieseveryaxiomAinAIsatisfiesanKBK(I⊨K)iffIsatisfiesbothTandAChina201134ReasoningTasksforConceptChina201135ReductiontoSubsumptionChina201136ReductiontoUnsatisfiabilityChina201137ReducingUnsatisfiabilityThefollowingsareequivalent:China201138描述逻辑系统统命名规则DLNamingBasicdescriptionlogicisALC(equivmodalK(m))Conceptsconstructedusing⊓,⊔,,andSoftenusedforALCwithtransitiverolesAdditionallettersindicateotherextension,e.g.:Hforroleinclusionaxioms(rolehierarchy)Ofornominals(singletonclasses,written{x})IforinverserolesNfornumberrestrictions(offormnR,≥nR)Qforqualifiednumberrestrictions(offormnR.C,≥nR.C)…China201139DL-Lite:A“Scalable”DLFamilyRAtomicRole=>R,R-BasicRoleAAtomicConcept=>ABasicConcept,RAtomicRole=>RBasicConceptCBasicConcept=>C,CGeneralConceptRBasicRole=>R,RGeneralRoleChina201140SimplifiedDL-LiteSyntaxRulesR->P|P-B->A|RC->B|BE->R|RWhereRisbasicrole,Pisatomicrole,Aisatomicconcept,Bisbasicconcept,Cisgeneralconcept,EisgeneralroleChina201141DL-LiteFamilyDL-LitecoreTboxisasetofinclusionaxiomsofthefromB⊑CDL-LiteR=DL-Litecore+roleinclusionaxiomsofthefromR⊑EDL-LiteF=DL-Litecore+functionalityonroleorontheirinversewiththeform(functR)China201142想一想想：DL-Lite能不能能表达达下列列描述述?A1⊔A2⊑CB⊑C1⊓C2Disjoint(A,B)A1⊓A2⊑CB⊑C1⊔C2China201143思考：：描述述逻辑辑的下下一步步扩