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China20111语义万维网的逻辑基础

LogicalFoundationoftheSemanticWeb主讲：黄智生ZhishengHuangVrijeUniversityAmsterdam，TheNetherlandshuang@cs.vu.nl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-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-LanguageU: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):

CALEN=AL+[E]+[N]SmallestpropositionallyclosedDLisALC(equivmodalK(m))=AL+CConceptsconstructedusing⊓,⊔,

,and

China201118Exampleswoman≡person⊓femaleman≡person⊓

womanmother≡woman⊓

hasChild.personfather≡man⊓

hasChild.personChina201119一个实例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|=\=pM，s|=C⊓DiffM,s|=CandM,s|=D

M，s|=

R.CiffM,s’|=Cforalls’suchthat<s,s’>

R想想看：

，，R.T对应的真值条件是什么China201124DLSemanticsSemanticsdefinedbyinterpretations

AninterpretationI=(DI,.I),where

DIisthedomain(anon-emptyset).Iisaninterpretationfunctionthatmaps:Concept(class)nameA

subsetAIofDIRole(property)nameR

binaryrelationRIoverDIIndividualnamei

iIelementofDIChina201125DLSemantics(cont.)Interpretationfunction¢Iextendstoconcept(androle)expressions

intheobviousway,e.g.:China201126规范的AL语义{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I被称作一个解释（Interpretation

），实质上就是一个模型。China201127Axiomsdefinerelationsbetweenconcepts

概念包含（Subsumption）:C⊑

DiffCI

DI

定义：概念相等(Equivalence):C

DiffC⊑

D

而且D

⊑

C

概念不相交（Disjointness）:C⊓D

China201128GeneralConceptInclusionExpressivitywithGCIsDisjointness:C⊓D⊑

Identity:{a}⊑{b}Distinctiveness:{a}⊓{b}⊑

China201129DLKnowledgeBaseADLKnowledgebase

Kisapair<T,A>whereTisasetof“terminological”axioms(theTbox)A

isasetof“assertional”axioms(theAbox)Tboxaxiomsareoftheform: C

⊑

D,C

D,R

⊑

S,R

SandR+

⊑

R whereC,

Dconcepts,R,Sroles,andR+setoftransitiverolesAboxaxiomsareoftheform: x:D,<x,y>:R wherex,yareindividualnames,DaconceptandRaroleChina201130MoreaboutFamilyofALLanguageAdditionallettersindicateotherextension,e.g.:Hforroleinclusionaxioms(rolehierarchy)Ofornominals(singletonclasses,written{x})IforinverserolesQforqualifiednumberrestrictions(ofform

nR.C,≥

nR.C)SoftenusedforALCwithtransitiveroles(R+)SHIQ:ALC+R++rolehierarchy+inverseroles+QChina201131SHOINSHION:S:ALC+roletransitivityH:rolehierarchiesO:nominalsI:InverserolesN:cardinalityrestrictionSHOIN(D)=OWL-DLD:datatypesChina201132KnowledgeBaseSemanticsAninterpretation

Isatisfies(models)aTboxaxiomA,(I

⊨

A): I

⊨

C

⊑

DiffCI

DI

I

⊨

C

DiffCI=DI I

⊨

R

⊑

SiffRI

SI

I

⊨

R

SiffRI=SI I

⊨

R+

⊑

Riff(RI)+

RIChina201133IsatisfiesaTboxT(I⊨T)iffIsatisfieseveryaxiomAinTAninterpretationIsatisfies(models)anAboxaxiomA(I⊨A):I⊨x:DiffxI

DI

I⊨<x,y>:Riff<xI,yI>

RIIsatisfiesanAboxA(I⊨A)iffIsatisfieseveryaxiomAinAIsatisfiesanKBK(I⊨K)iffIsatisfiesbothTandAChina201134ReasoningTasksforConceptChina201135ReductiontoSubsumptionChina201136ReductiontoUnsatisfiabilityChina201137ReducingUnsatisfiabilityThefollowingsareequivalent:China201138描述逻辑系统命名规则DLNamingBasicdescriptionlogicisALC(equivmodalK(m))Conceptsconstructedusing⊓,⊔,

,and

SoftenusedforALCwithtransitiverolesAdditionallettersindicateotherextension,e.g.:Hforroleinclusionaxioms(rolehierarchy)Ofornominals(singletonclasses,written{x})IforinverserolesNfornumberrestrictions(ofform

nR,≥

nR)Qforqualifiednumberrestrictions(ofform

nR.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=