植入互聯(lián)網(wǎng)基因戴爾轉(zhuǎn)型電商課件

China20111語義萬維網(wǎng)的邏輯基礎(chǔ)

LogicalFoundationoftheSemanticWeb主講：黃智生ZhishengHuangVrijeUniversityAmsterdam，TheNetherlandshuang@cs.vu.nl助教：胡青QingHuWuhanUniversityofScienceandTechnologyhuqing@China20111語義萬維網(wǎng)的邏輯基礎(chǔ)

LogicalChina20112課程時(shí)間表Schedule

時(shí)間上午9:30-11:30下午2:30-4:302011.8.22報(bào)到第一講：現(xiàn)代邏輯導(dǎo)論2011.8.23第二講：描述邏輯導(dǎo)論專題討論：描述邏輯與知識表示2011.8.24第三講：語義Web與邏輯I集體活動：遠(yuǎn)足或?qū)ｎ}研討會I2011.8.25第四講：語義Web與邏輯II第五講：本體推理與管理2011.8.26第六講：語義技術(shù)與應(yīng)用開發(fā)專題研討會II2011.8.27CCFYOCSEF論壇：Large-ScaleandScalableSemanticComputing2011.8.28首屆“語義技術(shù)與與生命科學(xué)”高峰論壇China20112課程時(shí)間表Schedule

時(shí)間上午9China20113描述邏輯是什么？描述邏輯基本系統(tǒng)描述邏輯種類描述邏輯實(shí)例

講座2：描述邏輯導(dǎo)論

Lecture2:IntroductiontoDescriptionLogics

China20113描述邏輯是什么？

講座2：描述邏輯導(dǎo)China20114描述邏輯是一類知識表示語言表達(dá)應(yīng)用領(lǐng)域的概念定義（有可以被看作為專業(yè)術(shù)語知識）Descriptionlogics(DL)areafamilyofknowledgerepresentationlanguageswhichcanbeusedtorepresenttheconceptdefinitionsofanapplicationdomain(knownasterminologicalknowledge)描述邏輯是什么？

WhatareDescriptionLogics?China20114描述邏輯是一類知識表示語言表達(dá)應(yīng)用領(lǐng)域China20115描述邏輯簡史ABriefHistoryofDescriptionLogicsMajorfocusofKRresearchinthe80’sLedbyRonBrachman–(AT&TLabs)Grewoutofearlynetwork-basedKRsystemslikesemanticnetworksandframes.Majorsystemsandlanguages–80s:KL-ONE,NIKL,KANDOR,BACK,CLASSIC,LOOM90s:FACT,RACER,00s:DAML+OIL,OWLUsedasthebasisfortheSemanticweblanguagesDAML+OILandOWLSome(one)commercialsystemsChina20115描述邏輯簡史MajorfocusoChina20116概念與本體

ConceptsandOntologiesPhilosophicaldiscipline,branchofphilosophythatdealswiththenatureandtheorganisationofreality.ScienceofBeing(Aristotle,Metaphysics,IV,1)Whatisbeing?Whatarethefeaturescommontoallbeings?China20116概念與本體

ConceptsandChina20117VocabularyandOntology

Controlledvocabulary(Jernst2003):alistofcontrolledtermsunambiguousnon-redundantdefinitionOntology:acontrolledvocabularyexpressedinanontologyrepresentationlanguage(Jernst2003)China20117VocabularyandOntoChina20118Incomputerscience…Anontologyisanexplicitspecificationofaconceptualization.[Gruber93]Anontologyisasharedunderstandingofsomedomainofinterest.[Uschold,Gruninger96]TherearemanydefinitionsaformalspecificationEXECUTABLEofaconceptualizationofadomainCOMMUNITYofsomepartofworldthatisofinterestAPPLICATIONDefinesAcommonvocabularyoftermsSomespecificationofthemeaningofthetermsAsharedunderstandingforpeopleandmachinesChina20118IncomputerscienceChina20119Whydevelopanontology?TomakedomainassumptionsexplicitEasiertochangedomainassumptionsEasiertounderstandandupdatelegacydataToseparatedomainknowledgefromoperationalknowledgeRe-usedomainandoperationalknowledgeseparatelyAcommunityreferenceforapplicationsToshareaconsistentunderstandingofwhatinformationmeans.China20119WhydevelopanontoChina201110本體的主要特征

KeyfeaturesofanOntology概念層次性Concepthierarchy,概念包含關(guān)系conceptsubsumption特殊與一般關(guān)系

InstanceOfRelation(Instances)部分與整體關(guān)系

PartOfRelation(property)China201110本體的主要特征

KeyfeaturChina201111Whynototheralternatives一階謂詞邏輯thefirst-orderpredicatelogic集合論settheory程序語言programminglanguagesChina201111WhynototheralteChina201112概念與分類設(shè)定存在一個(gè)所有個(gè)體（Individual）的集合一個(gè)概念被看成是一個(gè)個(gè)體的集合（Setofindividuals）定義一個(gè)概念就是確定一個(gè)分類概念集合與個(gè)體集合是不相交的個(gè)體上的一個(gè)二元關(guān)系集合被稱為一個(gè)性質(zhì)（Property/Role)China201112概念與分類設(shè)定存在一個(gè)所有個(gè)體（InChina201113復(fù)合概念概念的否定，交與并CDCDChina201113復(fù)合概念概念的否定，交與并CDCChina201114描述邏輯

DescriptionLogicKnowledgeBaseTbox(schema)術(shù)語部分Abox(data)斷言部分Man

Human?MaleHappy-FatherMan?

has-childFemale?

…John:Happy-Father<John,Mary>:has-childInferenceSystemInterfaceChina201114描述邏輯DescriptionLChina201115描述邏輯

DescriptionLogicKnowledgeBaseTbox(schema)術(shù)語部分Abox(data)斷言部分InferenceSystemInterfaceRbox(data)關(guān)系部分Has-daughter?

has-childChina201115描述邏輯DescriptionLChina201116BasicDescriptionLogic:

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,andRisaroleexpressionChina201116BasicDescriptionChina201117FamilyofAL-LanguageU:C?

D(交union)E:R.C(完全存在量化fullexistentialquantification)N:

(數(shù)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

China201117FamilyofAL-LanguChina201118Exampleswoman≡person?femaleman≡person?

womanmother≡woman?

hasChild.personfather≡man?

hasChild.personChina201118Exampleswoman≡peChina201119一個(gè)實(shí)例Examplewhitehorse≡horse?white.color(white).whitehorse≡horse?hasColor.{white}.這里white是一個(gè)列名（nominal）whitehorse≡horse?hasColor.{white}?

hasColor.{white}.China201119一個(gè)實(shí)例ExamplewhitehoChina201120AL句法規(guī)則，ALpAtomicConcept=>pAL，pAtomicConcept=>

pAL，C，DAL=>C?

DAL，CAL,RRole=>R.CAL,RRole=>R.TALChina201120AL句法規(guī)則，ALChina201121描述邏輯的語義模型一個(gè)描述邏輯語言DL上的一個(gè)語義模型M=(S,{R1,R2,…Rn},V)這里S是所有可能個(gè)體（Individual)的集合RiSXS是一個(gè)S上的二元關(guān)系V：P->

PowerSet(S)是一個(gè)賦值函數(shù)，它給一個(gè)原子概念賦予S的一個(gè)子集。China201121描述邏輯的語義模型一個(gè)描述邏輯語言DChina201122對照：模態(tài)邏輯的語義模型命題模態(tài)邏輯語言L上的一個(gè)語義模型M=(S,A,V)這里S是可能世界的集合ASXS是一個(gè)可達(dá)世界的關(guān)系V：P->

PowerSet(S)是一個(gè)賦值函數(shù)，它給一個(gè)原始命題賦予一個(gè)可能世界子集。所以說，一個(gè)描述邏輯實(shí)質(zhì)上就是一個(gè)多模態(tài)邏輯China201122對照：模態(tài)邏輯的語義模型命題模態(tài)邏輯China201123描述邏輯AL的真值條件M，s|=pifsV(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對應(yīng)的真值條件是什么China201123描述邏輯AL的真值條件M，s|=China201124DLSemanticsSemanticsdefinedbyinterpretations

AninterpretationI=(DI,.I),where

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

subsetAIofDIRole(property)nameR

binaryrelationRIoverDIIndividualnamei

iIelementofDIChina201124DLSemanticsSemantChina201125DLSemantics(cont.)Interpretationfunction￠Iextendstoconcept(androle)expressions

intheobviousway,e.g.:China201125DLSemantics(contChina201126規(guī)范的AL語義{x}I={xI}{p}I=S/pI{C?D}I={C}I{D}I{R.C}I={x|y(<x,y>RI=>yCI}這里I被稱作一個(gè)解釋（Interpretation

），實(shí)質(zhì)上就是一個(gè)模型。China201126規(guī)范的AL語義{x}I={xI}China201127Axiomsdefinerelationsbetweenconcepts

概念包含（Subsumption）:C?

DiffCIDI

定義：概念相等(Equivalence):C

DiffC?

D

而且D

?

C

概念不相交（Disjointness）:C?D

China201127AxiomsdefinerelaChina201128GeneralConceptInclusionExpressivitywithGCIsDisjointness:C?D?

Identity:{a}?Distinctiveness:{a}??

China201128GeneralConceptInChina201129DLKnowledgeBaseADLKnowledgebase

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,DaconceptandRaroleChina201129DLKnowledgeBaseAChina201130MoreaboutFamilyofALLanguageAdditionallettersindicateotherextension,e.g.:Hforroleinclusionaxioms(rolehierarchy)Ofornominals(singletonclasses,written{x})IforinverserolesQforqualifiednumberrestrictions(ofform

nR.C,≥

nR.C)SoftenusedforALCwithtransitiveroles(R+)SHIQ:ALC+R++rolehierarchy+inverseroles+QChina201130MoreaboutFamilyChina201131SHOINSHION:S:ALC+roletransitivityH:rolehierarchiesO:nominalsI:InverserolesN:cardinalityrestrictionSHOIN(D)=OWL-DLD:datatypesChina201131SHOINSHION:China201132KnowledgeBaseSemanticsAninterpretation

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)+

RIChina201132KnowledgeBaseSemChina201133IsatisfiesaTboxT(I?T)iffIsatisfieseveryaxiomAinTAninterpretationIsatisfies(models)anAboxaxiomA(I?A):I?x:DiffxI

DI

I?<x,y>:Riff<xI,yI>RIIsatisfiesanAboxA(I?A)iffIsatisfieseveryaxiomAinAIsatisfiesanKBK(I?K)iffIsatisfiesbothTandAChina201133IsatisfiesaTboxChina201134ReasoningTasksforConceptChina201134ReasoningTasksfoChina201135ReductiontoSubsumptionChina201135ReductiontoSubsuChina201136ReductiontoUnsatisfiabilityChina201136ReductiontoUnsatChina201137ReducingUnsatisfiabilityThefollowingsareequivalent:China201137ReducingUnsatisfiChina201138描述邏輯系統(tǒng)命名規(guī)則DLNamingBasicdescriptionlogicisALC(equivmodalK(m))Conceptsconstructedusing?,?,,and

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

nR,≥

nR)Qforqualifiednumberrestrictions(ofform

nR.C,≥

nR.C)…China201138描述邏輯系統(tǒng)命名規(guī)則DLNaminChina201139DL-Lite:A“Scalable”DLFamilyRAtomicRole=>R,R-BasicRoleAAtomicConcept=>ABasicConcept,RAtomicRole=>RBasicConceptCBasicConcept=>C,CGeneralConceptRBasicRole=>R,RGeneralRoleChina201139DL-Lite:A“ScalabChina201140SimplifiedDL-LiteSyntaxRulesR->P|P-B->A|RC->B|BE->R|RWhereRisbasicrole,Pisatomicrole,Aisatomicconcept,Bisbasicconcept,Cisgeneralconcept,EisgeneralroleChina201140SimplifiedDL-LiteChina201141DL-LiteFamilyDL-LitecoreTboxisasetofinclusionaxiomsofthefromB?

CDL-LiteR=DL-Litecore+roleinclusionaxiomsofthefromR?

EDL-LiteF=DL-Litecore+functionalityonroleorontheirinversewiththeform(functR)China201141DL-LiteFamilyDL-LChina201142想一想：DL-Lite能不能表達(dá)下列描述?A1?

A2

?

CB?

C1

?

C2Disjoint(A,B)A1?

A2

?

CB?

C1

?

C2China201142想一想：DL-Lite能不能表達(dá)下China201143思考：描述邏輯的下一步擴(kuò)展？想一想，如果讓你對現(xiàn)有的描述邏輯的表達(dá)功能進(jìn)行擴(kuò)展，你將會添加一些什么？今天下午：描述邏輯與知識表示的專題討論為什么？如何對其進(jìn)行形式化描述？China201143思考：描述邏輯的下一步擴(kuò)展？想一想，China201144練習(xí)題思考題2.1：如何用描述邏輯來表示下列一些概念? “至少有一個(gè)女孩的女人” “沒有女孩的女人” “所有女孩都上學(xué)的女人” “有一個(gè)女孩不上學(xué)的女人”China201144練習(xí)題思考題2.1：如何用描述邏輯來China201145練習(xí)題思考題2.2用ALC語言能不能來表示下列一些概念?為什么？ “有3個(gè)女孩的女人” “最大的孩子是女孩的女人” “非女青年人” “所有的女兒都沒上學(xué)的女人”China201145練習(xí)題思考題2.2用ALC語言能不China201146練習(xí)題思考題2.3判斷下列一些公式哪些是滿足的，哪些是不可滿足的，哪些是永真的？

(R.

C)?

C(R.

C)?

R.C

(R.

C)?

R.C

(R.C)?

R.T.China201146練習(xí)題思考題2.3判斷下列一些公式China201147練習(xí)題思考題2.4.證明DL-LiteF不滿足有限模型性(FiniteModelProperty),并分析其問題特征。一個(gè)邏輯具有有限模型性則表明其任何一個(gè)公式集如果是可滿足的，那么必存在它的一個(gè)有限模型。China201147練習(xí)題思考題2.4.證明DL-LiChina201148語義網(wǎng)邏輯基礎(chǔ)演義第二回：本體為綱描述邏輯展頭角

概念當(dāng)先形式方法顯風(fēng)采

欲知后事如何，請聽下回分解。。。

China201148語義網(wǎng)邏輯基礎(chǔ)演義第二回：本體為綱描China201149QuestionsandDiscussionsChina201149QuestionsandDisc植入互聯(lián)網(wǎng)基因戴爾轉(zhuǎn)型電商China201151語義萬維網(wǎng)的邏輯基礎(chǔ)

LogicalFoundationoftheSemanticWeb主講：黃智生ZhishengHuangVrijeUniversityAmsterdam，TheNetherlandshuang@cs.vu.nl助教：胡青QingHuWuhanUniversityofScienceandTechnologyhuqing@China20111語義萬維網(wǎng)的邏輯基礎(chǔ)

LogicalChina201152課程時(shí)間表Schedule

時(shí)間上午9:30-11:30下午2:30-4:302011.8.22報(bào)到第一講：現(xiàn)代邏輯導(dǎo)論2011.8.23第二講：描述邏輯導(dǎo)論專題討論：描述邏輯與知識表示2011.8.24第三講：語義Web與邏輯I集體活動：遠(yuǎn)足或?qū)ｎ}研討會I2011.8.25第四講：語義Web與邏輯II第五講：本體推理與管理2011.8.26第六講：語義技術(shù)與應(yīng)用開發(fā)專題研討會II2011.8.27CCFYOCSEF論壇：Large-ScaleandScalableSemanticComputing2011.8.28首屆“語義技術(shù)與與生命科學(xué)”高峰論壇China20112課程時(shí)間表Schedule

時(shí)間上午9China201153描述邏輯是什么？描述邏輯基本系統(tǒng)描述邏輯種類描述邏輯實(shí)例

講座2：描述邏輯導(dǎo)論

Lecture2:IntroductiontoDescriptionLogics

China20113描述邏輯是什么？

講座2：描述邏輯導(dǎo)China201154描述邏輯是一類知識表示語言表達(dá)應(yīng)用領(lǐng)域的概念定義（有可以被看作為專業(yè)術(shù)語知識）Descriptionlogics(DL)areafamilyofknowledgerepresentationlanguageswhichcanbeusedtorepresenttheconceptdefinitionsofanapplicationdomain(knownasterminologicalknowledge)描述邏輯是什么？

WhatareDescriptionLogics?China20114描述邏輯是一類知識表示語言表達(dá)應(yīng)用領(lǐng)域China201155描述邏輯簡史ABriefHistoryofDescriptionLogicsMajorfocusofKRresearchinthe80’sLedbyRonBrachman–(AT&TLabs)Grewoutofearlynetwork-basedKRsystemslikesemanticnetworksandframes.Majorsystemsandlanguages–80s:KL-ONE,NIKL,KANDOR,BACK,CLASSIC,LOOM90s:FACT,RACER,00s:DAML+OIL,OWLUsedasthebasisfortheSemanticweblanguagesDAML+OILandOWLSome(one)commercialsystemsChina20115描述邏輯簡史MajorfocusoChina201156概念與本體

ConceptsandOntologiesPhilosophicaldiscipline,branchofphilosophythatdealswiththenatureandtheorganisationofreality.ScienceofBeing(Aristotle,Metaphysics,IV,1)Whatisbeing?Whatarethefeaturescommontoallbeings?China20116概念與本體

ConceptsandChina201157VocabularyandOntology

Controlledvocabulary(Jernst2003):alistofcontrolledtermsunambiguousnon-redundantdefinitionOntology:acontrolledvocabularyexpressedinanontologyrepresentationlanguage(Jernst2003)China20117VocabularyandOntoChina201158Incomputerscience…Anontologyisanexplicitspecificationofaconceptualization.[Gruber93]Anontologyisasharedunderstandingofsomedomainofinterest.[Uschold,Gruninger96]TherearemanydefinitionsaformalspecificationEXECUTABLEofaconceptualizationofadomainCOMMUNITYofsomepartofworldthatisofinterestAPPLICATIONDefinesAcommonvocabularyoftermsSomespecificationofthemeaningofthetermsAsharedunderstandingforpeopleandmachinesChina20118IncomputerscienceChina201159Whydevelopanontology?TomakedomainassumptionsexplicitEasiertochangedomainassumptionsEasiertounderstandandupdatelegacydataToseparatedomainknowledgefromoperationalknowledgeRe-usedomainandoperationalknowledgeseparatelyAcommunityreferenceforapplicationsToshareaconsistentunderstandingofwhatinformationmeans.China20119WhydevelopanontoChina201160本體的主要特征

KeyfeaturesofanOntology概念層次性Concepthierarchy,概念包含關(guān)系conceptsubsumption特殊與一般關(guān)系

InstanceOfRelation(Instances)部分與整體關(guān)系

PartOfRelation(property)China201110本體的主要特征

KeyfeaturChina201161Whynototheralternatives一階謂詞邏輯thefirst-orderpredicatelogic集合論settheory程序語言programminglanguagesChina201111WhynototheralteChina201162概念與分類設(shè)定存在一個(gè)所有個(gè)體（Individual）的集合一個(gè)概念被看成是一個(gè)個(gè)體的集合（Setofindividuals）定義一個(gè)概念就是確定一個(gè)分類概念集合與個(gè)體集合是不相交的個(gè)體上的一個(gè)二元關(guān)系集合被稱為一個(gè)性質(zhì)（Property/Role)China201112概念與分類設(shè)定存在一個(gè)所有個(gè)體（InChina201163復(fù)合概念概念的否定，交與并CDCDChina201113復(fù)合概念概念的否定，交與并CDCChina201164描述邏輯

DescriptionLogicKnowledgeBaseTbox(schema)術(shù)語部分Abox(data)斷言部分Man

Human?MaleHappy-FatherMan?

has-childFemale?

…John:Happy-Father<John,Mary>:has-childInferenceSystemInterfaceChina201114描述邏輯DescriptionLChina201165描述邏輯

DescriptionLogicKnowledgeBaseTbox(schema)術(shù)語部分Abox(data)斷言部分InferenceSystemInterfaceRbox(data)關(guān)系部分Has-daughter?

has-childChina201115描述邏輯DescriptionLChina201166BasicDescriptionLogic:

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,andRisaroleexpressionChina201116BasicDescriptionChina201167FamilyofAL-LanguageU:C?

D(交union)E:R.C(完全存在量化fullexistentialquantification)N:

(數(shù)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

China201117FamilyofAL-LanguChina201168Exampleswoman≡person?femaleman≡person?

womanmother≡woman?

hasChild.personfather≡man?

hasChild.personChina201118Exampleswoman≡peChina201169一個(gè)實(shí)例Examplewhitehorse≡horse?white.color(white).whitehorse≡horse?hasColor.{white}.這里white是一個(gè)列名（nominal）whitehorse≡horse?hasColor.{white}?

hasColor.{white}.China201119一個(gè)實(shí)例ExamplewhitehoChina201170AL句法規(guī)則，ALpAtomicConcept=>pAL，pAtomicConcept=>

pAL，C，DAL=>C?

DAL，CAL,RRole=>R.CAL,RRole=>R.TALChina201120AL句法規(guī)則，ALChina201171描述邏輯的語義模型一個(gè)描述邏輯語言DL上的一個(gè)語義模型M=(S,{R1,R2,…Rn},V)這里S是所有可能個(gè)體（Individual)的集合RiSXS是一個(gè)S上的二元關(guān)系V：P->

PowerSet(S)是一個(gè)賦值函數(shù)，它給一個(gè)原子概念賦予S的一個(gè)子集。China201121描述邏輯的語義模型一個(gè)描述邏輯語言DChina201172對照：模態(tài)邏輯的語義模型命題模態(tài)邏輯語言L上的一個(gè)語義模型M=(S,A,V)這里S是可能世界的集合ASXS是一個(gè)可達(dá)世界的關(guān)系V：P->

PowerSet(S)是一個(gè)賦值函數(shù)，它給一個(gè)原始命題賦予一個(gè)可能世界子集。所以說，一個(gè)描述邏輯實(shí)質(zhì)上就是一個(gè)多模態(tài)邏輯China201122對照：模態(tài)邏輯的語義模型命題模態(tài)邏輯China201173描述邏輯AL的真值條件M，s|=pifsV(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對應(yīng)的真值條件是什么China201123描述邏輯AL的真值條件M，s|=China201174DLSemanticsSemanticsdefinedbyinterpretations

AninterpretationI=(DI,.I),where

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

subsetAIofDIRole(property)nameR

binaryrelationRIoverDIIndividualnamei

iIelementofDIChina201124DLSemanticsSemantChina201175DLSemantics(cont.)Interpretationfunction￠Iextendstoconcept(androle)expressions

intheobviousway,e.g.:China201125DLSemantics(contChina201176規(guī)范的AL語義{x}I={xI}{p}I=S/pI{C?D}I={C}I{D}I{R.C}I={x|y(<x,y>RI=>yCI}這里I被稱作一個(gè)解釋（Interpretation

），實(shí)質(zhì)上就是一個(gè)模型。China201126規(guī)范的AL語義{x}I={xI}China201177Axiomsdefinerelationsbetweenconcepts

概念包含（Subsumption）:C?

DiffCIDI

定義：概念相等(Equivalence):C

DiffC?

D

而且D

?

C

概念不相交（Disjointness）:C?D

China201127AxiomsdefinerelaChina201178GeneralConceptInclusionExpressivitywithGCIsDisjointness:C?D?

Identity:{a}?Distinctiveness:{a}??

China201128GeneralConceptInChina201179DLKnowledgeBaseADLKnowledgebase

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,DaconceptandRaroleChina201129DLKnowledgeBaseAChina201180MoreaboutFamilyofALLanguageAdditionallettersindicateotherextension,e.g.:Hforroleinclusionaxioms(rolehierarchy)Ofornominals(singletonclasses,written{x})IforinverserolesQforqualifiednumberrestrictions(ofform

nR.C,≥

nR.C)SoftenusedforALCwithtransitiveroles(R+)SHIQ:ALC+R++rolehierarchy+inverseroles+QChina201130MoreaboutFamilyChina201181SHOINSHION:S:ALC+roletransitivityH:rolehierarchiesO:nominalsI:InverserolesN:cardinalityrestrictionSHOIN(D)=OWL-DLD:datatypesChina201131SHOINSHION:China201182KnowledgeBaseSemanticsAninterpretation

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)+

RIChina201132KnowledgeBaseSemChina201183IsatisfiesaTboxT(I?T)iffIsatisfieseveryaxiomAinTAninterpretationIsatisfies(models)anAboxaxiomA(I?A):I?x:DiffxI

DI

I?<x,y>:Riff<xI,yI>RIIsatisfiesanAboxA(I?A)iffIsatisfieseveryaxiomAinAIsatisfiesanKBK(I?K)iffIsatisfiesbothTandAChina201133IsatisfiesaTboxChina201184ReasoningTasksforConceptChina201134ReasoningTasksfoChina201185ReductiontoSubsumptionChina201135ReductiontoSubsuChina201186ReductiontoUnsatisfiabilityChina201136ReductiontoUnsatChina201187ReducingUnsatisfiabilityThefollowingsareequivalent:China201137ReducingUnsatisfiChina201188描述邏輯系統(tǒng)命名規(guī)則DLNamingBasicdescriptionlogicisALC