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1、China 20111语义万维网的逻辑基础 Logical Foundation of the Semantic Web主讲：黄智生 Zhisheng HuangVrije University Amsterdam，The Netherlandshuangcs.vu.nl助教：胡青 Qing HuWuhan University of Science and T China 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
2、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II2011.8.27CCF YOCSEF论坛：Large-Scale and Scalable Semantic Computing 2011.8.28首届“语义技术与与生命科学”高峰论坛China 20113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Lecture 2:Introduction to Description LogicsChina 20114描述逻辑是一类知识表示语言表达应
3、用领域的概念定义（有可以被看作为专业术语知识）Description logics(DL)are a family of knowledge representation languages which can be used to represent the concept definitions of an application domain(known as terminological knowledge)描述逻辑是什么？What are Description Logics?China 20115描述逻辑简史A Brief History of Description Logics
4、Major focus of KR research in the 80sLed by Ron Brachman (AT&T Labs)Grew out of early network-based KR systems like semantic networks and frames.Major systems and languages 80s:KL-ONE,NIKL,KANDOR,BACK,CLASSIC,LOOM90s:FACT,RACER,00s:DAML+OIL,OWLUsed as the basis for the Semantic web languages DAML+OI
5、L and OWLSome(one)commercial systemsChina 20116概念与本体Concepts and OntologiesPhilosophical discipline,branch of philosophy that deals with the nature and the organisation of reality.Science of Being(Aristotle,Metaphysics,IV,1)What is being?What are the features common to all beings?China 20117Vocabula
6、ry and Ontology Controlled vocabulary(Jernst 2003):a list of controlled termsunambiguousnon-redundant definitionOntology:a controlled vocabulary expressed in an ontology representation language(Jernst 2003)China 20118In computer science An ontology is an explicit specification of a conceptualization
7、.Gruber93An ontology is a shared understanding of some domain of interest.Uschold,Gruninger96There are many definitionsa formal specification EXECUTABLEof a conceptualization of a domain COMMUNITYof some part of world that is of interest APPLICATIONDefinesA common vocabulary of termsSome specificati
8、on of the meaning of the termsA shared understanding for people and machinesChina 20119Why develop an ontology?To make domain assumptions explicitEasier to change domain assumptionsEasier to understand and update legacy dataTo separate domain knowledge from operational knowledgeRe-use domain and ope
9、rational knowledge separatelyA community reference for applicationsTo share a consistent understanding of what information means.China 201110本体的主要特征Key features of an Ontology概念层次性Concept hierarchy,概念包含关系concept subsumption特殊与一般关系 InstanceOf Relation(Instances)部分与整体关系 PartOf Relation(property)China
10、201111Why not other alternatives一阶谓词逻辑 the first-order predicate logic集合论 set theory程序语言 programming languagesChina 201112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（Set of individuals）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)China 201113复合概念复合概念q概念的否定，交 与并CDC DChina 201114描述逻
11、辑 Description LogicKnowledge BaseTbox(schema)术语部分Abox(data)断言部分Man Human MaleHappy-Father Man has-child Female John:Happy-Father:has-childInference SystemInterfaceChina 201115描述逻辑 Description LogicKnowledge BaseTbox(schema)术语部分Abox(data)断言部分Inference SystemInterfaceRbox(data)关系部分Has-daughter has-chi
12、ld China 201116Basic Description Logic:AL（Attributive Language）Concept Expressions:A(原子概念atomic concept)(全概念，universal concept)(空概念，bottom concept)A(原子否定，atomic negation)C D(并，intersection)R.C(值限制，value restriction)R.T(有限存在量化limited existential quantification)where A is a concept name,C and D are co
13、ncept expressions,and R is a role expressionChina 201117Family of AL-LanguageU:C D (交union)E:R.C(完全存在量化full existential quantification)N:(数量限制Number restrictions)(n R)(至少限制at least restriction)(n R)(最多限制at most restriction)C:(Negation):CALEN=AL+E+N Smallest propositionally closed DL is ALC(equiv mod
14、al K(m)=AL+CConcepts constructed using,and China 201118Exampleswoman person femaleman person womanmother woman hasChild.personfather man hasChild.personChina 201119一个实例Examplewhitehorse horse white.color(white).whitehorse horse hasColor.white.这里white是一个列名（nominal）whitehorse horse hasColor.white hasC
15、olor.white.China 201120AL句法规则，ALp AtomicConcept =p AL，p AtomicConcept =p AL，C，D AL=C D AL，C AL,R Role=R.C AL,R Role =R.T ALChina 201121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。China 201122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
16、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China 201123描述逻辑AL的真值条件M，s|=p if s V(p)M，s|=p iff M,s|=pM，s|=C D iff M,s|=C and M,s|=D M，s|=R.C iff M,s|=C for all s such that R想想看：，R.T 对应的真值条件是什么China 201124DL SemanticsSemantics defined by interpr
17、etations An interpretation I=(DI,.I),where DI is the domain(a non-empty set).I is an interpretation function that maps:Concept(class)name A subset AI of DIRole(property)name R binary relation RI over DIIndividual name i iI element of DIChina 201125DL Semantics(cont.)Interpretation function I extends
18、 to concept(and role)expressions in the obvious way,e.g.:China 201126规范的AL语义xI=xIp I=S/pIC D I=C I DIR.CI=x|y(RI=y CI这里I被称作一个解释（Interpretation），实质上就是一个模型。China 201127Axioms define relations between concepts概念包含（Subsumption）:C D iff CI DI 定义：概念相等(Equivalence):C D iff C D 而且 D C 概念不相交（Disjointness）:C
19、D China 201128General Concept Inclusion Expressivity with GCIsDisjointness:C D Identity:a b Distinctiveness:a b China 201129DL Knowledge BaseA DL Knowledge base K is a pair whereT is a set of“terminological”axioms(the Tbox)A is a set of“assertional”axioms(the Abox)Tbox axioms are of the form:C D,C D
20、,R S,R S and R+Rwhere C,D concepts,R,S roles,and R+set of transitive rolesAbox axioms are of the form:x:D,:Rwhere x,y are individual names,D a concept and R a roleChina 201130More about Family of AL LanguageAdditional letters indicate other extension,e.g.:H for role inclusion axioms(role hierarchy)O
21、 for nominals(singleton classes,written x)I for inverse rolesQ for qualified number restrictions(of form nR.C,nR.C)S often used for ALC with transitive roles(R+)SHIQ:ALC+R+role hierarchy+inverse roles+QChina 201131SHOINSHION:S:ALC+role transitivityH:role hierarchiesO:nominalsI:Inverse rolesN:cardina
22、lity restrictionSHOIN(D)=OWL-DLD:datatypesChina 201132Knowledge Base SemanticsAn interpretation I satisfies(models)a Tbox axiom A,(I A):I C D iff CI DI I C D iff CI=DII R S iff RI SI I R S iff RI=SII R+R iff(RI)+RIChina 201133I satisfies a Tbox T (I T)iff I satisfies every axiom A in T An interpreta
23、tion I satisfies(models)an Abox axiom A(I A):I x:D iff xI DI I :R iff RII satisfies an Abox A(I A)iff I satisfies every axiom A in A I satisfies an KB K(I K)iff I satisfies both T and AChina 201134Reasoning Tasks for ConceptChina 201135Reduction to SubsumptionChina 201136Reduction to Unsatisfiabilit
24、yChina 201137Reducing UnsatisfiabilityThe followings are equivalent:China 201138描述逻辑系统命名规则DL NamingBasic description logic is ALC(equiv modal K(m)Concepts constructed using,and S often used for ALC with transitive rolesAdditional letters indicate other extension,e.g.:H for role inclusion axioms(role
25、 hierarchy)O for nominals(singleton classes,written x)I for inverse rolesN for number restrictions(of form n R,n R)Q for qualified number restrictions(of form n R.C,n R.C)China 201139DL-Lite:A“Scalable”DL FamilyR AtomicRole=R,R-BasicRoleA AtomicConcept=A BasicConcept,R AtomicRole=R BasicConceptC Bas
26、icConcept=C,C GeneralConceptR BasicRole=R,R GeneralRoleChina 201140Simplified DL-Lite Syntax RulesR-P|P-B-A|RC-B|BE-R|RWhere R is basic role,P is atomic role,A is atomic concept,B is basic concept,C is general concept,E is general roleChina 201141DL-Lite FamilyDL-Litecore Tbox is a set of inclusion
27、axioms of the from B C DL-LiteR =DL-Litecore+role inclusion axioms of the from R EDL-LiteF =DL-Litecore+functionality on role or on their inverse with the form(funct R)China 201142想一想：DL-Lite能不能表达下列描述?A1 A2 C B C1 C2Disjoint(A,B)A1 A2 C B C1 C2China 201143思考：描述逻辑的下一步扩展？想一想，如果让你对现有的描述逻辑的表达功能进行扩展，你将会添
28、加一些什么？今天下午：描述逻辑与知识表示的专题讨论为什么？如何对其进行形式化描述？China 201144练习题思考题2.1：如何用描述逻辑来表示下列一些概念?“至少有一个女孩的女人”“没有女孩的女人”“所有女孩都上学的女人”“有一个女孩不上学的女人”China 201145练习题思考题2.2 用ALC语言能不能来表示下列一些概念?为什么？“有3个女孩的女人”“最大的孩子是女孩的女人”“非女青年人”“所有的女儿都没上学的女人”China 201146练习题思考题2.3 判断下列一些公式哪些是满足的，哪些是不可满足的，哪些是永真的？(R.C)C (R.C)R.C(R.C)R.C(R.C)R.T.China 201147练习题思考题2.4.证明DL-LiteF不满足有限模型性(FiniteModel Property),并分析其问题特征。一个逻辑具有有限模型性 则表明其任何一个公式集如果是可满足的，那么必存在它的一个有限模型。China 201148语义网逻辑基础演义第二回：本体为纲描述逻辑展头角 概念当先形式方法显风采 欲知后事如何，请听下回分解。China 201149Questions and Discussions