Metamodeling Architecture of Web Ontology Languages

Transcription

1 Meamodeling Archiecure of Web Onology Languages Jeff Z. Pan and Ian Horrocks Informaion Managemen Group Deparmen of Compuer Science Universiy of Mancheser Oxford Road Mancheser M13 9PL, UK Absrac. Recen research has shown ha RDF Schema, as a schema layer Semanic Web language, has a non-sandard meamodeling archiecure. As a resul, i is difficul o undersand and lacks clear semanics. This paper 1 proposes RDFS(FA) (RDFS wih Fixed meamodeling Archiecure) and demonsraes how he problems of RDF Schema can be solved under RDFS(FA). Based on he fixed meamodeling archiecure, a clear model-heoreic semanics of RDFS(FA) is given. Ineresingly, RDFS(FA) also benefis DAML+OIL by offering a firm semanic basis and by solving he layer misake problem. 1 Inroducion The Semanic Web, wih is vision saed by Berners-lee [1], aims a developing languages for expressing informaion in a machine undersandable form. The recen explosion of ineres in he World Wide Web has also fuelled ineres in onologies. I has been prediced (Broeksra e al. [3]) ha onologies will play a pivoal role in he Semanic Web since onologies can provide shared domain models, which are undersandable o boh human being and machines. Onology (Uschold and Gruninger [21]) is, in general, a represenaion of a shared concepualisaion of a specific domain. I provides a shared and common undersanding of a domain ha can be communicaed beween people and heerogeneous and disribued applicaion sysems. An onology necessarily enails or embodies some sor of world view wih respec o a given domain. The world view is usually conceived as a hierarchical descripion of imporan conceps (is-a hierarchy), a se of crucial properies, and heir iner-relaionships. Berners-lee [1] oulined he archiecure of Semanic Web. We would like o call i a funcional archiecure because he expressive primiives are incremenally inroduced from languages in he lowes layer (i.e. meadaa layer) o hose in he higher layer (e.g. logical layer), so ha he languages in each layer can saisfy he requiremens of differen kinds (or levels) of applicaions: 1. In he meadaa layer, a simple and general model of semanic asserions of he Web is inroduced. The simple model conains jus he conceps of resource and propery, which are used o express he mea informaion and will be needed by languages in he upper layers. The Resource Descripion Framework (RDF) (Lassila and R.Swick [14]) is believed o be he general model in meadaa layer. 1 Also available a hp://img.cs.man.ac.uk/jpan/zhilin/download/paper/pan-horrocks-rdfsfa-2001.pdf

2 2. In he schema layer, simple Web onology languages are inroduced, which will define a hierarchical descripion of conceps (is-a hierarchy) and properies. These languages use he general model in meadaa layer o define he basic meamodeling archiecure of Web onology languages. RDF Schema (RDFS) (Brickley and Guha [2]) is a candidae schema layer language. 3. In he logical layer, more powerful Web onology languages are inroduced. These languages are based on he basic meamodeling archiecure defined in schema layer, and defines a much richer se of modelling primiives ha can e.g. be mapped o very expressive Descripion Logics (Horrocks e al. [11], Horrocks [10]) o supply reasoning services for he Semanic Web. OIL (Horocks e al. [9]) and DAML+OIL (van Harmelen e al. [23]) are well known logical layer languages. This paper will focus on he meamodeling archiecure oher han he funcional archiecure. We should poin ou ha meamodeling and he meadaa layer in he funcional archiecure are no he same. Meadaa means daa abou daa. Meamodeling concerns he definiion of he modelling primiives (vocabulary) used in a modelling language. Many sofware engineering modelling languages, including UML, are based on meamodels. Among he Semanic Web languages, he schema layer languages are responsible o build he meamodeling archiecure. In his paper, we argue ha RDFS, as a schema layer language, has a non-sandard and non-fixed layer meamodeling archiecure, which makes some elemens in he model have dual roles in he RDFS specificaion (Nejdl e al. [17]). Therefore, i makes he RDFS specificaion iself quie difficul o undersand by he modellers. The even worse hing is ha since he logical layer languages (e.g. OIL, DAML+OIL) are all based on he meamodeling archiecure defined by schema layer languages (RDFS), hese languages herefore have he similar problems, e.g. he layer misake discussed in Secion 2.3. We propose RDFS(FA) (RDFS wih Fixed meamodeling Archiecure), which has a meamodeling archiecure similar o ha of UML. We analyse he problems of he non-fixed meamodeling archiecure of RDFS and demonsrae how hese problems can be solved under RDFS(FA). Furhermore, We give a clear model heoreic semanics o RDFS(FA). The res of he paper is organized as follows. In Secion 2 we explain he daa model of RDF, RDFS and DAML+OIL, he languages belonging o he meadaa level, schema level and logical level of he Semanic Web Archiecure respecively. We will focus on he meamodeling archiecure of RDFS and locae wha he problems are and where hey come from. In Secion 3 we discuss he advanages and disadvanages of fixed and non-fixed layer meamodeling archiecure and hen briefly explain he meamodeling archiecure of UML. In Secion 4 we propose RDFS(FA), and give a clear semanics o RDFS(FA). We also demonsrae how he layer misake problem wih DAML+OIL is solved in RDFS(FA). Secion 5 briefly discuss he advanages of RDFS(FA) and our aiudes on how o make use of UML in he Web onology languages. 2 Curren Daa Models of Semanic Web Languages 2.1 RDF Daa Model As a Semanic Web language in he meadaa layer of he funcional archiecure, RDF is a foundaion for processing meadaa. I provides ineroperabiliy beween applicaions ha exchange machineundersandable informaion on he Web. The foundaion of RDF is a model for represening named properies and propery values. The RDF daa model provides an absrac, concepual framework for defining and using meadaa. The basic daa model consiss of hree objec ypes: Resources: All hings being described by RDF expressions are called resources. A resource may be an enire Web page, a par of a Web page, a whole collecion of pages (Web sie); or an objec ha is no direcly accessible via he Web, e.g. a prined book. Resources are always named by URIs.

3 Properies: A propery is a specific aspec, characerisic, aribue, or relaion used o describe a resource. Saemens: A specific resource ogeher wih a named propery plus he value of ha propery for ha resource is an RDF saemen. hp://img.cs.man.ac.uk/memberlis#jpan Homepage Creaor hp://img.cs.man.ac.uk/jpan/zhilin Tile Home Page of Jeff Z. Pan Figure 1: An Example of RDF in a Direced Labeled Graph In a nushell, he RDF daa model is an objec-propery-value mechanism. The meadaa informaion is inroduced by a se of saemens in RDF. There are several ways o express RDF saemens. Firs, we can use he binary predicae form Propery(objec,value), e.g. Tile( hp://img. cs.man.ac.uk/jpan/zhilin, Home Page of Jeff Z. Pan ). Secondly, we can diagram an RDF saemen picorially using direced labeled graphs: [objec ]-Propery->[value] (see Figure 1). Thirdly, RDF uses an Exensible Markup Language (XML) encoding as is inerchange synax: <rdf:descripion rdf:id="hp://img.cs.man.ac.uk/jpan/zhilin"> <Tile>Home Page of Jeff Z. Pan</Tile> The RDF daa model is so called propery-cenric. We can use he abou aribue o add more properies o he exising resource. Generally speaking, wih he objec-propery-value mechanism, RDF can be used o express: aribues of resources: in his case, he value is a lieral (e.g he Tile propery above); relaionships beween any wo resources: in his case, he value is a resource, and he involved properies represen differen roles of he wo resources wih his relaionship; in he following example, here exiss a creaor-homepage relaionship beween hp://img.cs.man.ac.uk/jpan/zhilin and hp://img.cs.man.ac.uk/memberlis#jpan (see also Figure 1): <rdf:descripion rdf:id="hp://img.cs.man.ac.uk/memberlis#jpan"> <Homepage rdf:resource="hp://img.cs.man.ac.uk/jpan/zhilin"/> <rdf:descripion abou="hp://img.cs.man.ac.uk/jpan/zhilin"> <Creaor rdf:resource="hp://img.cs.man.ac.uk/memberlis#jpan"/> weak ype of resources: he ype is weak because RDF iself has no sandard way o define a Class, so he ype here is regarded only as a special aribue; for example, <rdf:descripion abou="hp://img.cs.man.ac.uk/memberlis#jpan"> <rdf:ype rdf:resource="#person"/> saemen abou saemen: RDF can be used for making saemens abou oher RDF saemens, which are referred o as higher-order saemens. This feaure of RDF has ye o be clearly defined and is beyond he scope of his paper.

4 2.2 RDF Schema Daa Model As we have seen, on he one hand, RDF daa model is enough for defining and using meadaa. On he oher hand, he modelling primiives offered by RDF are very basic. Alhough you can define Class and subclassof as resources in RDF (no one can sop you doing ha), RDF provides no sandard mechanisms for declaring classes and (global) properies, nor does i provide any mechanisms for defining he relaionships beween properies or beween classes. Tha is he role of RDFS a Semanic Web language in he schema layer. RDFS is expressed by using RDF daa model. I exends RDF by giving an exernally specified semanics o specific resources. In RDFS, rdfs:class is used o define conceps, i.e. every class mus be an insance of rdfs:class. Resources ha are described by RDF expressions are viewed o be insances of he class rdfs:resource. The class rdf:propery is he class of all properies used o characerise insances rdfs:resource. The rdfs:consrainresource defines he class of all consrains. The rdfs:consrainpropery is a subse of rdfs:consrainresource and rdf:propery, all of is insances are properies used o specify consrains, e.g. rdfs:domain and rdfs:range. For example, he following RDFS expressions <rdfs:class rdf:id="animal"> <rdfs:commen>this class of animals is illusraive of a number of onological idioms. </rdfs:class> <rdfs:class rdf:id="person"> <rdfs:subclassof rdf:resource="#animal"/> </rdfs:class> <rdf:descripion rdf:id="john"> <rdf:ype rdf:resource="#person"/> <rdfs:commen>john is a person. <rdf:descripion rdf:id="mary"> <rdf:ype rdf:resource="#person"/> <rdfs:commen>mary is a person. define he classes Animal and Person, wih he laer being he subclass of he former, and wo individuals John and Mary, which are insances of he class Person. Individual John can also be defined in his way, <Person rdf:id="john"> <rdfs:commen>john is a person. </Person> which is an implici way o define rdf:ype propery. Noe ha here Person is a class. Figure 2 picures he subclass-of and insance-of hierarchy of RDFS: rdfs:resource, rdfs:class, rdf:propery, rdfs:consrainresource and rdfs:consrainpropery are all insances of rdfs:class, while rdfs:class, rdf:propery and rdfs:consrainresource are subclass of rdfs:resource. I is confusing ha rdfs:class is a sub-class of rdfs:resource, while rdfs:resource iself is an insance of rdfs:class a he same ime. I is also srange ha rdfs:class is an insance of iself. In RDFS, all properies are insances of rdf:propery. The rdf:ype propery models insance-of relaionships beween resources and classes. The rdfs:subclassof propery models he subsumpion hierarchy beween classes, and is ransiive. The rdfs:subproperyof propery models he subsumpion hierarchy beween properies, and is also ransiive. The rdfs:domain and rdfs:range properies are used o resric domain and range properies. For example, he following RDFS expressions <rdf:propery rdf:id="hasfriend">

5 rdfs:resource rdfs:subclassof d r s s s rdfs:class rdfs:consrainresource r r d d rdfs:subproperyof d r rdfs:propery rdfs:domain s rdfs:range rdfs:lieral rdfs:consrainpropery s rdf:ype r =rdf:ype d=rdfs:domain s=rdfs:subclassof r=rdfs:range Figure 2: Direced Labeled Graph of RDF Schema rdfs:class s rdfs:resource s Animal s rdf:propery s=rdfs:subclassof =rdf:ype r=rdfs:range d=rdfs:domain John s Person hasfriend d r Mary hasfriend Figure 3: A Person hasfriend Example of RDF Schema <rdfs:domain rdf:resource="#person"/> <rdfs:range rdf:resource="#person"/> </rdf:propery> <rdf:descripion abou="#john"> <hasfriend rdf:resource="#mary"/> define a propery hasfriend beween wo Person s and John, Mary is an insance of has- Friend (see Figure 3). In RDFS, properies are regarded as ses of binary relaionships beween insances of classes, e.g. a propery hasfriend is a se of binary uples beween wo insances of he class Person. One excepion is he rdf:ype, since i is jus he insance-of relaionship. In his sense, rdf:ype is regarded as a special predefined propery. Figure 2 also shows he range and domain consrains in RDFS rdfs:domain and rdfs:range can be used o specify he wo classes ha a cerain propery can associae wih. So he rdfs:domain of rdfs:domain and rdfs:range is he class rdf:propery, he rdfs:range of rdfs:domain and rdfs:range is he class rdfs:class. The rdfs:domain and rdfs:range of rdfs:subclassof is rdfs:class. The rdfs:domain and rdfs:range of rdfs:subproperyof is rdf:propery. The rdfs:range of rdf:ype is he class rdfs:class. The rdf:ype propery is regarded as a se of binary links beween insances and classes (as menioned above), while he value of he rdfs:domain propery should be a class, herefore rdf:ype does no have he rdfs:domain propery (cf. Brickley and Guha [2]). As we have seen, RDFS use some primiive modelling primiives o define oher modelling prim-

6 iives (e.g. rdf:ype, rdfs:domain, rdfs:range, rdf:ype and rdfs:subclassof). A he same ime, hese primiives can be used o define onologies as well, which makes i raher unique when compared o convenional model and meamodeling approaches, and makes he RDFS specificaion very difficul o read and o formalise (Nejdl e al. [17], Broeksra e al. [3]). For example, in Figure 3, i is confusing ha alhough rdfs:class is he rdf:ype of Animal, boh Animal and rdfs:class are rdfs:subclassof rdfs:resource, where rdfs:class is a modelling primiive and Animal is an user-defined onology class. 2.3 DAML+OIL Daa Model DAML+OIL is an expressive Web onology language in he logical layer. I builds on earlier W3C sandards such as RDF and RDFS, and exends hese languages wih much richer modelling primiives. DAML+OIL inheris many aspecs from OIL, and provides modelling primiives commonly found in frame-based languages. I has a clean and well defined semanics based on descripion logics. A complee descripion of he daa model of DAML+OIL is beyond he scope of his paper. However, we will illusrae how DAML+OIL exends RDFS by inroducing some new subclasses of rdfs:class and rdf:propery. One of he mos imporan classes ha DAML+OIL inroduces is daml:daaype. DAML+OIL divides he universe ino wo disjoin pars, he objec domain and he daaype domain. The objec domain consis of objecs ha are members of classes described in DAML+OIL. The daaype domain consiss of he values ha belong o XML Schema daaypes. Boh daml:class (objec class) and daml:daaype are rdfs:subclassof rdfs:class. Accordingly, properies in DAML+OIL should be eiher objec properies, which relae objecs o objecs and are insances of daml:objecpropery; or daaype propery, which relae objecs o daaype values and are insances of daml:daaype- Propery. Boh daml:objecpropery and daml:daaypepropery are rdfs:subclassof rdf:pro- pery. For example, we can define a daaype propery called birhday : <daml:daaypepropery rdf:id="birhday"> <rdf:ype rdf:resource="hp:// <rdfs:domain rdf:resource="#animal"/> <rdfs:range rdf:resource="hp:// </daml:daaypepropery> Besides being an insance of daml:daaypepropery, he birhday propery is also an insance of daml:uniquepropery, which means ha birhday can only have one (unique) value for each insance of he Animal class. In fac, daml:uniquepropery is so useful ha some people even wan o use i o refine DAML+OIL predefined properies, e.g. daml:maxcardinaliy: <rdf:propery rdf:abou="#maxcardinaliy"> <rdf:ype rdf:resource="hp:// </rdf:propery> This saemen seems obviously righ, however, i is wrong because he semanics of daml:uniquepropery requires ha only he onology properies can be regarded as is insances (cf. van Harmelen e al. [22]). This is he so called layer misake. The reason ha people can easily make he above layer misake lies in he fac ha he schema layer language RDFS doesn disinguish he modelling informaion in he onology level and ha in he language level. Anoher example is wha we had menioned before in Figure 3, i is no appropriae ha boh rdfs:class and Animal are rdfs:subclassof rdfs:resource. I is he exisence of he dual roles of some RDFS modelling elemens, e.g. rdfs:subclassof, ha makes RDFS have unclear semanics. This parially explains why Brickley and Guha [2] didn define he semanics of RDFS. We should sress ha DAML+OIL is buil on op of he synax of RDFS, bu

7 no he semanics of RDFS. On he conrary, RDFS relies on DAML+OIL o give semanics o is modelling primiives. In oher words, DAML+OIL no only defines he semanics of is newly inroduced modelling primiives, e.g. daml:uniquepropery, daml:maxcardinaliy ec., bu also he modelling primiives of RDFS, e.g. rdfs:subclassof, rdfs:subproperyof, rdfs:domain, rdfs:range ec (van Harmelen e al. [22]). This breaks he dependency beween logical layer languages and schema layer languages and indicaes ha RDFS is no ye a fully qualified schema layer Semanic Web language. 3 Fixed or Non-fixed Meamodeling Archiecure? 3.1 The Advanages and Disadvanages of Non-fixed Meamodeling Archiecure The dual roles of some RDFS modelling elemens indicae ha somehing migh be wrong wih he meamodeling archiecure of RDFS. The RDFS has a non-fixed meamodeling archiecure, which means ha i can have possibly infinie layers of classes. The advanage is ha i makes iself compac. However, i has a leas he following hree disadvanages or problems: 1. The class rdfs:class is an insance of iself. Usually, a class is regarded as a se, and an insance of he class is a member of he se. A Class of classes can be inerpreed as a se of ses, which means is members are ses. In RDFS, all classes (including rdfs:class) are insances of rdfs:class, which is suspicious by close o Russell paradox. The paradox arises when considering he se of all ses ha are no members of hemselves. Such a se appears o be a member of iself if and only if i is no a member of iself, hence he paradox. 2. The class rdfs:resource is a superclass and insance of rdfs:class a he same ime, which means ha he super se (rdfs:resource) is a member of he subse (rdfs:class). 3. The properies rdfs:subclassof, rdf:ype, rdfs:range and rdfs:domain are used o define boh he oher RDFS modelling primiives and he onology, which makes heir semanics unclear and makes i very difficul o formalise RDFS. E.g. i is no clear ha he semanic of rdfs:subclassof is a se of binary relaionships beween wo ses of objecs or a se of binary relaionships beween wo ses of ses of objecs, or else. As a resul, RDFS has no clear semanics, i even rely on DAML+OIL o give iself semanics, which makes RDFS a no so saisfacory schema layer semanic Web language. 3.2 The Advanages and Disadvanages of Fixed Meamodeling Archiecure We can demonsrae he advanages of fixed meamodeling archiecure by showing how he problems of RDF Schema menioned in Secion 3.1 are solved under he fixed meamodeling archiecure. The reason ha problem 1 exiss is ha RDFS uses a single primiive rdfs:class o implicily represen possibly infinie layers of classes. Bu do we really need infinie layers of classes? In pracice, rdfs:class usually acs as a modelling primiive in he onology language and is used o define onology classes (e.g. Person ). One reasonable soluion is o explicily specify a cerain number of layers of class primiives, wih one being an insance of anoher, and he class primiives in he op layer having no ype a all, which means ha i is no an insance of anyhing. I isn because i can have a ype, bu because i doesn have o have a ype. From he pragmaic poin of view, we are only ineresed in he several layers on he ground and i is very imporan ha he modelling primiives in hese layers have clear semanics. This is he main difference beween he fixed and non-fixed meamodeling archiecure. So how many class primiives do we really need? Problem 2 indicaes ha we need a leas wo class primiives in differen meamodeling layers one as he ype of rdfs:resource, he oher as a subclass of rdfs:resource. In fac, in he four-layer meamodeling archiecure of UML, here exis wo

8 class primiives in differen meamodeling layers, which are Class in meamodel layer and MeaClass in mea-meamodel layer (see Secion 3.3). In pracice, i has no been found useful o have more han wo class primiives in he meamodeling archiecure (echnology Inc. [20, pg. 298]). Therefore, i is reasonable o explicily define wo class primiives in differen meamodeling layers of RDF Schema, one is MClass in Mealanguage Layer and he oher is LClass in Onology Language Layer 2 (see Secion 4.1). This makes RDFS have a similar meamodeling archiecure o ha of he well known UML, so ha i is easy for he modellers o undersand. Problem 3 is mainly abou predefined properies. I can be solved by specifying which level of class we inend o refer o when we use hese predefined properies. (see Secion 4.1). From he discussion above, we believe ha alhough he schema layer language won be as compac as i is, here will be several advanages if i has a fixed meamodeling archiecure: 1. We don have o worry abou Russell s Paradox. 2. I has clear formalised semanics. 3. DAML+OIL and oher logical layer Semanic Web languages can be buil on op of boh he synax and semanics of he RDFS wih fixed meamodeling archiecure. 4. I is similar o he meamodeling archiecure of UML, easy o undersand and use. 3.3 UML Meamodeling Archiecure The Unified Modelling Language (OMG [18]) is a general-purpose visual modelling language ha is designed o specify, visualise, consruc and documen he arifacs of a sofware sysem. I is a sandard objec-oriened design language ha has gained virually global accepance. UML has a fourlayer meamodeling archiecure. 1) The Mea-meamodel Layer forms he foundaion for he meamodeling archiecure. The primary responsibiliy of his layer is o define he language for specifying a meamodel. A mea-meamodel can define muliple meamodels, and here can be muliple mea-meamodels associaed wih each meamodel. Examples of mea-objecs in he meamodeling layer are: MeaClass, MeaAribue. 2) A Meamodel is an insance of a Mea-meamodel. The primary responsibiliy of he Meamodel layer is o define a language for specifying models. Examples of mea-objecs in he meamodeling layer are: Class, Aribue. 3) A Model is an insance of a Meamodel. The primary responsibiliy of he Model Layer is o define a language ha describes an informaion domain. Examples in Model layer are class Person and propery hasfriend. 4) User Objecs are an insance of a Model. The primary responsibiliy of he User Objecs Layer is o describe a specific informaion domain. Examples in User Objecs Layer are John, Mary and John, Mary. The four-layer meamodel archiecure is a proven mehodology for defining he srucure of complex models ha need o be reliably sored, shared, manipulaed and exchanged (Kobryn [13]). In he nex secion, we will use he meamodeling mehods of UML o build a fixed layer meamodeling archiecure for RDFS. 2 In his sense, here are hree kinds of classes: mea classes in he Mealanguage Layer, language classes in he Language Layer and onology classes, which are insance of LClass, in Onology Layer.

9 4 Web Onology Language Daa Model wih Fixed Meamodeling Archiecure We will now illusrae wha he daa model of an RDF-based Web onology language will look like under he fixed meamodeling archiecure. 4.1 RDF Schema Daa Model wih Fixed Meamodeling Archiecure Firsly, we will map he original RDFS ino RDFS wih Fixed meamodeling Archiecure (or RDFS(FA) for shor). One principle during his mapping is ha we ry o minimise he changes we make o RDFS. As we discussed in Secion 3.2, we believe i is reasonable o define a four-layer meamodeling archiecure for RDFS(FA). These four meamodeling layers are: 1. The Mealanguage Layer (M Layer, corresponding o he Mea-meamodel Layer in UML) forms he foundaion for he meamodeling archiecure. Is primary responsibiliy is o define he language layer. All he modelling primiives in his layer have no ypes (see Secion 3.2). Examples of modelling primiives in his layer are rdfsfa:mclass and rdfsfa:mpropery. 2. The Language Layer (L Layer, corresponding o he Meamodel Layer in UML), or Onology Language Layer, is an insance of he Mealanguage Layer. Is primary responsibiliy is o define a language for specifying onologies. Examples of modelling primiives in his layer are rdfsfa:lclass, rdfsfa:lpropery. Boh of hem are insances of rdfsfa:mclass. 3. The Onology Layer (O Layer, corresponding o he Model Layer in UML) is an insance of Language Layer. Is primary responsibiliy is o define a language ha describes a specific domain, i.e. an onology. Examples of modelling primiives in his layer are Person and Car, which are insances of rdfsfa:lclass, and hasfriend, which is an insance of rdfsfa:lpropery. 4. The Insance Layer (I Layer, corresponding o he User Objecs Layer in UML) is an insance of Onology Layer. Is primary responsibiliy is o describe a specific domain, in erms of he onology defined in he Onology Layer. Examples in his layer are Mary, John and hasfriend John, Mary. RDFS(FA) is illusraed in Figure 4. We map he modelling primiives of RDFS o he primiives in corresponding meamodeling layers of RDFS(FA), so ha no modelling primiives will have dual roles in he meamodeling archiecure of RDFS(FA). Firs, we map rdfs:class and is insance primiives in RDFS o he meamodeling archiecure of RDFS(FA) as follows: 1. rdfs:class is mapped o rdfsfa:mclass in Mealanguage Layer and rdfsfa:lclass in Language Layer, so ha rdfsfa:lclass is an insance of rdfsfa:mclass. <rdf:descripion rdf:id="mclass"> <rdfs:commen>the concep of class in he Mealanguage Layer. <rdfsfa:msubclassof rdf:resource="#mresource"/> <rdfsfa:mclass rdf:id="lclass"> <rdfs:commen>the concep of class in he Language Layer. <rdfsfa:lsubclassof rdf:resource="#lresource"/> </rdfsfa:mclass> 2. rdfs:resource is mapped o rdfsfa:mresource in he Mealanguage Layer and rdfsfa:lresource in Language Layer, so ha rdfsfa:mresource is he super class of all he modelling primiives in he

10 M L O rdfsfa:lsubclassof md rdfsfa:mclass rdfsfa:osubclassof ld m rdfsfa:lclass l mr rdfs:lieral rdfsfa:ldomain lr mr ls m m rdfsfa:mresource rdfs:consrainresource md lr ms mr ms ms rdfs:consrainpropery lr rdfsfa:lresource rdfsfa:odomain rdfsfa:orange m=rdfsfa:mype l=rdfsfa:lype md=rdfsfa:mdomain ld=rdfsfa:ldomain ms md rdfsfa:lrange ld m ld ls rdfsfa:lsubproperyof md mr rdfsfa:mpropery ld ms m rdfsfa:osubproperyof lr rdfsfa:lpropery ms=rdfsfa:msubclassof ls=rdfsfa:lsubclassof mr=rdfsfa:mrange lr=rdfsfa:lrange Figure 4: Direced Labeled Graph of RDFS(FA) Mealanguage Layer, while rdfsfa:lresource is an insance of rdfsfa:mclass and he superclass of rdfsfa:lclass. <rdf:descripion rdf:id="mresource"> <rdfs:commen>the mos general resource in he Mealanguage Layer. <rdfsfa:mclass rdf:id="lresource"> <rdfs:commen>the mos general resource in he Language Layer. </rdfsfa:mclass> 3. The rdfs:propery is mapped o rdfsfa:mpropery in he Mealanguage Layer and rdfsfa:lpropery in he Language Layer. <rdf:descripion rdf:id="mpropery"> <rdfs:commen>the concep of propery in he Mealanguage Layer. <rdfsfa:msubclassof rdf:resource="#mresource"/> <rdfsfa:mclass rdf:id="lpropery"> <rdfs:commen>the concep of propery in he Language Layer. <rdfsfa:lsubclassof rdf:resource="#lresource"/> </rdfsfa:mclass> 4. The rdfs:consrainresource is in he Mealanguage Layer, where i is rdfsfa:msubclassof rdfsfa: MResource. <rdf:descripion rdf:id="consrainresource">

11 <rdfsfa:msubclassof rdf:resource="#mresource"/> 5. The rdfs:consrainpropery is in he Mealanguage Layer, where i is rdfsfa:msubclassof rdfsfa: MPropery and rdfs:consrainresource. <rdf:descripion rdf:id="consrainpropery"> <rdfsfa:msubclassof rdf:resource="#mpropery"/> <rdfsfa:msubclassof rdf:resource="#consrainresource"/> As shown in Figure 4, modelling primiives are divided ino hree groups in he Mealanguage Layer, Language Layer and Onology Layer. rdfsfa:lclass is no an insance of iself, bu an insance of rdfsfa:mclass. rdfsfa:lresource is an insance of rdfsfa:mclass and a super class of rdfsfa:lclass. In general, here are hree kinds of classes in he meamodeling archiecure of RDFS(FA) 3 : mea classes in he Mealanguage Layer (e.g. rdfsfa:mclass, rdfsfa:mpropery), language classes in he Language Layer (insances of rdfsfa:mclass, e.g. rdfsfa:lclass, rdfsfa:lpropery) and onology class in he Onology Layer (insance of rdfsfa:lclass, e.g. Person, Car ). In order o solve problem 3 menioned in Secion 3.1, we need o be able o specify which kind of class (ou of he hree kinds of classes menioned above) we wan o refer o. In RDFS(FA), we add he layer prefix (e.g. m- for Mealanguage Layer, l- for Language Layer ec.) on he properies when we use he predefined propery primiives. Based on he above principle, we can map he propery primiives in RDFS o he meamodeling archiecure of RDFS(FA) as follows: 1. rdfs:domain is a se of binary relaionships beween insances of rdf:propery and rdfs:class. As classes and properies occur in hree differen layers of RDFS(FA), rdfs:domain is mapped o hree differen properies in RDFS(FA): rdfsfa:odomain, rdfsfa:ldomain and rdfsfa:mdomain. As shown in Figure 4, he rdfsfa:ldomain is defined in he Mealanguage Layer and used in he Language Layer, while rdfsfa:odomain is defined in he Language Layer and used in he Onology Layer (see Figure 5). <rdfs:consrainpropery rdf:id="odomain"> <rdfs:commen>this is how we specify ha all insances of a paricular onology propery describes insances of a paricular onology class. </rdfs:consrainpropery> <rdf:descripion rdf:id="ldomain"> <rdfs:commen>this is how we specify ha all insances of a paricular language propery describes insances of a paricular language class. <rdf:descripion rdf:id="mdomain"> <rdfs:commen>this is how we specify ha all insances of a paricular mea propery describes insances of a paricular mea class. 2. Similarly, rdfs:range is mapped o rdfsfa:orange, rdfsfa:lrange and rdfsfa:mrange. <rdfs:consrainpropery rdf:id="orange"> <rdfs:commen>this is how we specify ha all insances of a paricular onology propery have values ha are insances of a paricular onology class. 3 Accordingly, here are hree kinds of properies as well.

12 </rdfs:consrainpropery> <rdf:descripion rdf:id="lrange"> <rdfs:commen>this is how we specify he values of an insance of a paricular language propery have values ha are insances of a paricular language class. <rdfsfa:mpropery rdf:id="mrange"> <rdfs:commen>this is how we specify he values of an insance of a paricular mea propery should be insances of a paricular mea class. </rdfsfa:mpropery> 3. rdf:ype is a se of binary relaionship beween resource and rdfs:class. As RDFS(FA) has mea classes, language classes and onology classes, rdf:ype is mapped o rdfsfa:oype, rdfsfa:lype and rdfsfa:mype. E.g. in Figure 4, rdfsfa:mclass is he rdfsfa:mype of rdfsfa:lresource and rdfsfa:lclass. <rdfsfa:mpropery rdf:id="oype"> <rdfs:commen>indicaes membership of an insance of rdfsfa:lclass <rdfsfa:lrange rdf:resource="#lclass"/> </rdfsfa:mpropery> <rdf:descripion rdf:id="lype"> <rdfs:commen>indicaes membership of rdfsfa:lclass or rdfsfa:lpropery <rdfsfa:mrange rdf:resource="#mclass"/> <rdf:descripion rdf:id="mype"> <rdfs:commen>indicaes membership of rdfsfa:mclass or rdfsfa:mpropery. 4. rdfs:subclassof is a se of binary relaionship beween wo insances of rdfs:class, so rdfs:subclassof is mapped o rdfsfa:osubclassof and rdfsfa:lsubclassof. E.g. in Figure 4, rdfsfa:lclass is an rdfsfa:lsubclassof rdfsfa:lresource and rdfsfa:mclass is an rdfsfa:msubclassof rdfs:mresource. <rdfsfa:mpropery rdf:id="osubclassof"> <rdfs:commen>binary relaionship beween wo onology classes. <rdfsfa:ldomain rdf:resource="#lclass"/> <rdfsfa:lrange rdf:resource="#lclass"/> </rdfsfa:mpropery> <rdf:descripion rdf:id="lsubclassof"> <rdfs:commen>binary relaionship beween wo language classes. <rdfsfa:mdomain rdf:resource="#mclass"/> <rdfsfa:mrange rdf:resource="#mclass"/> <rdf:descripion rdf:id="msubclassof"> <rdfs:commen>binary relaionship beween wo mea classes.

13 5. Similarly, rdfs:subproperyof is a se of binary relaionships beween insances of rdf:propery, so i is mapped o rdfsfa:osubproperyof, rdfsfa:lsubproperyof and rdfsfa:msubproperyof. <rdfsfa:mpropery rdf:id="osubproperyof"> <rdfs:commen>binary relaionship beween wo onology properies. <rdfsfa:ldomain rdf:resource="#lpropery"/> <rdfsfa:lrange rdf:resource="#lpropery"/> </rdfsfa:mpropery> <rdf:descripion rdf:id="lsubproperyof"> <rdfs:commen>binary relaionship beween wo language properies. <rdfsfa:mdomain rdf:resource="#mpropery"/> <rdfsfa:mrange rdf:resource="#mpropery"/> <rdf:descripion rdf:id="msubproperyof"> <rdfs:commen>binary relaionship beween wo mea properies. 6. The rdfs:commen, rdfs:label, rdfs:seealso and rdfs:isdefinedby are reaed as documenaion in RDFS, and are no relaed o he semanics of RDFS(FA), so we are no going o discuss hem in his paper. Below is an RDFS(FA) version of he Person hasfriend example. As wih oher Web onology languages, hese saemens describe resources in he Onology Layer and he Insance Layer. <rdfsfa:lclass rdf:id="animal"> <rdfs:commen>this class of animals is illusraive of a number of onological idioms. </rdfsfa:lclass> <rdfsfa:lclass rdf:id="person"> <rdfs:osubclassof rdf:resource="#animal"/> </rdfsfa:lclass> <rdfsfa:lpropery rdf:id="hasfriend"> <rdfsfa:odomain rdf:resource="#person"/> <rdfsfa:orange rdf:resource="#person"/> </rdfsfa:lpropery> <rdf:descripion rdf:id="john"> <rdfsfa:oype rdf:resource="#person"/> <rdfs:commen>john is a person. <rdf:descripion rdf:id="mary"> <rdfsfa:oype rdf:resource="#person"/> <rdfs:commen>mary is a person. <rdf:descripion abou="#john"> <hasfriend rdf:resource="#mary"/> In he Onology Layer, Animal and Person are onology classes, so hey are insances of rdfsfa:l- Class. The onology class Person is he rdfsfa:odomain and rdfsfa:orange of he propery has- Friend, so boh he values of and resource described by insances of hasfriend are insances of

14 M L O I rdfsfa:lclass l Animal m=rdfsfa:mype l=rdfsfa:lype o=rdfsfa:oype rdfsfa:mclass m m ls rdfsfa:lresource l os Person o hasfriend John m ls od or o Mary rdfsfa:lpropery l hasfriend ls=rdfsfa:lsubclassof os=rdfsfa:osubclassof or=rdfsfa:orange od=rdfsfa:odomain Figure 5: A Person hasfriend example in RDFS(FA) Person. In he Insance Layer, he rdfsfa:oype of individuals such as John and Mary is he onology class Person. Figure 5 is a direced labeled graph of he above RDFS(FA) saemens. Here he rdfsfa:mype of rdfsfa:lclass is he mea class rdfsfa:mclass, he rdfsfa:lype of Person is he language class rdfsfa:lclass and he rdfsfa:oype of John is he onology class Person. The language class rdf:propery is rdfsfa:lsubclassof he language class rdfs:resource while he onology class Person is rdfsfa:osubclassof he onology class Animal. This example clearly shows ha he modelling primiives in RDFS(FA) no longer have dual roles. Thus a clear semanics can be given o hem. Noe ha, as in RDFS (see Secion2.2), we can define rdfsfa:oype, rdfsfa:lype and rdfsfa:mype properies wihin RDFS(FA) in an implici way as well. E.g., individual John can also be defined as <Person rdf:id="john"> <rdfs:commen>john is a person. </Person> Here Person is an onology class, so he above expressions use an implici way o define rdfsfa:oype propery. 4.2 Daa Model Semanics of RDFS(FA) In his secion, we use a Tarski syle ([19]) model heoreic semanics o inerpre he daa model of RDFS(FA). Classes and properies are aken o refer o ses of objecs in he domain of ineress and ses of binary relaionships (or uples) beween hese objecs. In RDFS(FA), he meaning of individuals, pairs of individuals, onology classes and properies is given by an inerpreaion I, which is a pair( I, I), where I is he domain (a se) and I is an inerpreaion funcion, which maps every individual name x o an objec in he domain I : x I I every pair of individual names x, y o a pair of objecs in I I : every onology class name OC o a subse of I : x I, y I I I OC I I every onology propery name OP o a subse of I I : OP I I I.

15 In he Language Layer, he inerpreaion funcion I maps rdfsfa:lclass (LC) o 2 I : LC I = 2 I rdfsfa:lpropery (LP) o 2 I I : rdfsfa:lresource (LR) o LC I LP I : LP I = 2 I I LR I = LC I LP I so ha he inerpreaion of every possible onology class (OC I ) is an elemen of he inerpreaion of rdfsfa:lclass (LC I ), he inerpreaion of every possible onology propery (OP I ) is an elemen of he inerpreaion of rdf:propery (LP I ). Noe ha LR I is inerpreed as he union of LC I and LP I, and no as 2 I ( I I), so insances of rdfsfa:lresource mus be eiher onology classes (ses of objecs), or onology properies (ses of uples), and can be inerpreed as a mixure of ses of objecs and uples. In he Mealanguage Layer, inerpreaion funcion I maps rdfsfa:mclass (MC) o 2 LRI : MC I = 2 LRI rdfsfa:mpropery (MP) o 2 LCI LC I 2 LCI LP I 2 LP I LC I 2 LP I LP I : MP I = 2 LCI LC I 2 LCI LP I 2 LP I LC I 2 LP I LP I rdfsfa:mresource (MR) o MC I MP I : MR I = MC I MP I Predefined Propery Inerpreaion Semanic Consrain osubclassof (OSC) OSC I LC I LC I C1 I, C2 I OSC I iff. C1 I, C2 I LC I and C1 I C2 I lsubclassof (LSC) LSC I MC I MC I C1 I, C2 I LSC I iff. C1 I, C2 I MC I and C1 I C2 I msubclassof (MSC) MSC I 2 MRI 2 MRI C1 I, C2 I MSC I iff. C1 I, C2 I 2 MRI and C1 I C2 I osubproperyof (OSP) OSP I LP I LP I P1 I, P2 I OSP I iff. P1 I, P2 I LP I and P1 I P2 I lsubproperyof (LSP) LSP I MP I MP I P1 I, P2 I LSP I iff. P1 I, P2 I MP I and P1 I P2 I msubproperyof (MSP) MSP I Φ Φ P1 I, P2 I LSP I iff. P1 I, P2 I Φ and P1 I P2 I odomain (OD) OD I LP I LC I P I, C I OD I iff. P I LP I, C I LC I and x. x I, y I P I x I C I ldomain (LD) LD I MP I MC I P I, C I LD I iff. P I MP I, C I MC I and x. x I, y I P I x I C I mdomain (MD) MD I Φ 2 MRI P I, C I MD I iff. P I Φ, C I 2 MRI and x. x I, y I P I x I C I orange (ORG) ORG I LP I LC I P I, C I ORG I iff. P I LP I, C I LC I and x. x I, y I P I x I C I lrange (LRG) LRG I MP I MC I P I, C I LRG I iff. P I MP I, C I MC I and x. x I, y I P I x I C I mrange (MRG) MRG I Φ 2 P I, C I MRG I iff. P I Φ, C I 2 MRI and MRI x. x I, y I P I x I C I oype (OT) OT I I LC I x I, C I OT I iff. x I I, C I LC I and x I C I lype (LT) LT I LR I MC I R I, C I LT I iff. R I LR I, C I MC I and x I C I mype (MT) MT I MR I 2 MRI R I, C I MT I iff. R I MR I, C I 2 MRI and x I C I Figure 6: Semanics of Predefined Properies in RDFS(FA)

16 rdfs:consrainresource (CR) o subse of MR I : CR I MR I rdfs:consrainpropery (CP) o subse of boh CR I and MP I : CP I CR I MP I so ha he inerpreaions of rdfsfa:lclass (LC I ), rdfsfa:lpropery (LP I ) and rdfsfa:lresource (LR I ) are all elemens of he inerpreaion of rdfsfa:mclass (MC I ), and all he possible pairs of subses of LC I and subses of LP I are elemens of MP I. Unlike rdfs:class in RDFS, classes in RDFS(FA) have clear semanics. Clean semanics can also be given o he predefined properies of RDFS(FA) as shown in Figure 6, where Φ = 2 MCI MC I 2 MCI MP I 2 MP I MC I 2 MP I MP I As menioned above, in order o specify which kind of class we wan o refer o when we use he predefined properies, we add he layer prefixes o hese properies. Subclass-of and subpropery-of are he subse relaionship beween he classes or properies wihin he same layer. Domain and range are foundaion modelling primiives of RDFS(FA) properies, which can be used o specify wo classes ha a cerain propery can describe/use in descripions in a cerain layer. Type is a special cross-layer propery, which is used o link insances o classes. 4.3 DAML+OIL Daa Model wih Fixed Meamodeling Archiecure Wih a fixed meamodeling archiecure, RDFS(FA) has is own semanics and makes iself a fully qualified schema layer Semanic Web language. Thus, DAML+OIL (or any oher logical layer Semanic Web language) can be buil on boh is synax and semanics. From he poin of view of meamodeling archiecure, he modelling primiives ha DAML+ OIL inroduces are mainly locaed in he Language Layer (a complee descripion of he DAML+OIL daa model wih fixed meamodeling archiecure will be given in a forhcoming paper). daml:class is rdfsfa:lsubclassof rdfsfa:lclass and daml:objecpropery is rdfsfa:lsubclassof rdfsfa:lpropery; boh daml:daaype and daml:daaypepropery are rdfsfa:lsubclassof rdfsfa:lresource. The above four are disjoin wih each oher. The birhday propery lies in he Onology Layer and can be defined in he following way: <daml:daaypepropery rdf:id="birhday"> <rdfsfa:lype rdf:resource="hp:// Propery"/> <damlfa:odaadomain rdf:resource="#animal"/> <damlfa:odaarange rdf:resource="hp:// </daml:daaypepropery> where damlfa:odaadomain is a se of binary relaionships beween insances of daml:daaypepropery and daml:class, and damlfa:odaarange is a se of binary relaionships beween insances of daml:daaypepropery and daml:daaype. On he oher hand, i is clear ha Language Layer primiives can be used o define/modify oher Language Layer primiives, e.g. UniquePropery can no be used o resric he numbers of values of he maxcardinaliy as follows: <rdfsfa:mpropery rdf:abou="#maxcardinaliy"> <rdfsfa:lype rdf:resource="hp:// Propery"/>

17 </rdfsfa:mpropery> In RDFS(FA), Language Layer properies can only be defined using Mealanguage Layer primiives, for which DAML+OIL doesn provide any semanics. This is no clear in RDFS, where modellers migh be emped o hink ha hey can modify DAML+OIL in he above manner, exploiing he semanics of DAML+OIL iself. To solve he above problem, one can define MUniquePropery in he Mealanguage Layer and hen se daml:maxcardinaliy as is insance. In shor, RDFS(FA) no only provides a firm semanic basis for DAML+OIL, i also eradicaes he possibiliy of he layer misake menioned above. 5 Discussion As we have seen, RDFS has a leas he following problems: 1. Some elemens of RDFS have dule roles, i.e. hey have more han one semanics: (a) rdfs:class is he ype of boh language classes, e.g. rdfs:resource, and onology classes, e.g. Animal ; (b) rdfs:resource is he super-class of boh language classes, e.g. rdfs:class, and onology classes, e.g. Animal ; (c) rdfs:subclassof is used o express he sub-class/super-class relaionship beween boh language classes, e.g. rdfs:class is rdfs:subclassof rdfs:resource, and onology classes. e.g. Person is rdfs:subclassof Animal. 2. Because of dule roles, RDFS doesn have is semanics. DALM+OIL is only buil on op of he synax of RDFS. RDFS relies on DAML+OIL o give semanics o is modelling primiives. This indicaes ha RDFS is no ye a fully qualified schema layer Semanic Web language. 3. The even worse hing is ha since he logical layer languages, e.g. DAML+OIL, are buil on op of RDFS, affeced by he dule roles problem of RDFS, people ofen make he layer misake when using DAML+OIL. A fixed layer meamodeling archiecure for RDFS is proposed in his paper. We demonsrae how o map he original RDFS o RDFS(FA) (RDFS wih Fixed meamodeling Archiecure) and give a clear model-heoreic semanics o RDFS(FA). We believe ha alhough RDFS(FA) won be as compac as RDFS, here will be several advanages if RDFS has a fixed meamodeling archiecure: 1. We don have o worry abou Russell s Paradox. (Oher ways of hinking may include non wellfounded ses.) 2. RDFS(FA) has a clear model heoreic semanics and here are no dule roles wih is elemens. RDFS(FA) eradicaes he possibiliy of he layer misake. 3. DAML+OIL and oher logical layer Semanic Web languages can be buil on op of boh he synax and semanics of RDFS(FA). 4. The meamodeling archiecure of RDFS(FA) is similar o ha of UML, so i is easy for people o undersand and use. Some oher papers have also alked abou UML and he Web onology language. Chang [4] summarised he relaionship beween RDF-Schema and UML. Melnik [15] ried o make UML RDFcompaible, which allows mixing and exending UML models and he language elemens of UML iself on he Web in an open manner. Cranefield and Purvis [7] invesigaed he use of UML and OCL (Objec Consrain Language) for he represenaion of informaion sysem onologies. Cranefield [5]

18 proposed UML as a Web onology language. Cranefield [6] described echnology ha faciliaes he applicaion of objec-oriened modelling, and UML in paricular, o he Semanic Web. However, none of hese works address he problem of he meamodeling archiecure of RDFS iself. I is well known ha UML has a well-defined meamodeling archiecure (Kobryn [13]). I refines he semanic consrucs a each layer, provides an infrasrucure for defining meamodel exensions, and aligns he UML meamodel wih oher sandards based on a four-layer meamodeling archiecure, such as he Case Daa Inerchange Forma (EIA [8]), Mea Objec Faciliy (MOF-Parners [16]) and XMI Faciliy for model inerchange (XMI-Parners [24]). However, We believe Semanic Web languages and UML have differen moivaion and applicaion domain. Besides he meamodeling archiecure, Semanic Web languages also have a funcional archiecure. Wihin his funcional archiecure, RDF is a good candidae for he meadaa layer language, while UML is obviously no designed as a meadaa language. The schema layer languages mus suppor global properies (anyone can say anyhing abou anyhing) raher han he local ones, while he consideraions of UML mainly focus on he local properies. The modelling primiives of logical layer languages, e.g. OIL and DAML+OIL, are carefully seleced so ha hey can be mapped ono very expressive descripion logics (DLs), so as o faciliae he provision of reasoning suppor; on he UML side, reasoning over OCL is sill under research. Therefore, we prefer o enhance Web onology languages by using he mehodologies in UML, raher han making UML a componen in Web onology languages. Accordingly, we have used he meamodeling mehods of UML o build a fixed layer meamodeling archiecure for RDFS in his paper. And a similar approach can be found in Kampman and van Harmelen [12]. Furher research will include a deailed sudy of he daa model of DAML+OIL based on RDFS(FA) and he reasoning suppor provided by corresponding Descripion Logics. References [1] Tim Berners-lee. Semanic Web Road Map. W3C Design Issues. URL hp:// org/designissues/semanic.hml, Oc [2] Dan Brickley and R.V. Guha. Resource Descripion Framework (RDF) Schema Specificaion 1.0. W3C Recommendaion, URL hp:// Mar [3] J. Broeksra, M. Klein, S. Decker, D. Fensel, F. can Harmelen, and I. Horrocks. Enabling knowledge represenaion on he Web by exending RDF Schema, Nov [4] Waler W. Chang. A Discussion of he Relaionship Beween RDF-Schema and UML. W3C Noe, URL hp:// Aug [5] Sephen Cranefield. Neworked Knowledge Represenaion and Exchange using UML and RDF. In Journal of Digial Informaion, volume 1 issue 8. Journal of Digial Informaion, Feb [6] Sephen Cranefield. UML and he Semanic Web, Feb ISSN Discussion Paper. [7] Sephen Cranefield and M. Purvis. UML as an onology modelling language. In IJCAI-99 Workshop on Inelligen Informaion Inegraion, [8] EIA. CDIF Framework for Modeling and Exensibiliy, EIA/IS-107. Nov [9] I. Horocks, D.Fensel, J.Broesra, S.Decker, M.Erdmann, C.Goble, F.van Harmelen, M.Klein, S.Saab, R.Suder, and E.Moa. The Onology Inference Layer OIL. Aug [10] I. Horrocks. Benchmark Analysis wih FaCT. In TABLEAUX-2000, number 1847 in LNAI, pages Springer-Verlag, 2000.

19 [11] I. Horrocks, U. Saler, and S. Tobies. Pracical Reasoning for Expressive Descripion Logics. In H. Ganzinger, D. McAlleser, and A. Voronkov, ediors, Proceedings of he 6h Inernaional Conference on Logic for Programming and Auomaed Reasoning (LPAR 99), number 1705 in Lecure Noes in Arificial Inelligence, pages Springer-Verlag, [12] Arjohn Kampman and Frank van Harmelen. Sesame s inerpreaion of RDF Schema. Aidminisraor Nederland Noe, URL hp://sesame.aidminisraor.nl/doc/ rdf-inerpreaion.hml, Apr [13] Cris Kobryn. UML 2001: A Sandardizaion Odyssey. In Communicaions of he ACM, Vol.42, No. 10, Oc [14] Ora Lassila and Ralph R.Swick. Resource Descripion Framework (RDF) Model and Synax Specificaion. Feb [15] S. Melnik. Represening UML in RDF. URL hp://www-db.sanford.edu/ melnik/rdf/uml/, [16] MOF-Parners. Mea Objec Faciliy Revision 1.1b1. Jan [17] W. Nejdl, M. Wolpers, and C. Capelle. The RDF Schema Specificaion Revisied. In Modelle und Modellierungssprachen in Informaik und Wirschafsinformaik, Modellierung 2000, Apr [18] OMG. OMG Unified Modeling Language Specificaion verion 1.3. Jun [19] A. Tarski. Logic, Semanics, Mahemeics: Papers from 1923 o Oxford Universiy Press, [20] PLATINUM echnology Inc. Objec Analysis and Design Faciliy, Response o OMG/OA&D RFP-1,Version 1.0, Jan [21] M. Uschold and M. Gruninger. Onologies: Principles, Mehods and Applicaions. The Knowledge Engineering Review, [22] Frank van Harmelen, Peer F. Pael-Schneider, and Ian Horrocks. A Model-Theoris Semanics of DAML+OIL(March 2001). Mar [23] Frank van Harmelen, Peer F. Pael-Schneider, and Ian Horrocks. Reference Descripion of he DAML+OIL(March 2001) Onology Markuk Language. DAML+OIL Documen, URL hp: // Mar [24] XMI-Parners. XML Meadaa Inerchange (XMI) v Oc