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Ontology Generation and Applications

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Title: Ontology Generation and Applications


1
Ontology Generation and Applications
  • Dr. A.C.M. Fong, CEng
  • Professor of Computer Engineering
  • School of Computing and Mathematical Sciences
  • Faculty of Design and Creative Technologies
  • Auckland University of Technology
  • afong_at_aut.ac.nz

2
Contents
  • Introduction Semantic Web and Ontology
  • Related Work Ontology Generation
  • Toward Automated Ontology Generation
  • Fuzzy Ontology Generation Framework
  • Application 1 Scholarly Info
  • Application 2 Service Helpdesk

3
IntroductionSemantic Web
  • The basis for the Semantic Web is on its ability
    to represent real-life domains accurately so that
    it enables programs to completely understand the
    environment in which they operate.
  • In summary, Semantic Web provides the following
    benefits
  • SWeb offers an expressive metadata model to
    represent data, so that data can be managed
    effectively.
  • Programs can understand the semantic concepts
    described in metadata used on Semantic Web.
    Hence, knowledge carried on the Semantic Web can
    be shared and reused among different programs.
  • Users can interact with programs using a semantic
    query language to specify their requests and
    thereby improving the retrieval performance.
  • Deductive mechanism that is used to derive new
    information from existing information can be
    described clearly, so that knowledge can be
    reasoned with efficiently.

4
IntroductionSemantic Web Architecture
5
IntroductionSemantic Web Architecture - Layers
  • Foundation Layer. Semantic Web uses Uniform
    Resource Identifier URI to identify resources and
    uses Unicode to encode the documents.
  • Schema Layer. This layer comprises XML NS
    (Namespace) xmlschema layer and the RDF
    rdfschema layer.
  • This layer defines objects and classes, their
    relations and constrains. The XML Schema (XMLS)
    and RDF Schema (RDFS), which are based on XML and
    RDF respectively, are used for these layers.
  • RDFS has widely been used to describe classes at
    the Schema Layers.

6
IntroductionSemantic Web Architecture - Layers
  • Ontology Layer. This layer provides constructs on
    using meta-information to represent domain
    knowledge.
  • In this layer, information is represented as
    ontology, which is adopted by the Semantic Web to
    define knowledge.
  • Logic Layer. This layer infers more knowledge
    from the existing knowledge. It can be integrated
    with the Ontology Layer.
  • In this layer, concepts and relationships defined
    in lower layers are converted into
    Turing-complete logic languages in order to
    generate new knowledge.

7
IntroductionSemantic Web Architecture - Layers
  • Proof Layer. This layer provides a mechanism to
    check whether a statement is true or not.
  • Trust Layer. This Layer provides a mechanism
    which resolves conflicts between knowledge
    carried by the Semantic Web to form the "Web of
    Trust"
  • Digital Signature Layer. This layer uses public
    key cryptography to secure documents.

8
IntroductionOntology Definition
  • Ontology has different definitions. A commonly
    cited definition defines ontology as a formal,
    explicit specification of a shared
    conceptualization.
  • Conceptualization refers to an abstract model of
    phenomena in the world by having identified the
    relevant concepts of those phenomena.
  • Explicit means that the type of concepts used,
    and the constraints on their use are explicitly
    defined.
  • Formal should be machine readable.
  • Shared should capture consensual knowledge
    accepted by the communities.

9
IntroductionOntology Research
  • Ontology is regarded as a standard conceptual
    model for knowledge representation, especially on
    Semantic Web.
  • The term ontology engineering has been proposed
    to imply ontology-related research in computer
    science
  • Current interesting issues on ontology
    engineering include ontology generation, ontology
    mapping, ontology integration and ontology
    versioning.
  • This presentation focuses on ontology generation.

10
IntroductionOntology Description Languages
  • Ontology is described using an ontology
    description language.
  • Ontology description languages are based on Web
    metadata description languages, which can be
    classified into the following three groups
  • HTML-based
  • XML-based
  • RDF- based

11
IntroductionHTML-based Ontology Description
Languages
  • The tags supported by traditional Web are
    sufficient to represent some semantic knowledge.
  • Simple HTML Extension (SHOE) and Ontobroker have
    embedded additional tags into HTML to represent
    knowledge.
  • However, HTML does not support self-defined tags.
    Therefore, HTML-based approach is difficult to
    define classes for ontology.
  • Hence, XML-based ontology description languages
    have been proposed to overcome this limitation.

12
IntroductionXML-based Ontology Description
Languages
  • These languages are usually based on XML Schema
    (XMLS) or Document Type Definition (DTD).
  • DTD allows users to define new markup types to
    describe information. Therefore, users can define
    ontology classes using DTD.
  • Moreover, XMLS supports the definition of
    relations between classes.
  • Thus, XMLS and DTD can be used directly to embed
    semantic information.
  • However, since XML actually only renders
    syntactic support for knowledge representation,
    XML-based ontology description languages face the
    following problems when representing knowledge

13
IntroductionXML-based Ontology Description
Languages
  • A mechanism to define some relationships that are
    usually central in ontologies such as is-a or
    element-of relationships is lacking in XML.
  • XML does not support any notion of inheritance,
    which is an important attribute in ontologies.
  • In XML, concepts are defined through tags, which
    can be either a string or a combination of other
    nested tags. Such mechanism may not be sufficient
    for defining concepts in ontology, which may
    require richer data structures to be represented.
  • In XML, the order of tags appearing in a document
    must be previously defined. In contrast, the
    ordering of attribute description does not matter
    on ontology.

14
IntroductionRDF-based Ontology Description
Languages
  • RDF extends XML to become a standard for
    knowledge representation.
  • In addition, RDF Schema (RDFS) can be used to
    define classes and class hierarchies in a domain.
  • The standardization supported by RDF provides two
    important contributions
  • A standard set of modeling primitives (e.g.
    class, instance, etc.) and their relationships
    (e.g. subclass) are provided.
  • A standardized syntax for writing ontologies is
    supported.
  • Popular RDF-based ontology description languages
    include DARPA Agent Markup Language (DAML),
    Ontology Inference Language (OIL), DAMLOIL and
    Web Ontology Language (OWL)

15
Introduction DARPA Agent Markup Language
  • DAML or DAML-ONT extends RDFS to represent
    ontology using the object-oriented approach.
  • It embeds some object-oriented concepts to
    represent classes. Thus, the class representation
    of DMAL-ONT is better than RDF.
  • Example of DAML-ONT to represent the class
    "Journal", which is a subclass of the class
    "Publication Medium", but is disjoint with
    classes "Conference" and "Workshop" (i.e. an
    object which belongs to class "Journal" can not
    belong to classes "Conference" or "Workshop"
  • ltClass ID"Journal"gt
  • ltsubClassOf resource"Publication Medium" gt
  • ltdisjointFrom resource"Conference" gt
  • ltdisjointFrom resource"Workshop" gt
  • lt Classgt

16
IntroductionOntology Inference Language
  • OIL extends RDFS to represent ontology.
  • It is designed based on three criteria
  • Frame-based. It supports frames to define classes
    and properties of classes. Thus, class contents
    can be described more informatively (e.g.
    constraints can be used for class properties)
  • Description Logic. It describes knowledge using
    logic rules. Thus, knowledge is represented
    mathematically and can be processed by programs.
  • Uses Web Standard. It is based on XML and RDFS.

17
IntroductionOntology Inference Language
  • ltrdfsClass rdfID"animal" gt
  • ltrdfsClass rdfID"plant"gt
  • ltrdfssubClassOfgt
  • ltoilNOTgt
  • ltoilhasOperand rdfresource"animal" gt
  • ltoilNOT gt
  • lt rdfssubClassOfgt
  • lt rdfsClassgt
  • ltrdfsClass rdfID"tree"gt
  • ltrdfssubClassOf rdfresource"plant"gt
  • lt rdfsClassgt
  • Class "animal" is defined, followed by class
    "plant", which is defined with the operator "NOT"
    used to state that it is strictly not identical
    with class "animal (i.e. objects which belong to
    class "animal" can not belong to class "plant"
    and vice-versa).
  • Finally, class "tree" is defined as a subclass of
    "plant".

18
IntroductionDAML vs. OIL
  • Compared with DAML, OIL can represent class
    properties better, but DAML can represent class
    relationships more clearly.
  • Hence, they can be combined to form a better
    ontology description language
  • DAML OIL
  • It defines class relationships based on DAML.
  • Class properties are defined in a similar way as
    OIL.
  • Hence, DAMLOIL takes the advantages of both DAML
    and OIL.

19
IntroductionWeb Ontology Language
  • OWL is extended from DAMLOIL to allow users to
    define various types of relationships between
    classes.
  • Properties can also be defined using additional
    constructs in OWL.
  • OWL has three sublanguages
  • OWL Lite
  • OWL DL
  • OWL Full.

20
IntroductionWeb Ontology Language
  • Even though there is the same OWL syntax used
    among these sublanguages, they have a little
    difference in design aimed at various communities
    of implementers and users
  • OWL Lite only primarily supports classification
    hierarchy and simple constrains when designing
    classes.
  • OWL DL includes all OWL language constructs but
    they can be used only under certain restriction
    (e.g. a class cannot be an instance of another
    class).
  • OWL Full allows all OWL language constructs to be
    used without any restriction.

21
IntroductionWeb Ontology Language
  • ltrdfRDFgt
  • xmlnsowl "http//www.w3.org/2002/07/owl"
  • xmlnsrdf "http//www.w3.org/1999/02/22-rdf-synt
    ax-nsl"
  • xmlnsrdfs"http//www.w3.org/2000/01/rdf-schema
    "
  • xmlnsxsd "http//www.w3.org/2000/10/XMLSchema"
  • xmlnsdaml"http//www.w3.org/2001/10/damloil"
  • ltowlOntology rdfabout"Scholarly Information"gt
  • ltowlversionInfogtv 1.0 2009-12-07
    190640lt/owlversionInfogt
  • lt owlOntologygt
  • ltowlClass rdfID"Concept1"gt
  • ltowlrdfLabel"Data Mining"gt
  • lt owlClassgt
  • ltowlClass rdfID"Concept2"gt
  • ltowlrdfLabel"Fuzzy Logic"gt
  • lt owlClassgt
  • lt owlClass rdfID"Concept2"gt
  • lt owlClass rdfID"Concept3"gt
  • ltowlrdfLabel"Data Mining, Fuzzy Logic" gt
  • ltrdfsubClassOfgt

Header Info
Ontology Name and Version
3 classes Concept1 (labelled Data mining),
Concept2 (labelled Fuzzy Logic) and Concept3.
Concept3 is a subclass of both Concept 1 and
Concept2.
22
2. Related WorkOntology Generation
  • Ontology uses classes, which contain attributes,
    to represent concepts.
  • Ontology also supports taxonomy and non-taxonomy
    relations between classes.
  • Although editing tools such as Protege 1 and
    OilEd 2 have been developed to help users to
    create and edit ontology, it is a tedious task to
    manually derive ontology from data.

23
2. Related WorkOntology Generation Approaches
  • Ontology can be generated from various types of
    data, mostly textual.
  • Large corpora 3,4 are considered as good
    sources for mining knowledge for constructing
    ontology, since the information in the corpus is
    usually well annotated. Therefore, it can be
    easily processed by other programs.
  • Ontology can also be generated from a knowledge
    base of rules 5, which is represented as a tree
    with rules residing at tree nodes. Statistical
    approaches have been used to estimate the
    existence of relationships between entities
    involved in rules 6.

24
2. Related WorkOntology Generation Approaches
  • When knowledge is represented in semi-structured
    schemata such as XML and RDF, its contents can
    easily be parsed by programs techniques have
    been proposed to generate ontology from
    semi-structured schemata based on Graph Theory
    7 and statistical approaches 8.
  • Learning Source Description (LSD) proposed 9 to
    generate ontology from any arbitrary formalisms
    of semi-structured schemata.
  • Entity-Relationship model used in database schema
    has also been adopted as an information source
    for generating ontology 10,11.

25
2. Related WorkOntology Generation Textual Data
  • For textual data, ontology concepts can be
    extracted efficiently using Natural Language
    Processing (NLP) techniques 12,13.
  • NLP for preprocessing the textual data in order
    to extract significant keywords.
  • WordNet 14 can be used to improve accuracy of
    ontology generated by NLP-based techniques.
  • However, the NLP techniques have difficulty in
    finding semantic relationships among the
    keywords.
  • Data mining techniques can be combined with NLP
    to improve the efficiency of ontology generation.
    In Text-to-Onto 15, association rules are used
    to find associative relations between keywords,
    which are used to construct non-taxonomy
    relations for the ontology.

26
2. Related WorkOntology Generation Textual Data
  • Keywords' frequencies are often used in
    statistical approaches 16,17 to identify
    significant keywords that can be used to
    represent a certain concept.
  • Clustering techniques have also been applied to
    generate ontology from textual data 18.
  • Using significant keywords extracted from textual
    data, clustering techniques can cluster documents
    and interpret topics from the generated clusters.

27
2. Related WorkOntology Generation Clustering
  • Clustering can be used to mine hidden knowledge
    from data to construct an ontology. It can also
    be used to enrich existing ontology.
  • Traditional clustering techniques are useful for
    generating non-taxonomy relations for ontology.
  • In particular, conceptual clustering techniques
    are powerful clustering techniques that can
    conceptualize clusters and construct a concept
    hierarchy of clusters useful for generating
    taxonomy relations for ontology.
  • E.g. approach based on COBWEB 18 that can
    generate taxonomy relations among concepts on a
    domain for ontology generation.
  • Mo'K 19 is a system that can obtain taxonomy
    relations from tagged text using conceptual
    clustering.

28
2. Related WorkOntology Applications Scholarly
Info
  • In E-Scholar Knowledge Inference MOdel (ESKIMO)
    20, knowledge on scholarly publications is
    represented as a simple ontology, known as
    OntoPortal, which is manually developed and
    maintained.
  • OntoPortal describes and provides links to other
    external research pages on the Web. Hypertext
    links between the web pages are also described in
    the OntoPortal ontology.
  • ESKIMO allows users to retrieve scholarly
    information from the constructed ontology by
    using queries represented as Prolog-like rules.

29
2. Related WorkOntology Applications Scholarly
Info
  • In the Scholarly Ontology Project 21, a digital
    library Web server is constructed using Semantic
    Web technologies in order to support scholarly
    retrieval.
  • Developed using a collaborative approach in which
    researchers will submit their documents in a
    specifically structured format.
  • As such, the contents of the submitted documents
    can be further processed in the system and
    converted into scholarly ontology accordingly.

30
2. Related WorkOntology Applications Scholarly
Info
  • In the Research in Semantic Scholarly Publishing
    (RSSP) project, scientific publications are
    collected from online archives such as the Open
    Archive Initiative (OAI) 22.
  • Information of the documents (e.g. their authors,
    titles, citations, publishers, etc.) is
    extracted, indexed and converted into ontology
    formalism.
  • DAMLOIL is used to annotate the ontology as
    Semantic Web pages to support scholarly retrieval

31
2. Related WorkSummary
  • Many techniques to construct ontology from
    various data types/sources mainly textual data
  • Traditionally, NLP techniques are used to analyze
    textual data.
  • Recently, data mining techniques have been
    incorporated into NLP to further discover hidden
    knowledge from textual data.
  • Conceptual clustering is an advanced data mining
    technique that can organize data in a
    hierarchical conceptual structure.
  • Thus, conceptual clustering is a useful technique
    to discover knowledge for generating ontology
    from textual data.

32
3. Toward Automated Ontology GenerationBasics
  • Initial focus on Scholarly info
  • Scholarly ontology generated directly from
    explicit information on scientific publications
    (e.g. their titles, authors, citations, etc.).
  • Other advanced scholarly knowledge such as
    research experts and areas are usually inferred
    manually by human experts.

33
3. Toward Automated Ontology GenerationBasics
  • To construct scholarly ontology from citation
    database, we use data mining techniques to
    discover hidden knowledge in the database.
  • Data mining techniques include Context-based
    Cluster Analysis (CCA) and Fuzzy Concept
    Hierarchy Generation (FCHG)
  • Discovered knowledge then converted and
    integrated into the ontology formalism.
  • As such, apart from the implicit information
    available on scientific publications, Scholarly
    Ontology can also support other useful scholarly
    retrieval functions such as research experts
    finding and trends detection

34
3. Toward Automated Ontology GenerationContext-ba
sed Cluster Analysis
  • CCA is based on Formal Concept Analysis (FCA)
    23 technique.
  • FCA provides a formal model, known as formal
    context, to represent relations between objects
    and attributes in a data set.
  • We use formal contexts to represent multiple
    resultant clustering data.
  • Then, relations between the formal contexts are
    analyzed to find the relations between the
    corresponding resultant clustering data

35
3. Toward Automated Ontology GenerationFuzzy
Concept Hierarchy Generation
  • Concept hierarchy is a data structure useful for
    knowledge presentation.
  • Widely used in data mining applications.
  • Size of a concept hierarchy may be large to
    reflect the knowledge in a domain precisely.
  • Manual construction may be difficult and tedious.
  • Need conceptual clustering

36
3. Toward Automated Ontology GenerationFuzzy
Concept Hierarchy Generation
  • Many conceptual clustering techniques organize
    knowledge as a concept hierarchy. It may not be
    sufficient for representing information in a real
    domain.
  • FCA, which is a data exploratory technique,
    supports concept lattice that provides a more
    informative conceptual model for representing
    knowledge.
  • FCA-based conceptual clustering techniques are
    potentially useful for constructing taxonomy
    knowledge of ontology.
  • However, the typical FCA-based conceptual
    clustering techniques do not support uncertainty
    information.

37
3. Toward Automated Ontology GenerationFuzzy
Concept Hierarchy Generation
  • Traditional FCA-based conceptual clustering
    approaches cant represent vague information
    Need fuzziness
  • L-Fuzzy context uses linguistic variables to
    represent uncertainty in the context.
  • But needs human interpretation to define
    linguistic variables.
  • Fuzzy concept lattice generated from L-fuzzy
    context usually causes a combinatorial explosion
    of concepts (compared to traditional concept
    lattice)

38
3. Toward Automated Ontology GenerationFuzzy
Concept Hierarchy Generation
  • We combine fuzzy logic and FCA as Fuzzy Formal
    Concept Analysis (FFCA).
  • In FFCA, uncertainty information is directly
    represented by a real number of membership value
    in the range of 0,1.
  • Linguistic variables are no longer needed.
  • Compared to fuzzy concept lattice generated from
    L-fuzzy context, the fuzzy concept lattice
    generated using FFCA will be simpler in terms of
    the number of formal concepts.
  • It also supports a formal mechanism for
    calculating concept similarities.
  • Based on FFCA, we propose the Fuzzy Conceptual
    Clustering technique in FCHG to generate fuzzy
    concept hierarchy.

39
4. Fuzzy Ontology Generation FrameworkFuzzy
Ontology
  • Application of fuzzy logic offers a possible
    solution for dealing with uncertainty information
  • Fuzzy ontology is generated and used in text
    retrieval and search engines, where membership
    values are used to evaluate the similarities
    between the concepts in a concept hierarchy
  • Manual generation of fuzzy ontology from a
    predefined concept hierarchy is a difficult and
    tedious task that often requires expert
    interpretation.

40
4. Fuzzy Ontology Generation FrameworkIntroductio
n
  • Efficient method for generation of concept
    hierarchy and fuzzy ontology is highly desirable
  • We propose a Fuzzy Ontology Generation Framework
    (FOGF) that can automate fuzzy ontology
    generation from uncertainty data based on Formal
    Concept Analysis (FCA) theory
  • Generated fuzzy ontology is mapped to a semantic
    representation in OWL

41
4. Fuzzy Ontology Generation FrameworkOverview
  • Fuzzy Formal Concept Analysis incorporates fuzzy
    logic into Formal Concept Analysis to represent
    vague information
  • Concept Hierarchy Generation clusters the fuzzy
    concept lattice generated by FFCA to construct a
    concept hierarchy in two steps Fuzzy Conceptual
    Clustering and Hierarchical Relation Generation
  • Fuzzy Ontology Generation constructs fuzzy
    ontology from a fuzzy context using the concept
    hierarchy created by fuzzy conceptual clustering
  • Semantic Representation Conversion make
    knowledge accessible and sharable on the Web
    environment. Use OWL

42
4. Fuzzy Ontology Generation Framework Step 1
Fuzzy Formal Concept Analysis
  • Definition (Fuzzy Formal Context)
  • A fuzzy formal context is a triple
  • K (G, M, I ?(G ? M))
  • where G is a set of objects, M is a set of
    attributes, and I is a fuzzy set on domain G ? M.
  • Each relation (g, m) ? I has a membership value
    ?(g,m) in 0,1.

43
4. Fuzzy Ontology Generation Framework Step 1
Fuzzy Formal Concept Analysis
  • Fuzzy formal context can be represented as a
    cross-table (Table 1)
  • An a-cut can be set to eliminate relations with
    low membership values, e.g. a 0.5 (Table 2)
  • The context has 3 objects representing 3
    documents, D1, D2 and D3. It also has 3
    attributes, Data Mining, Clustering and
    Fuzzy Logic representing 3 research topics. The
    relationship between an object and an attribute
    is represented by a membership value in 0, 1.

44
4. Fuzzy Ontology Generation Framework Step 1
Fuzzy Formal Concept Analysis
  • Definition (Fuzzy Representation of Object)
  • Each object O in a fuzzy formal context K can be
    represented by a fuzzy set ?(O) as where A1,
    A2,, Am is the set of attributes in K and µi is
    the membership of O with attribute Ai in K. ? (O)
    is called the fuzzy representation of O.

45
4. Fuzzy Ontology Generation Framework Step 1
Fuzzy Formal Concept Analysis
  • Generally, we can consider the attributes of a
    formal concept as the description of the concept.
  • Thus, the relationships between the object and
    the concept should be the intersection of the
    relationships between the objects and the
    attributes of the concept
  • Since each relationship between the object and an
    attribute is represented as a membership value in
    fuzzy formal context, the intersection of these
    membership values should be the minimum of these
    membership values, hence

46
4. Fuzzy Ontology Generation Framework Step 1
Fuzzy Formal Concept Analysis
  • Definition (Fuzzy Formal Concept)
  • Given a fuzzy formal context K (G, M, I) and a
    confidence threshold T, we define A m ? M ?g
    ? A ?(g, m) ? T for A ? G and B g ? G ?m
    ? B ?(g,m) ? T for B ? M. A fuzzy formal
    concept (or fuzzy concept) of a fuzzy formal
    context (G, M, I) with a confidence threshold T
    is a pair (Af ?(A), B) where A ? G, B ? M, A
    B and B A. Each object g ? ?(A) has a
    membership ?g defined as
  • ?g min (g,m)
  • m ? B
  • where ?(g,m) membership value between object g
    and attribute m defined in I. If B then ?g
    1 for every g. A and B are the extent and intent
    of the formal concept (?(A), B) respectively.

47
4. Fuzzy Ontology Generation Framework Step 1
Fuzzy Formal Concept Analysis
  • This version of FFCA as presented in these
    Definitions preserves differently continuous
    values of objects memberships, crucial for
    calculating concepts similarities.
  • In a formal context, a concept can have many
    superconcepts and subconcepts. However, the
    similarities of a concept to its superconcepts
    and subconcepts are different.
  • With fuzzy concept lattice, we can make use of
    the fuzzy set theory to calculate the
    similarities between a concept and its
    subconcepts.

48
4. Fuzzy Ontology Generation Framework Step 1
Fuzzy Formal Concept Analysis
  • Definition (Fuzzy Formal Concept Cardinality)
  • Since the fuzziness of a fuzzy formal concept is
    represented by membership values of objects of
    the concept, the cardinality of a fuzzy formal
    concept Kf (?(A), B) is defined as Kf
    ?(A).

49
4. Fuzzy Ontology Generation Framework Step 1
Fuzzy Formal Concept Analysis
  • Definition (Fuzzy Formal Concept Similarity)
  • The similarity of a fuzzy formal concept Kf1
    (?(A1), B1) and its subconcept Kf2 (?(A2), B2)
    is defined as E(Kf1,Kf2) E(?(A1), ?(A2)).

50
4. Fuzzy Ontology Generation Framework Step 1
Fuzzy Formal Concept Analysis
  • Fuzzy concept lattice generated from fuzzy formal
    context in Table 2 (similarities between concepts
    shown)
  • Traditional concept lattice generated from Table
    1 without membership values

Fig. 3
Fig. 2
51
4. Fuzzy Ontology Generation Framework Overview
52
4. Fuzzy Ontology Generation Framework Step 2
Concept Hierarchy Generation
  • Concept Hierarchy Generation clusters the fuzzy
    concept lattice generated by FFCA to construct a
    concept hierarchy in two steps Fuzzy Conceptual
    Clustering and Hierarchical Relation Generation

53
4. Fuzzy Ontology Generation Framework Step 2
a)Fuzzy Conceptual Clustering
  • Compared to traditional clusters, the conceptual
    clusters generated have the following properties
  • Each conceptual cluster is considered as a human
    interpretable concept in the domain of the fuzzy
    concept lattice
  • Each conceptual cluster is a sublattice extracted
    from the fuzzy concept lattice
  • A formal concept must belong to at least one
    conceptual cluster e.g. a scientific document can
    belong to more than one research area

54
4. Fuzzy Ontology Generation Framework Step 2
a)Fuzzy Conceptual Clustering
  • Conceptual clusters are generated based on the
    idea at if a formal concept A belongs to a
    conceptual cluster R, then its subconcept B also
    belongs to R if B is similar to A. We can use a
    similarity confidence threshold Ts to determine
    whether two concepts are similar or not.

55
4. Fuzzy Ontology Generation Framework Step 2
a)Fuzzy Conceptual Clustering
  • Definition (Conceptual Cluster).
  • A conceptual cluster of a concept lattice K with
    a similarity confidence threshold Ts is a
    sublattice SK of K which has the following
    properties
  • SK has a supremum concept CS that is not
    similar to any of its superconcepts.
  • Any concept C ? CS in SK must have at least one
    superconcept C ? SK so that E(C,C) gt Ts.

56
4. Fuzzy Ontology Generation Framework Step 2
a)Fuzzy Conceptual Clustering
  • Fig. 5 shows the conceptual clusters generated
    from the fuzzy concept lattice given in Fig. 3
    with similarity confidence threshold Ts 0.5

Fig. 5
57
4. Fuzzy Ontology Generation Framework Step 2
b)Hierarchical Relation Generation
  • Fuzzy conceptual clustering generates a set of
    conceptual clusters SC. To construct a concept
    hierarchy from the conceptual clusters, we need
    to find the hierarchy relations from the
    clusters.
  • We first define a concept hierarchy
  • Definition (Concept Hierarchy)
  • A concept hierarchy is a poset (partially ordered
    set) (H,?) where H is a finite set of concepts,
    and ? is a partial order on H.

58
4. Fuzzy Ontology Generation Framework Step 2
b)Hierarchical Relation Generation
  • Definition of superconcept and subconcept
    relations on conceptual clusters assures that
    each conceptual cluster has at least one
    superconcept, unless it corresponds to the root
    node of the concept hierarchy generated. However,
    we must prove that the ? relation is a partial
    order.
  • Definition (Subconcept and Superconcept on a
    Concept Hierarchy)
  • Let C1 and C2 be two conceptual clusters
    corresponding to two sublattices L1 and L2 of a
    fuzzy concept lattice F (K). Let the fuzzy formal
    concept I be the supremum of L1, i.e. I
    sup(L1). C1 is the subconcept of C2, denoted as
    C1 ? C2 , if I is the subconcept of any concept
    C ? L2, or I ? C where ? is the partial order
    defined on F (K). Equivalently, C2 is the
    superconcept of C1.

59
4. Fuzzy Ontology Generation Framework Step 2
b)Hierarchical Relation Generation
  • Figure 8(b) illustrates the hierarchical
    relations constructed from the conceptual
    clusters given in Figure 8(a). Each concept in
    the concept hierarchy is represented by a set of
    its attributes. The supremum and infimum of the
    lattice are considered as Thing and Nothing
    concepts, respectively.

60
4. Fuzzy Ontology Generation Framework Overview
61
4. Fuzzy Ontology Generation Framework Step 3
Fuzzy Ontology Generation
  • This step constructs fuzzy ontology from a fuzzy
    context using the concept hierarchy created by
    fuzzy conceptual clustering.
  • This is done based on the characteristic that
    both FCA and ontology support formal definitions
    of concepts.
  • However, a concept defined in FCA has both
    extensional and intensional information in a
    balanced manner, whereas a concept in ontology
    emphasizes on its intensional aspect.
  • To construct the fuzzy ontology, we need to
    convert both intensional and extensional
    information of FCA concepts into the
    corresponding classes and relations of the
    ontology.
  • Thus, we define the fuzzy ontology as follows

62
4. Fuzzy Ontology Generation Framework Step 3
Fuzzy Ontology Generation
  • Definition (Fuzzy Ontology).
  • A fuzzy ontology FO consists of 4 elements
    (C,AC,R, X), where C set of concepts AC
    represents a collection of attributes sets, one
    for each concept R (RT, RN) represents a set
    of relationships, which consists of 2 elements
    RN is a set of non-taxonomy relationships and RT
    is a set of taxonomy relationships. Each concept
    ci in C represents a set of objects, or
    instances, of the same kind. Each object oij of a
    concept ci can be described by a set of
    attributes values denoted by AC(ci). Each
    relationship ri(cp,cq) in R represents a binary
    association between concepts cp and cq, and the
    instances of such a relationship are pairs of
    (cp,cq) concept objects. Each attribute value of
    an object or relationship instance is associated
    with a fuzzy membership value between 0,1
    implying the uncertainty degree of this attribute
    value or relationship. X is a set of axioms. Each
    axiom in X is a constraint on the concepts and
    relationships attribute values or a constraint
    on the relationships between concept objects

63
4. Fuzzy Ontology Generation Framework Step 3
Fuzzy Ontology Generation
  • Example (Fuzzy Ontology).
  • the Scholarly Ontology OS (C, AC, R, X) is a
    fuzzy ontology where its components are as
    follows.
  • C Document, Research Area
  • AC(Document) Name ,Author, Title,
    Keywords, Abstract, Body, Publisher,
    Publication Date
  • AC(Research Area) Name,Keyword
  • RN belong-to(Document, Research Area),
    consist-of(Research Area,Document)
  • RT superarea-of(Research Area, Research
    Area), subarea-of(Research Area, Research
    Area)
  • X Implies(Antecedent(consist-of(I-variable(x1)
    I-variable(x2)))
  • Consequent(belong-to(I-variable(x2)
    I-variable(x1))))
  • Implies(Antecedent(belong-to(I-variable(x1)
    I-variable(x2)))
  • Consequent(consist-of(I-variable(x2)
    I-variable(x1))))
  • Implies(Antecedent(superarea(I-variable(x1)
    I-variable(x2)))
  • Consequent(subarea(I-variable(x2)
    I-variable(x1))))
  • Implies(Antecedent(subarea(I-variable(x1)
    I-variable(x2)))
  • Consequent(superarea(I-variable(x2)
    I-variable(x1))))

64
4. Fuzzy Ontology Generation Framework Step 3
Fuzzy Ontology Generation
Figure 9. Fuzzy ontology generation process.
65
4. Fuzzy Ontology Generation Framework Step 3
Fuzzy Ontology Generation
  • Class Mapping furnishes C E, I in which E and
    I are classes corresponding to extent and intent
    of the fuzzy context. For example, the extent
    class mapped from the extent of the fuzzy context
    given in Table 1(b) can be labeled manually as
    Document. We can use appropriate names to
    represent keyword attributes and use them to
    label the intent class names as well. For
    example, the class Research Area can be used to
    label the initial intent class.

66
4. Fuzzy Ontology Generation Framework Step 3
Fuzzy Ontology Generation
  • Taxonomy Relation Generation furnishes RT
    superclass(I,I), subclass(I,I). Thus, the
    hierarchical relations between instances of
    intent classes are defined. Also, two rules are
    added to X accordingly
  • superclass(X,Y)-subclass(Y,X).
  • subclass(X,Y)-superclass(Y,X).

67
4. Fuzzy Ontology Generation Framework Step 3
Fuzzy Ontology Generation
  • Non-taxonomy Relation Generation furnishes RN
    RIE(I,E), REI(E,I), in which REI is the
    relation between the extent class and intent
    class. RIE is the reversed relation of REI.
    However, we still need to label the non-taxonomy
    relation. For example, the relation between class
    Document and class Research Area can be labeled
    as belong-to, which implies that a document can
    belong to one or more research areas. Also, two
    rules are added to X accordingly
  • REI(X,Y)- RIE(Y,X).
  • RIE (X,Y)- REI (Y,X).

68
4. Fuzzy Ontology Generation Framework Step 3
Fuzzy Ontology Generation
  • Instances Generation generates instances set I
    II, IE where II and IE are instances of the
    intent and extent class.
  • Then, it furnishes membership values for the
    instances attributes and relationships

69
4. Fuzzy Ontology Generation Framework Overview
70
4. Fuzzy Ontology Generation Framework Step 4
Semantic Representation Conversion
  • The generated fuzzy ontology provides a
    conceptual model of knowledge in the
    corresponding domain
  • However, to make such knowledge accessible and
    sharable, we must convert it into a semantic
    representation that can be embedded into the
    contents of Web pages.
  • In Semantic Web, ontology description language
    such as OWL can be used to annotate ontology.
  • Therefore, the generated fuzzy ontology can be
    automatically converted into the corresponding
    semantic representation in OWL, in which each
    class and instance is annotated as shown on the
    next slide

71
4. Fuzzy Ontology Generation Framework Step 4
Semantic Representation Conversion
  • Ontology for the concept hierarchy represented by
    OWL
  • lt?xml version"1.0"?gtltrdfRDF
    xmlnsrdf"http//www.w3.org/1999/02/22-rdf-syntax
    -ns" xmlnsxsd"http//www.w3.org/2001/XMLSche
    ma" xmlnsrdfs"http//www.w3.org/2000/01/rdf-
    schema" xmlnsowl"http//www.w3.org/2002/07/o
    wl" xmlns"http//www.owl-ontologies.com/unnam
    ed.owl" xmlbase"http//www.owl-ontologies.com/
    unnamed.owl"gt ltowlOntology rdfabout""/gt
    ltowlClass rdfID"Concept_2"/gt ltowlClass
    rdfID"Concept_1"/gt ltowlClass
    rdfID"Concept_3"gt ltrdfssubClassOf
    rdfresource"Concept_1"/gt ltrdfssubClassOf
    rdfresource"Concept_2"/gt lt/owlClassgt
    ltowlDatatypeProperty rdfID"Data_Mining"/gt
    ltowlDatatypeProperty rdfID"DataMining"gt
    ltrdfsdomain rdfresource"Concept_1"/gt
    ltrdfsrange rdfresource"http//www.w3.org/2001/X
    MLSchemafloat"/gt lt/owlDatatypePropertygt
    ltowlDatatypeProperty rdfID"FuzzyLogic"gt
    ltrdfsrange rdfresource"http//www.w3.org/2001/X
    MLSchemafloat"/gt ltrdfsdomain
    rdfresource"Concept_2"/gt lt/owlDatatypePropert
    ygt ltConcept_2 rdfID"Document2"gt ltFuzzyLogic
    rdfdatatype"http//www.w3.org/2001/XMLSchemaflo
    at" gt0.87lt/FuzzyLogicgt lt/Concept_2gt
    lt/rdfRDFgt

72
5. Scholarly OntologyOntology Generation
  • Collected scientific documents on the research
    area Information Retrieval published in
    1987-1997 from ISI
  • Downloaded documents are preprocessed to extract
    related information such as the title, authors,
    citation keywords, and other citation information
  • Extracted information then stored in a citation
    database

73
5. Scholarly OntologyOntology Generation
  • First, we construct a fuzzy formal context Kf
    G,M,I, with G as the set of documents and M as
    the set of citation keywords. The membership
    value of a document D on a citation keyword CK in
    Kf is computed as
  • where n1 is the number of documents that cite D
    and contain CK, and n2 is the number of documents
    that cite D
  • This formula is based on the premise that the
    more frequent a keyword occurs in the citing
    paper, the more important the keyword is in the
    cited paper.

74
5. Scholarly OntologyOntology Generation
  • Then, conceptual clustering is performed from the
    fuzzy formal context
  • Each generated conceptual cluster represents a
    research area
  • The generated conceptual clusters form a
    hierarchy of research areas of documents in the
    Citation Database, or Research Area Hierarchy

75
5. Scholarly Ontology Example of concept
hierarchy generated
Figure 11
  • Each research area is represented by a set of
    most frequent keywords occurring in the documents
    that belong to that research area. In FFCA,
    sub-areas inherit keywords from their
    super-areas. Note that the inherited keywords are
    not shown in Figure 11 when labeling the
    concepts. Only keywords specific to the concepts
    are used for labeling.

76
5. Scholarly Ontology Ontology Generation
  • The generated ontology contains scholarly
    information as a hierarchy of research areas as
    well as research areas for each document.
  • Taking advantages of the Semantic Web, such
    knowledge can be easily shared and reused by
    other systems for browsing or retrieval.
  • For example, we can use Protégé-2000 for browsing
    the scholarly ontology.

77
5. Scholarly Ontology Part of the generated
concept hierarchy of research areas
Fig. 12
We use the keyword that has the highest
membership value to label the research area.
Nevertheless, users can browse more information
of each research area.
78
5. Scholarly Ontology Performance Evaluation
  • Performance of the ontology generation is
    evaluated based on the generated Research Area
    Hierarchy.
  • Firstly, we measure the typical recall, precision
    and F-measure to evaluate the clustering results.
  • Secondly, we use the relaxation error and the
    corresponding cluster goodness measure to
    evaluate the goodness of the conceptual clusters
    generated. We also show whether the use of fuzzy
    membership instead of crisp value can help
    improve cluster goodness.
  • Finally, we use the Average Uninterpolated
    Precision (AUP), which is a typical measure for
    evaluating a hierarchical construct, to evaluate
    the goodness of the generated concept hierarchy.

79
5. Scholarly Ontology Performance Evaluation
  • Keyword attributes are descriptors for the
    generated clusters, if more keywords are
    extracted and used, the more meaningful the
    cluster descriptors are constructed?
  • To verify this, we vary the number of keywords N
    extracted from documents from 2 to 10, and the
    similarity threshold Ts from 0.2 to 0.9 when
    performing conceptual clustering
  • We have classified the documents downloaded from
    ISI into classes based on their research themes.
    These classes are used as a benchmark to evaluate
    the clustering results in terms of recall,
    precision and F-measure.

80
5. Scholarly Ontology Performance Evaluation -
Precision
Precision implies accuracy of the clustering
results. Table 6 shows that when N is small, the
precision is poor. It implies that noisy data
in clusters.
Table 6. Performance results using precision
measurement.
The precision is improved when the number of
extracted keywords is increased. However, this
will also cause the recall to decrease as shown
in Table 7.
81
5. Scholarly Ontology Performance Evaluation -
Recall
When the number of clusters is gradually
increased, the efficiency of the clustering
results will gradually be decreased.
Table 7. Performance results using recall
measurement.
82
5. Scholarly Ontology Performance Evaluation -
F-measure
When N is low, the F-measure is quite poor.
Nevertheless, the F-measure is stable and good
when a sufficient number of keywords are
extracted. The results also show that the
F-measure tends to have the best performance
when Ts 0.5.
Table 8. Performance results using F-measure
measurement.
83
5. Scholarly Ontology Performance Evaluation
Relaxation Error
  • Relaxation error implies dissimilarities of items
    in a cluster based on attributes values.
  • Since conceptual clustering techniques typically
    use a set of attributes for concept generation,
    relaxation error is quite commonly used for
    evaluating the goodness of conceptual clusters.

84
5. Scholarly Ontology Performance Evaluation
Relaxation Error
  • The relaxation error RE of a cluster C is defined
    as
  • where A is the set of the attributes of items in
    C, P(xi) is the probability of item xi occurring
    in C and da(xi,xj) is the distance of xi and xj
    on attribute a.
  • The cluster goodness G of cluster C is defined as
    G(C) 1 - RE(C).

85
5. Scholarly Ontology Performance Evaluation
Relaxation Error
  • Comparison of FFCA and COBWEB while the number of
    extracted keywords is varied from 2 to 10

we vary the number of keywords extracted to
observe the effect of the keyword generated on
cluster goodness. Besides, since COBWEB is
considered as one of the most popular techniques
for conceptual clustering, we also apply COBWEB
to the citation database to compare the
performance. It shows that FFCA achieves better
cluster goodness than COBWEB
86
5. Scholarly Ontology Performance Evaluation
AUP
  • Average Uninterpolated Precision (AUP) is defined
    as the sum of the precision value at each point
    (or node) in a hierarchical structure where a
    relevant item appears, divided by the total
    number of relevant items
  • Typically, AUP implies the goodness of a concept
    hierarchical structure.
  • For evaluating AUP, we have manually classified
    the downloaded documents into classes based on
    their research themes.
  • For each class, we extract 5 most frequent
    keywords from the documents in the class. Then,
    we use these keywords as inputs to form retrieval
    queries and evaluate the retrieval performance
    using AUP

87
5. Scholarly Ontology Performance Evaluation
AUP
  • There are two ways to generate document keywords.
    The first is to use the set of keywords, known as
    attribute keywords, from each conceptual cluster
    as the document keywords. The second is to use
    the keywords from each document as the document
    keywords. Then, we vectorize the document
    keywords and the input query, and calculate the
    vectors distance for measuring the retrieval
    performance.

88
5. Scholarly Ontology Performance Evaluation
AUP
  • Two methods
  • AUP measured using attribute keywords
    Hierarchical Average Uninterpolated Precision
    (AUP(H)), as each concept inherits attribute
    keywords from its superconcepts.
  • AUP measured using keywords from documents
    Unconnected Average Uninterpolated Precision
    (AUP(U)).

89
5. Scholarly Ontology Performance Evaluation
AUP
  • Fig. 14 shows the results for AUP(H) and AUP(U)
    using different numbers of extracted keywords N.

It shows that when N gets larger, the
performance on AUP(H) and AUP(U) gets better. In
addition, performance on AUP(H) is generally
better than AUP(U). It means that the attribute
keywords generated for conceptual clusters are
appropriate
Fig. 14
90
6. Semantic Helpdesk Application Introduction
  • Developed in collaboration with a multinational
    company, the Semantic Help-Desk Environment
    comprises the Web Service Requester, Matchmaking
    Agent and Web Service Provider.
  • The focus is on the fuzzy ontology generation
    process that generates Machine Service Ontology
    from a customer service database.
  • This approach enables individual machine service
    knowledge to be shared over the Semantic Web.
    Thus, machine service knowledge from different
    machines or models provided by different
    manufacturers can be shared and integrated. This
    is important as many customers may have different
    types of machines and models from different
    manufacturers.

91
6. Semantic Helpdesk Application Introduction -
Web Service Requester
  • A kind of Web Service that enables access to
    customer support for machine services.
  • Instances of the Web Service Requester can be
    created from a Web Requester Server where its
    address is accessible for all users through the
    Web.
  • When encountering a problem, a user can use the
    Web to connect the Web Requester Server in order
    to create an instance of the Web Service
    Requester.
  • The created instance runs as a web-based program.
    That is, it can use the Web to interact with the
    user and other programs.

92
6. Semantic Helpdesk Application Introduction -
Web Service Requester
  • Through the Web, the Web Service Requester
    instance provides an interface for the user to
    enter their reported problem.
  • Through the interface, the user can specify the
    encountered fault as a textual string. The user
    is also required to enter the code of the machine
    model. The given information is used to form a
    profile for the Web Service Requester.
  • The profile is then sent as a request to the
    Matchmaking Agent to seek a potential Web Service
    Provider for solving the problem

93
6. Semantic Helpdesk Application Introduction -
Web Service Provider
  • It offers its machine service support as a Web
    Service extended with ontology capabilities.
  • There are probably many instances of a Web
    Service Provider existing concurrently on the
    Internet.
  • An instance of the Web Service Provider can be
    considered as a program that can access the
    Machine Service Ontology to retrieve machine
    service knowledge for a given reported problem.
  • An instance of the Web Service Provider can
    interact with other programs. That is, it can be
    called by other programs and return the outputs
    to the calling programs.
  • Instances of the Web Service Provider must be
    registered with a specific agent known as the
    Matchmaking Agent that serves as a registry and
    look-up service.

94
6. Semantic Helpdesk Application Introduction -
Web Service Provider
  • Each instance of the Web Service Provider also
    provides a profile file that describes its
    parameters and capabilities. XML is used in most
    Web Services to represent the information
    contained in the profiles.
  • However, traditional XML lacks the capabilities
    of representing semantic information.
  • To overcome this problem, the Web Service
    Provider uses ontology-based service description
    language OWL-S (formerly DAML-S) to describe
    information in its profile. Hence, we describe
    the service as OWL ontology and its intentional
    information can be fully understood by other
    programs.

95
6. Semantic Helpdesk Application Introduction -
Matchmaking Agent
  • When the Matchmaking Agent receives machine
    service requests from the Web Service Requester,
    it locates the appropriate Web Services that can
    fulfill the request

96
6. Semantic Helpdesk Application Overview

97
6. Semantic Helpdesk Application Customer
Service Database
  • The customer service database contains 9000
    service records, each record consists of
    fault-condition and checkpoint information
  • Fault-condition contains the service engineers
    description of the machine fault. Checkpoint
    information indicates the suggested actions to be
    carried out to repair the machine based on the
    occurred fault-condition given by the customer

98
6. Semantic Helpdesk Application Customer
Service Database
99
6. Semantic Helpdesk Application Machine
Service Ontology Generation
  • Apply FOGF to obtain Fuzzy Fault Concept Lattice
    ? Fault Concept Hierarchy ? Machine Service
    Ontology

Part of the Fault Concept Hierarchy of the
machine model AV_2011
100
6. Semantic Helpdesk Application Machine
Service Ontology Generation
  • The generation process creates classes, relations
    and instances for the service ontology.
  • The machine fault service knowledge stored in the
    Customer Service Database is known as
    non-taxonomy knowledge, whereas the machine fault
    hierarchy knowledge from the Fault Concept
    Hierarchy is called taxonomy knowledge. These two
    types of knowledge are combined to form the
    Machine Service Ontology.

101
6. Semantic Helpdesk Application Machine
Service Ontology in OWL
102
6. Semantic Helpdesk Application Experiments
  • Data stored in the database was divided into 10
    subsets. Each subset was sequentially used as a
    testing set while others were used for generating
    conceptual clustering.
  • Keywords in fault conditions in each testing set
    were extracted and fuzzified as testing fuzzy
    queries.
  • To verify whether fuzzy queries can improve the
    retrieval performance, the keywords extracted are
    also used for retrieving without membership as
    crisp queries for comparison.

103
6. Semantic Helpdesk Application Experiments
  • Manually classified faults in each machine model
    into groups based on the machine components in
    which the fault occurred.
  • Retrieval accuracy is evaluated based on the
    number of the retrieved faults that are in the
    same classified group with the query.

104
6. Semantic Helpdesk Application Performance
Measures
  • Recall, Precision and F-measure

105
6. Semantic Helpdesk Application Retrieval
Performance
106
6. Semantic Helpdesk Application Performance
Comparison
  • Retrieval accuracy compared with four other
    techniques
  • Two variations of k-nearest neighbor (kNN)
    technique. The first variation (kNN1) is based on
    vectors normalized Euclidean distance to perform
    the retrieval. The second (kNN2) makes use of
    fuzzy-trigram technique to do so.
  • Two kinds of artificial neural networks (ANN)
    the supervised learning vector quantization
    (LVQ3) neural network and the unsupervised
    Self-Organizing Maps (SOM).

107
6. Semantic Helpdesk Application Performance
Comparison
(Confidence Threshold 0.2)
  • FFCA with fuzzy query outperformed kNN.
  • LVQ3 performed marginally better, but requires
    prior expert knowledge
  • for training, which would be a problem when
    dealing with large amounts
  • of uncertainty information.
  • The proposed technique can generate a concept
    hierarchy from the
  • clusters, which is important information for
    generating a corresponding
  • meaningful ontology.

108
7. Summary
  • Proposed a framework for fuzzy ontology
    generation with uncertainty information
  • FOGF consists of the following steps
  • Fuzzy Formal Concept Analysis
  • Fuzzy Conceptual Clustering
  • Fuzzy Ontology Generation
  • Semantic Representation Conversion

109
7. Summary
  • FOGF can represent uncertainty information and
    construct a concept hierarchy from the
    uncertainty information
  • Apart from constructing scholarly ontology from
    citation database, FOGF has also been used to
    generate Machine Service Ontology for Semantic
    Help-desk and Reuters News Topic Themes Ontology
  • Also, the scholarly ontology has been partially
    used to construct a Scholarly Semantic Web, a
    Semantic Web-based information retrieval system
    to support scholarly activities in the Semantic
    Web environment

110
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  • Ontology Editors
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  • 2 S. Bechhofer, I. Horrocks, P.
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  • Wordnet
  • 14 http//wordnet.princeton.edu/wordnet/download
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  • Text-to-Onto
  • 15 A. Maedche and S. Staab, Ontology learning
    for the Semantic Web," IEEE Intelligent Systems,
    Special Issue on the Semantic Web, vol. 16, no.
    2, 2001.
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  • 16 A. Faatz and R. Steinmetz, Ontology
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    at ECML/PKDD-2002, (Helsinki, Finland), 2002.
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    automated terminology translation," IEEE
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  • 18 P. Clerkin, P. Cunningham, and C. Hayes,
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