A multi scale multi context ontology for fusion and fission
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A multi-scale, multi-context ontology for fusion and fission. Data Fusion and Separation Meeting June 24-26, 2001, Carnuntum, Austria. Margarita Kokla & Marinos Kavouras National Technical University of Athens. Central notion: multi-scale, multi-context ontology.

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A multi-scale, multi-context ontology for fusion and fission

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A multi-scale, multi-context ontologyfor fusion and fission

Data Fusion and Separation Meeting

June 24-26, 2001, Carnuntum, Austria

  • Margarita Kokla & Marinos Kavouras

  • National Technical University of Athens

Central notion: multi-scale, multi-context ontology

  • Extend the notion of multi-scale data to include, except from different levels of detail, different conceptualizations of geographic entities.

    • fusion of heterogeneous ontologies

    • fission: production of ontologies for specific uses

    • generalization

Integration and ontology research

  • Ontologies play important role in information integration.

  • A top-level ontology may provide the framework for integration (Guarino, 1998; Sowa 2000).

  • Fusion of different geographic domain ontologies (SDTS) with top-level ontologies (CYC, WordNet) for information exchange and reuse (Kokla & Kavouras, 2001)

  • Diversity of existent top-level ontologies (CYC, WordNet, Mikrokosmos)

  • Solution: embody theories of geographic information cognition and human categorization (Smith & Mark, 2000)

Principles of categorization and dimensions of categorical systems (Rosch, 1976)


level of abstraction


internal structure

Principles of categorization:

  • cognitive economy

  • perceived world structure

    Dimensions of categorical systems:

  • horizontal dimension:internal structure of categories

  • vertical dimension: level of abstraction

Categorical systems

categories are conceived in terms of their clear cases rather than their boundaries

basic level categorization = the most inclusive level with attributes common to all or most members of the category

Empirical evidence for the basic level

  • 9 taxonomies, e.g., tree, bird, furniture - 3 levels of abstraction (attributes in common, motor movements in common, similarity in shape) (Rosch, 1976)

  • 3 taxonomies (artificial and natural categories) - 3 levels of abstaction

Basic level categories

  • minimize ambiguity and maximize comprehension.

  • increase similarity, simplicity and commonality in user interaction (accessibility to a wider range of users).

  • help to resolve conflicts during the integration of complex categories.

Integration process

  • analysis of entity types-classes, attributes:

    • identification of heterogeneities in definitions and relationships between classes (equivalence, overlap, etc.)

    • semantic factoring

    • correspondences between attributes

  • creation of the integrated ontology

Two projects

1. Integration of:

  • CORINE Land Cover nomenclature for scales 1:100,000–1:1,000,000

  • Cadastral classification of land use characteristics developed by the Hellenic Mapping & Cadastral Organization referring to scales 1:1,000–1:5,000

    2. Definition of new land use/cover categories for conducting the 2001 agricultural census by Hellenic Statistical Service, associated with:

  • the former classification for conducting the 1991 agricultural census

  • CLUSTERS (Classification of Land Use Statistics Eurostat Remote Sensing Programme)

  • CORINE Land Cover nomenclature

Semantic factoring


Industrial or commercial units

Tertiary sector

  • decomposition of overlapping classes into fundamental, disjoint classes which:

    • constitute the most clear, unambiguous and coherent classes (elementary classes or building blocks of the categorization)

    • reflect the consensus across different conceptualizations of geographic entities

  • revelation of basic level categories during integration

Semantic factoring

  • the levels above and beneath the basic level result from synthesis and analysis correspondingly.

  • subordinate level: specialization of basic level, includes expert knowledge

  • superordinate level: abstract, usually artificial classes, e.g., «forests and semi-natural areas» (CLC) heterogeneity may occur as a result of different conceptualizations of space, e.g., land cover perspective (artificial surfaces, agricultural areas, waterbodies) vs. economic perspective (primary, secondary, tertiary sector).

Technical and transport infrastructures

Industrial, commercial and transport units


CORINE Land Cover


Technical Infrastructures

Industrial or commercial units

Semantic Factoring

(extraction of basic-level categories)

Correspondence of attributes

Cross-table of the integrated context (ascribe attributes to basic-level categories)

Creation of the integrated categorization

  • INPUT: cross-table of the integrated context

  • OUTPUT: set of final concepts and order relationships

  • modeling of basic categories, attributes, concepts and relationships using Formal Concept Analysis

Posets and trees

  • An ordered set (or partially ordered set) (P, ) is a set P with an order relation  defined on that set.

  • A binary relation on a set P is called an order relation () if for all elements, x, y, z  P the following conditions are satisfied:

    x  x (reflexivity)

    x  y and y  x implies that x = y (antisymmetry)

    x  y and y  z implies that x  z (transitivity)

  • In a poset an element may have multiple parents rather than being limited to one as in the case for trees. A poset is therefore a generalization of a tree.





a collection of sets such that for any two overlapping sets in the collection, the intersection of the sets is also in the collection

Let P be a partially ordered set. Then:

If for any two elements x, y  P the least upper bound x  y and greatest lower bound x  y always exist, then P is called a lattice. If the greatest lower bound  S and least upper bound  S exist for all S  P, then P is called a complete lattice.

Concept Lattices Formal Concept Analysis(Wille, 1992)

  • Formal Context: a triple (G, M, I) where G and M aresets of objects and attributes and I is a binary relation between G and M.

  • Incidence relation gIm: the object g has the attribute m.

  • Definition: For a set A  G of objects and a set B  M of attributes we define:

    A' = {mM gIm for all gA}

    B' = {gG gIm for all mB}

  • Formal Concept, Conceptual Class or Category:collection of entities or objects exhibiting one or more common characteristics or attributes.

    A pair (A, B) is a formal concept of the context (G, M, I) if AG, BM, A=B and B=A,

    whereAis called theextentandBtheintent of the formal concept.

Concept Lattices Formal Concept Analysis(Wille, 1992)

  • Superconcept/subconcept relation:the concept (A1, B1) is a subconcept of the concept (A2, B2) ( (A1, B1)  (A2, B2)), if A1 A2 (which is equivalent to B2 B1). (A2, B2) is then a superconcept of (A1, B1).

  • Concept Lattice: the set of all concepts of (G, M, I) ordered by the subconcept-superconcept relation is called the concept lattice of the context (G, M, I) and is denoted by B(G, M, I).

  • Basic Theorem on Concept Lattices: Let (G, M, I) be a context. Then B(G, M, I) is a complete lattice in which the greatest lower bound (meet) and the least upper bound (join) are given by:

Creation of the integrated categorization

  • incorporate multiple relationships

  • creation of extra categories based on the fusion or division of original ones: the least upper bound (join) and the greatest lower bound (meet) are given by definition

  • allow overlap, overcome the rigidity of tree structures

  • matrices in case of many classes and relationships

Algorithm for Creating Concept Lattices

  • step 1. Draw the list of object intents or attribute extents:

    {g}' = {m  M gIm}

    {m'} = {g  G gIm}

  • step 2. Use either the formulas:

  • substep 2.1. The intent M is entered into the list.

  • substep 2.m. For each set A’ entered into the list in an earlier step, we form the set:

    A'  g'

    and include it in the list, provided that it is not already contained within it.

Formal Concepts of the integrated context

Matrix Manipulations (for large contexts)

Matrix M

mij = 1 if concept Ci is subconcept of Cj mij = 0 otherwise

Matrix L

L = M-M*M

lij = 1 if concept Ci is directly below Cj

Excerpt of the Integrated Concept Lattice

Excerpt of the Integrated Concept Lattice (project 1)

CORINE Land Cover

Hellenic Cadastre

Common classes







Excerpt of the Integrated Concept Lattice (project 1)









Industrial, commercial


and transport units


vegetated areas






Industrial or

Green urban

Sport and leisure

commercial units









Port areas



Road and rail












Road network












Excerpt of the Integrated Concept Lattice (project 2)


«vertical» and «horizontal» integration

vertical: level of detail

horizontal: context (conceptualization, domain, application, etc.)

Level of detail


Classes are defined only by level of detail and context. Other parameters (e.g., spatial characteristics) are not dealt with. (e.g., building and building block)


  • Given a scale and a context, the CL makes it possible to determine the appropriate «band» and derive the classes to be used.

  • Different levels of detail correspond to «horizontal lines» (or «bands») in the CL.

  • Different contexts correspond to «vertical lines» in the CL.

Schema fission:

Different levels of detail

Schema fission:

Different Contexts

a context


  • The structure of the CL enables links between similar classes at different levels of detail

  • Dynamic generalization of geographic entities: transfer from one level of detail to the other, continuous on-the-fly generalization on the screen depending on the zoom factor

  • Generalization through time: links correspond to the evolution of classes through time

Dynamic model generalization process

Transition to different levels of detail and different classification schemata by changing the level of detail and the context.







  • development of a multi-scale, multi-context ontology for:

    • fusion

    • fission

    • generalization

  • revelation of implicit relationships between concepts

  • derivation of new classes from the fusion or division of originally overlapping ones (increase semantic completeness)

  • preservation of original ontologies

  • Conclusion

    • the CL incorporates different complementary conceptualizations, each suitable for some context and level of detail

    • fission: selection of appropriate categories according to the context and level of detail of specific applications facilitates information reuse

    • cognition should not be ignored in the integration of different ontologies - embody theories of human categorization

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