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Theory and Applications of Ontology: Computer Applications pp 533–563Cite as

The Institutional Approach

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Abstract

This chapter discusses the institutional approach for organizing and maintaining ontologies. The theory of institutions was named and initially developed by Joseph Goguen and Rod Burstall. This theory, a metatheory based on category theory, regards ontologies as logical theories or local logics. The theory of institutions uses the category-theoretic ideas of fibrations and indexed categories to develop logical theories. Institutions unite the lattice approach of Formal Concept Analysis of Ganter and Wille with the distributed logic of Information Flow of Barwise and Seligman. The institutional approach incorporates locally the lattice of theories idea of Sowa from the theory of knowledge representation. The Information Flow Framework, which was initiated within the IEEE Standard Upper Ontology project, uses the institutional approach in its applied aspect for the comparison, semantic integration and maintenance of ontologies. This chapter explains the central ideas of the institutional approach to ontologies in a careful and detailed manner.

Systems, scientific and philosophic, come and go. Each method of limited understanding is at length exhausted. In its prime each system is a triumphant success: in its decay it is an obstructive nuisance.

Alfred North Whitehead, Adventures of Ideas

(in memory of Joseph Goguen)

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Notes

  1. 1.

    Here is a key to the terminology used in this paper.

    This paper

    Category theory

    Object

    Object

    Link

    Arrow, morphism, 1-cell

    Connection

    2-cell

    Beginning, origin(ation)

    Source, domain

    Ending, destination

    Target, codomain

    Context

    Category

    Passage

    Functor

    Bridge

    Natural transformation

    Invertible passage

    Adjunction

    Equivalence

    Natural equivalence

    (Co)relation

    (Co)cone

    Sum (product)

    Colimit (limit)

    Relative sum

    Left Kan extension

  2. 2.

    We describe the semantic integration of ontologies in terms of theories.

    Alignment: Informally, identify the theories to be used in the construction. Decide on the semantic interconnection (semantic mapping) between theories. This may involve the introduction of some additional mediating (reference) theories. Formally, create a diagram of theories of shape (indexing) context that indicates this selection and interconnection. This diagram of theories is transient, since it will be used only for this computation. Other diagrams could be used for other sum constructions. Compute the base diagram of languages with the same shape. Form the sum language of this diagram, with language summing corelation. Being the basis for theory sums, language sums are important. They involve the two opposed processes of “summing” and “quotienting”. Summing can be characterized as “keeping things apart” and “preserving distinctness”, whereas quotienting can be characterized as “putting things together”, “identification” and “synonymy”. The “things” involved here are symbolic, and for a first order logic institution may involve relation type symbols, entity type symbols and the concepts that they denote.

    Unification: Form the sum theory of the diagram of theories, with theory summing corelation. The summing corelation is a universal corelation that connects the individual theories in the diagram to the sum theory. The sum theory may be virtual. Using direct flow, move the individual theories in the diagram of theories from the “lattice of theory diagrams over the language diagram” along the language morphisms in the language summing corelation to the lattice of theories over the language sum, getting a homogeneous diagram of theories with the same shape, where each theory in this direct flow image diagram has the same sum language (the meaning of homogeneous). Compute the meet of this direct flow diagram within the fiber “lattice of theories” over language sum, getting the sum theory. The language summing corelation is the base of the theory summing corelation. Using inverse flow, move the sum theory from the language sum back along the language morphisms in the language summing corelation to the language diagram, getting the system closure.

  3. 3.

    The category Cls of classifications and infomorphisms is the ambient category that is used for indexing in the institutional approach to ontologies. This is the category of “twisted relations” of (Goguen and Burstall, 1992). This is also the basic category used in the theory of Information Flow and Formal Concept Analysis (Kent, 2002).

  4. 4.

    The fusion of an indexed context might be called “fusion in the large” or “structural fusion”. The sums of diagrams, in particular sums of diagrams of theories of an institution, which takes place within the fused context of theories, might be called “fusion in the small” or “theoretical fusion”. Both are kinds of constrained sums.

  5. 5.

    This explains the flip in the definition of cocompleteness and cocontinuity for dual (inversely) indexed contexts.

  6. 6.

    See Footnote 2

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Authors and Affiliations

  1. Ontologos, Pullman, Washington, USA

    Robert E. Kent

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  1. Robert E. Kent
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Correspondence to Robert E. Kent .

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Editors and Affiliations

  1. Dipto. Sociologia e Ricerca Sociale, Universita di Trento, Via Verdi 26, Trento, 38100, Italy

    Roberto Poli

  2. 23rd Place NE., 13544, Seattle, 98125-3325, Washington, USA

    Michael Healy

  3. Computer Technology Institute, Hellenic Open University &, N. Kazantzaki Str., Patras, 265 00, Greece

    Achilles Kameas

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Kent, R.E. (2010). The Institutional Approach. In: Poli, R., Healy, M., Kameas, A. (eds) Theory and Applications of Ontology: Computer Applications. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-8847-5_23

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