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axioms), the methodology used to construct the ontology, the costs (hardware, soft-
ware, licensing, etc.) of using the ontology, and the tools available for working with
the ontology. Many of the criteria are simple enough that the score of an ontology
with respect to these criteria could be computed automatically or at least without
much human involvement. The authors also cite several earlier works in the same
area, with a more moderate number of criteria.
11.3 A Theoretical Framework for Ontology Evaluation
In this section we present a formal definition of ontologies, provide examples of how
various kinds of ontologies may be captured in the context of this formalization, and
discuss how evaluation fits into this formal framework.
A reasonable and well thoughtout formal definition of ontologies has been de-
scribed recently in the work of Ehrig et al. [6]. In this formalization, the on-
tology (with datatypes) is defined as a structure O =( C, T, R, A, I, V, ≤ C , ≤ T
R A C T R A ). It consists of (disjoint) sets of concepts ( C ), types ( T ), rela-
tions ( R ), attributes ( A ), instances ( I ) and values ( V ). The partial orders C (on
C ) and T (on T ) define a concept hierarchy and a type hierarchy. The function
σ R : R → C × C provides relation signatures (i.e., for each relation, the function
specifies which concepts may be linked by this relation), while σ A : A → C × T pro-
vides attribute signatures (for each attribute, the function specifies to which concept
the attribute belongs and what is its datatype). Finally, there are partial instantia-
tion functions ι C : C → 2 I (the assignment of instances to concepts), ι T : T → 2 V
(the assignment of values to types), ι R : R → 2 I×I (which instances are related by a
particular relation), and ι A : A → 2 I×V (what is the value of each attribute for each
instance). (Another formalization of ontologies, based on similar principles, has also
been described by Bloehdorn et al. [1].)
For some types of ontologies, this framework can be further extended, par-
ticularly with “concept attributes” in addition to the “instance attributes” men-
tioned above. The concept attributes would be a set A , with a signature function
σ A : A → T and an instantiation function ι A : A 2 C×V . The value of such an
attribute would not be associated to a particular instance of a concept, but would
apply to the concept as such. This extension will be useful for some of the evalu-
ation scenarios considered later in this section. Other possible extensions, such as
relations between concepts (as opposed to between instances), the introduction of
metaclasses, or the introduction of relations with arity greater than 2, are probably
of less practical interest.
A flexible formal network like this can accommodate various commonly-used
kinds of ontologies:
Terminological ontologies where concepts are word senses and instances are
words. The WordNet ontology (http://www.cogsci.princeton.edu/ wn/) is an
example of this. Attributes include things like natural-language descriptions of
word senses (for concepts) and string representations of words (for instances).
Topic ontologies where concepts are topics and instances are documents. Familiar
examples include the Open Directory at http://www.dmoz.org/ or the Yahoo!
directory at http://dir.yahoo.com/. Concept attributes typically consist of a
name and a short description of each topic, and instance attributes consist of a
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