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One of the most complex tasks in ontology enrichment is to find definitions of
classes. This is strongly related to Inductive Logic Programming (ILP) [121] and more
specifically supervised learning in description logics. Research in those fields has many
applications apart from being applied to enrich ontologies. For instance, it is used in
the life sciences to detect whether drugs are likely to be e
cient for particular dis-
eases. Work on learning in description logics goes back to e.g. [33,34], which used so-
called least common subsumers to solve the learning problem (a modified variant of the
problem defined in this article). Later, [17] invented a refinement operator for
ALER
and proposed to solve the problem by using a top-down approach. [40,66,67] combine
both techniques and implement them in the YINYANG tool. However, those algorithms
tend to produce very long and hard-to-understand class expressions. The algorithms
implemented in DL-Learner [86,87,78,88,80] overcome this problem and investigate
the learning problem and the use of top down refinement in detail. DL-FOIL [43] is
a similar approach, which is based on a mixture of upward and downward refinement
of class expressions. They use alternative measures in their evaluation, which take the
open world assumption into account, which was not done in ILP previously. Most re-
cently, [82] implements appropriate heuristics and adaptations for learning definitions
in ontologies. The focus in this work is e
ciency and practical application of learning
methods. The article presents plugins for two ontology editors (Protégé and OntoWiki)
as well stochastic methods, which improve previous methods by an order of magnitude.
For this reason, we will analyse it in more detail in the next subsection. The algorithms
presented in the article can also learn super class axioms .
Adi
erent approach to learning the definition of a named class is to compute the
so called most specific concept (msc) for all instances of the class. The most specific
concept of an individual is the most specific class expression, such that the individual is
instance of the expression. One can then compute the least common subsumer (lcs) [16]
of those expressions to obtain a description of the named class. However, in expressive
description logics, an msc does not need to exist and the lcs is simply the disjunction
of all expressions. For light-weight logics, such as
ff
EL
, the approach appears to be
promising.
Other approaches, e.g. [91] focus on learning in hybrid knowledge bases combining
ontologies and rules . Ontology evolution [92] has been discussed in this context. Usu-
ally, hybrid approaches are a generalisation of concept learning methods, which enable
powerful rules at the cost of e
ciency (because of the larger search space). Similar as
in knowledge representation, the tradeo
ff
between expressiveness of the target language
and e
ciency of learning algorithms is a critical choice in symbolic machine learning.
Another enrichment task is knowlege base completion . The goal of such a task is to
make the knowledge base complete in a particular well-defined sense. For instance, a
goal could be to ensure that all subclass relationships between named classes can be
inferred. The line of work starting in [133] and further pursued in e.g. [15] investigates
the use of formal concept analysis for completing knowledge bases. It is promising,
although it may not be able to handle noise as well as a machine learning technique. A
Protégé plugin [140] is available. [154] proposes to improve knowledge bases through
relational exploration and implemented it in the RELExO framework 24 . It focuses on
24 http://code.google.com/p/relexo/
 
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