Foundations of Refinement Operators for Description Logics

Abstract

In order to leverage techniques from Inductive Logic Programming for the learning in description logics (DLs), which are the foundation of ontology languages in the Semantic Web, it is important to acquire a thorough understanding of the theoretical potential and limitations of using refinement operators within the description logic paradigm. In this paper, we present a comprehensive study which analyses desirable properties such operators should have. In particular, we show that ideal refinement operators in general do not exist, which is indicative of the hardness inherent in learning in DLs. We also show which combinations of desirable properties are theoretically possible, thus providing an important step towards the definition of practically applicable operators.

DL-FOIL Concept Learning in Description Logics

“…As known from related works [10,13,17], the subsumption relationship (see Def. 2.1) induces a partial order on the space of all the possible concept descriptions.…”

“…These operators cannot be complete for most expressive DLs [17]. However, we are not looking for too precise operators that likely lead to overfit the data.…”

Class expression learning for ontology engineering

“…The refinement operator in the considered algorithm is defined in [25]. It is based on earlier work in [24] which in turn is build on theoretical foundations in [23]. It has been shown to be the best achievable operator with respect to a set of properties (not further described here), which are used to assess the performance of refinement operators.…”

“…However, those algorithms tend to produce very long and hard-to-understand class expressions. The algorithms implemented in DL-Learner [23,24,20,25] overcome this problem and investigate the learning problem and the use of top down refinement in detail. DL-FOIL [15] is a similar approach, which is based on a mixture of upward and downward refinement of class expressions.…”

ORE - A Tool for Repairing and Enriching Knowledge Bases

“…However, those algorithms tend to produce very long and hard-tounderstand class expressions, which are often not appropriate in an ontology enrichment context. Therefore, ORE is based on DL-Learner [20], which allows to select between a variety of learning algorithms [22,23,19,24]. Amongst them, CELOE is particularly optimised for learning easy to understand expressions.…”