The quality of ontologies and their alignments is crucial for developing high-quality ontology-based applications. In this paper we propose an approach for repairing incoherent ontologies and ontology networks that is based on axiom weakening and completion.1
As ontologies become more prevalent and are used extensively in many
different domains, the quality of ontologies and ontology networks, i.e., a set of
ontologies connected through alignments, has become a key factor for
supporting semantically-enabled applications. Therefore, ontologies with defects need
to be repaired. One kind of defect that often occurs is the fact that the
ontology or ontology network is incoherent, i.e., it contains unsatis able concepts.
After a detection phase that nds the unsatis able concepts, a common method
for repairing is to nd justi cations for the unsatis ability and remove axioms
in these justi cations. For an overview of methods and examples, we refer to
[
In this paper we propose an approach for repairing incoherent ontologies that deals with these issues using axiom weakening and completion. The approach also uses an oracle in di erent validation steps. Furthermore, the approach can directly be applied to ontology networks by considering the mappings in the ontologies as axioms and thus considering the ontology network as one ontology. 1 Copyright © 2021 for this paper by its authors. Use permitted under Creative
Commons License Attribution 4.0 International (CC BY 4.0).
In this case repairing the ontology may remove or weaken both axioms in the ontologies or in the mappings. We can also de ne a variant of the approach that deals with mapping repair, as most current approaches assume the knowledge in the ontologies is correct and only mappings may be removed or weakened. 2
In this paper we deal with the taxonomic part of the ontology, i.e., subsumption axioms between named concepts in the ontology. Equivalence axioms are treated as two subsumption axioms. We assume that we have a set of axioms W that when removed from the ontology lead to a coherent ontology. This set could be obtained by using a traditional approach for ontology debugging together with domain expert validation of the proposed solutions. Instead of just removing these axioms our approach will try to keep more knowledge in the ontology. Algorithm 1 Repairing Algorithm
Input: An incoherent ontology O, a set of unwanted axioms W
Output: A coherent ontology Or that repairs O 1: Or O 2: for each 3: 4: 5: 6: 7: 8: 9: 10: 11: Or 12: end for
v 2 W do Or Ornf v g wsup f sp 2 sup( ) j Or 2 v sp ^ Or( v sp) = True ^ : 9 sp0 2 sup( ): (Or( v sp0) = True ^ sp0 @ sp) g
Rw ? for each sp 2 wsup do
Source sup( ) sup(sp), T arget (sub(sp) sub( )) sub( )
W R f w v w j w 2 Source ^ w 2 T arget ^ Or( w v w) = True ^ : 9 w0 v w0: (Or( 0w v w0) = True ^ ( w @ w0 _ w0 @ w))
Rw Rw [ W R end for
Or [ Rw
Given an incoherent ontology O, Algorithm 1 describes the general process of repairing. In the algorithm we denote with sup(A) the set of all the superconcepts of a concept A and with sub(A) the set of all the sub-concepts of A. Further, the oracle Or represents the domain expert and assigns a truth value True or False to an axiom. For every unwanted axiom v we remove it from the ontology (line 3) and try to weaken it by nding axioms of the form v sp with sp a super-concept of , that are correct according to the domain expert and retain the most knowledge. The set wsup collects concepts sp that satisfy these requirements (line 4).
Further, we try to nd improved axioms for a weakened axiom and collect
these in the set W R. We try to improve a weakened axiom by nding an w v
w that is correct according to the domain expert and such that v w and w
v sp. We call this completing as in [
Fig. 1. An example of repairing an incoherent ontology
contains all super-concepts of that are not super-concepts of sp. The latter are
removed to not introduce equivalence relations between concepts that are not
equivalent in the original ontology. The Target set collects the candidates for w.
It contains all sub-concepts of sp that are not sub-concepts of and are not
subconcepts of . The sub-concepts of are removed to not introduce equivalence
relations between concepts that are not equivalent in the original ontology. The
sub-concepts of are removed to not re-introduce the derivation of the unwanted
axiom v . Furthermore, we also want to keep as much knowledge as possible
(line 7-8). Note that it may be the case that W R contains the weakened axiom
itself. Rw is the union of all the W R (lines 5 and 9). The ontology is updated
by adding completed weakened axioms in case such were found (line 11). In the
terminology of [
We exemplify our approach using the ontology shown in Fig.1a. In this ontology, concept P is unsatis able (as it is sub-concept of A and I which are disjoint). A domain expert that validates the result of a debugging system may decide that W = fK v Ag is a set of incorrect axioms. In Algorithm 1 this axiom is removed from the ontology. Then weakened axioms of the form K v sp with sp a super-concept of A are computed. These need to be true according to the domain expert and sp needs to be as speci c as possible to keep as much knowledge as possible. In this case we may get wsup = fXg representing the weakened axioms set fK v Xg. Then, we try to improve the weakened axioms by completing. Here, the computed source and target sets are sourceKvX = fK; T g and targetKvX = fX; Sg. The completed axioms are then K v X, K v S, T v X and T v S. A domain expert validates these and retains the one(s) that keep the most knowledge. Assuming Or(T v S) = True, the completed weakened axioms set RKvA is fT v Sg. The repaired ontology is shown in Fig 1b. 3
We can use the algorithm also for ontology networks. In the rst variant the network is considered as one large ontology and no distinction is made between mappings and axioms in the ontologies. In this case Algorithm 1 can be used as is. In many current approaches for alignment repair, however, only mappings are removed. In this case we can use a variant of Algorithm 1 (variant 2) that distinguishes between axioms and mappings, and only mappings are removed and weakened.
We used the ontologies MA and NCI-A from the OAEI Anatomy track [
In this paper, we proposed an approach for repairing incoherent ontologies which
focuses on preserving as much knowledge as possible. It combines a debugging
approach, an axiom weakening approach and a completion approach together
with domain expert validation. We intend to integrate the approach within the
RepOSE system [
Acknowledgements. This work has been nancially supported by the Swedish e-Science Research Centre (SeRC), the Swedish Research Council (Vetenskapsradet, dnr 2018-04147), and the Swedish Agency for Economic and Regional Growth (Tillvaxtverket).