Repairing Description Logic Ontologies

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Description Logics (DLs) are a family of logic-based knowledge representation languages, which are used to formalize ontologies for application domains such as biology and medicine. As the size of DL-based ontologies grows, tools for improving their quality become more important. DL reasoners can detect inconsistencies and infer other implicit consequences. However, for the developer of an ontology, it is often hard to understand why a consequence computed by the reasoner follows, and how to repair the ontology if this consequence is not intended. The classical algorithmic approach for repairing DL-based ontologies is to compute (one or more) maximal subsets of the ontology that no longer have the unintended consequence. In previous work we have introduced a more "gentle" approach for repairing ontologies that allows us to retain more consequences than the classical approach: instead of completely removing axioms, our gentle repair replaces them by "weaker" axioms, i.e., axioms that have less consequences. In addition to introducing the general framework, we have defined useful properties of weakening relations on axioms and investigated two particular such relations for the DL EL.The purpose of this project is foremost to investigate this gentle repair approach in more detail. On the one hand, we will consider variants of the general framework, e.g., w.r.t. which and how many axioms are chosen to be weakened. On the other hand, we will design different weakening relations, both for light-weight DLs such as EL and for expressive DLs such as ALC, and investigate their properties. In addition, we will clarify the relationship to similar approaches in other areas such as belief revision and inconsistency-tolerant reasoning, and extend our approach to the setting of privacy-preserving ontology publishing. Regarding belief revision, it should be noted that our gentle repair approach is related to what is called pseudo-contraction in that area. However, the emphasis in belief revision is more on abstract approaches for generating contractions that satisfy certain postulates than on defining and investigating concrete repair approaches. We will investigate which of these postulates are satisfied by our approaches. Inconsistency-tolerant reasoning is of interest since it is often based on considering what follows from some, all, or the intersection of all repairs. We will investigate how our new notion of repair influences these inconsistency-tolerant reasoning approaches. In privacy-preserving ontology publishing, removing consequences that are to be hidden from the ontology is not sufficient since an attacker might have additional background information. In previous work, we have considered this problem in a very restricted setting, where both the information to be published and the background knowledge are represented using EL concepts. We intend to generalize this to more general forms of knowledge bases and more expressive DLs.