Inconsistency-tolerant Semantics for Description Logic

Abstract

It is well-known that inconsistency causes severe problems in classical logic. In particular, since an inconsistent logical theory has no model, it logically implies every formula, and, therefore, query answering on an inconsistent knowledge base becomes meaningless. In this paper, we address the problem of dealing with inconsistencies in Description Logic (DL) knowledge bases. Our goal is both to study DL semantical frameworks which are inconsistency-tolerant, and to devise techniques for answering queries posed to DL knowledge bases under such inconsistency-tolerant semantics. A DL knowledge base is constituted by two components, called the TBox and the ABox, respectively. Intuitively, the TBox includes axioms sanctioning general properties of concepts and relations (such as Dog isa Animal), whereas the ABox contains axioms asserting properties of instances of concepts and relations (such as Bob is an instance of Dog). The various DLs differ in the language (set of constructs) used to express such axioms. We are particularly interested in using DLs for the so-called “ontology-based data access” [8] (ODBA), where a DL TBox acts as an ontology used to access a set of data sources. Since it is often the case that, in this setting, the size of the data at the sources largely exceeds the size of the ontology, DLs where query answering is tractable with respect to the size of the ABox have been studied recently. In this paper, we will consider DLs specifically tailored towards ODBA, in particular DLs of the DL-Lite family [8], where query answering can be done efficiently with respect to the size of the ABox. Depending on the expressive power of the underlying language, the TBox alone might be inconsistent, or the TBox might be consistent, but the axioms in the ABox might contradict the axioms in the TBox. Since in ODBA the ontology is usually represented as a consistent TBox, whereas the data at the sources do not necessarily conform to the ontology, the latter situation is the one commonly occurring in practice. Therefore, our study is carried out under the assumption that the TBox is consistent, and inconsistency may arise between the ABox and the TBox (inconsistencies in the TBox are considered, e.g., in [5, 9]). There are many approaches for devising inconsistency-tolerant inference systems [1], originated in different areas, including Logic, Artificial Intelligence, and Databases. Our work is especially inspired by the approaches to consistent query answering in databases [3], which are based on the idea of living with inconsistencies (i.e.,

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@inproceedings{Lembo2011InconsistencytolerantSF, title={Inconsistency-tolerant Semantics for Description Logic}, author={Domenico Lembo and Maurizio Lenzerini and Riccardo Rosati and Marco Ruzzi and Domenico Fabio Savo}, year={2011} }