Selecting accepted assertions in partially ordered inconsistent DL-Lite knowledge bases

AbstractThe problem of inconsistency handling in knowledge bases has received considerable research attention in several settings and has met many applications. Inconsistency usually stems from the fact that the information available for reasoning, query answering and decision-making tasks is obtained from different, scattered and potentially unreliable information sources. Performing these tasks is often computationally expensive, especially for knowledge bases in which the data is endowed with preferences and/or uncertainty. In the context of formal ontologies, enriching the assertions (i.e. the data pieces) with conceptual knowledge makes the query answering task harder computationally. Tractable results have been successfully established for the lightweight languages of the DL-Lite family. In this paper, we present two tractable methods for handling inconsistency in partially ordered lightweight ontologies. In essence, both methods are inspired from the well-known Intersection of ABox Repair (IAR) semantics, which proceeds by replacing the initial inconsistent knowledge base with the intersection of all of its maximally consistent sub-bases. The first method assumes a partial preorder over the knowledge base and identifies the accepted assertions, called ‘elected’, in polynomial time in data complexity. The second method captures uncertainty quantitatively in the framework of possibility theory and identifies the so-called ‘π-accepted’ assertions, also in polynomial time in data complexity. However, both characterisations require the conflict set to be readily available. This constitutes a serious limitation in frameworks and applications where the conflict set cannot be exhibited efficiently. In this paper, we propose a new and equivalent characterisation for each method. We show that the elected assertions and also the π-accepted assertions can be identified in polynomial time in the size of the dataset for lightweight ontologies.Keywords: Inconsistency managementknowledge basesontologiesDL-Litepartial order AcknowledgmentsThe authors would like to thank the reviewers for their useful comments which helped improving the paper.Disclosure statementNo potential conflict of interest was reported by the author(s).Notes1 The equivalence φi≡φj means that both φi⊵φj and φj⊵φi hold.2 The incomparability φi⋈φj means that neither φi⊵φj nor φj⊵φi holds.3 The equivalence relation φi≡φj means that both φi⊵φj and φj⊵φi hold.4 In the set Λ(ϕi), we omit the uncertainty degrees associated with the assertions in order to be able to use the standard consistency checking mechanism of the ontological language.Additional informationFundingThis research has received support from the European Union's Horizon Research and Innovation Programme under the MSCA-SE (Marie Skłodowska-Curie Actions Staff Exchange) grant agreement 101086252; Call: HORIZON-MSCA-2021-SE-01; Project title: STARWARS (STormwAteR and WastewAteR networkS heterogeneous data AI-driven management). This research has also received support from the French national project ANR (Agence Nationale de la Recherche) CROQUIS (Collecte, représentation, complétion, fusion et interrogation de données hétérogènes et incertaines de réseaux d'eaux urbains), grant number ANR-21-CE23-0004 and from the ANR project EXPIDA (EXplainable and parsimonious Preference models to get the most out of Inconsistent DAtabases), grant number ANR-22-CE23-0017.