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

Abstract

The 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.