Reasoning Efficiently with Ontologies and Rules in the Presence of Inconsistencies (Extended Abstract)

In this paper, we address the problem of dealing with inconsistent knowledge bases consisting of ontologies and non-monotonic rules, following a paraconsistent reasoning approach with a focus on efficiency. Description Logics (DLs) and Logic Programs (LPs) provide different strengths when used for Knowledge Representation and Reasoning. While DLs employ the Open World Assumption and are suited for defining ontologies, LPs adopt the Closed World Assumption and are able to express non-monotonic rules with exceptions and preference orders. Combining features of both formalisms has been actively pursued over the last few years, resulting in different proposals with different levels of integration and complexity: while some extend DLs with rules [18, 25], others follow a hybrid combination of ontologies with non-monotonic rules, either providing a modular approach where rules and ontologies use their own semantics, and allowing limited interaction between them [10], or defining a unifying framework for both components [29, 24]. Equipped with semantics that are faithful to their constitutive parts, these proposals allow for the specification of so-called hybrid knowledge bases (hybrid KBs) either from scratch, benefiting from the added expressivity, or by combining existing ontologies and rule bases. The complex interactions between the ontology component and the rule component of these hybrid KBs – even more so when they result from combining existing ontologies and rule bases developed independently – can easily lead to contradictions, which, under classical semantics, trivialize standard reasoning and prevent us from drawing any meaningful conclusions, ultimately rendering these hybrid KBs useless.