Abstract
AbstractIn this paper we develop a concept aware multi-preferential semantics for dealing with typicality in description logics, where preferences are associated with concepts, starting from a collection of ranked TBoxes containing defeasible concept inclusions. Preferences are combined to define a preferential interpretation in which defeasible inclusions can be evaluated. The construction of the concept-aware multipreference semantics is related to Brewka’s framework for qualitative preferences. We exploit Answer Set Programming (in particular,asprin) to achieve defeasible reasoning under the multipreference approach for the lightweight description logic ξ$\mathcal L_ \bot ^ + $.
Highlights
We propose a “concept-aware multipreference semantics” for reasoning about exceptions in ontologies taking into account preferences with respect to different concepts and integrating them into a preferential semantics which allows a standard interpretation of defeasible inclusions
To prove the feasibility of our approach, we develop a proof method for reasoning under the proposed multipreference semantics for the description logic EL+⊥ (Kazakov et al 2014), the fragment of OWL2 EL supported by ELK
In this paper we have developed an ASP approach for defeasible inference in a conceptwise multipreference extension of EL⊥
Summary
The need to reason about exceptions in ontologies has led to the development of many non-monotonic extensions of Description Logics (DLs), incorporating features from NMR formalisms in the literature (Straccia 1993; Baader and Hollunder 1995; Donini et al 2002; Giordano et al 2007; Britz et al 2008; Bonatti et al 2009; Casini and Straccia 2010; Motik and Rosati 2010), and notably including extensions of rule-based languages (Eiter et al 2008; Eiter et al 2011; Knorr et al 2012; Gottlob et al 2014; Giordano and Theseider Dupre 2016; Bozzato et al 2018), as well as new constructions and semantics (Casini and Straccia 2013; Bonatti et al 2015; Bonatti 2019). The ranked TBox for concept Horse describes the typical properties of horses, of running fast, having a long mane, being tall, having a tail and a saddle. These properties are defeasible and horses should not necessarily satisfy all of them. We introduce a notion of multipreference entailment and prove that it satisfies the KLM properties of preferential consequence relations This notion of entailment deals properly with irrelevance and specificity, is not subject to the “blockage of property inheritance” problem, which affects rational closure (Pearl 1990), i.e., if a subclass is exceptional with respect to a superclass for a given property, it does not inherit from that superclass any other property. As a consequence of the soundness and completeness of this reformulation of multipreference entailment, we prove that concept-wise multipreference entailment is Πp2-complete for EL+⊥ ranked knowledge bases
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