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Reasoning on defeasible knowledge is a topic of interest in the area ofdescription logics, as it is related to the need of representing exceptionalinstances in knowledge bases. In this direction, in our previous works wepresented a framework for representing (contextualized) OWL RL knowledge baseswith a notion of justified exceptions on defeasible axioms: reasoning in suchframework is realized by a translation into ASP programs. The resultingreasoning process for OWL RL, however, introduces a complex encoding in orderto capture reasoning on the negative information needed for reasoning onexceptions. In this paper, we apply the justified exception approach toknowledge bases in $\textit{DL-Lite}_{\cal R}$, i.e., the language underlyingOWL QL. We provide a definition for $\textit{DL-Lite}_{\cal R}$ knowledge baseswith defeasible axioms and study their semantic and computational properties.In particular, we study the effects of exceptions over unnamed individuals. Thelimited form of $\textit{DL-Lite}_{\cal R}$ axioms allows us to formulate asimpler ASP encoding, where reasoning on negative information is managed bydirect rules. The resulting materialization method gives rise to a completereasoning procedure for instance checking in $\textit{DL-Lite}_{\cal R}$ withdefeasible axioms. Under consideration in Theory and Practice of LogicProgramming (TPLP).

Reasoning on $\textit{DL-Lite}_{\cal R}$ with Defeasibility in ASP