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

Reasoning on defeasible knowledge is a topic of interest in the area of description logics, as it is related to the need of representing exceptional instances in knowledge bases. In this direction, in our previous works we presented a framework for representing (contextualized) OWL RL knowledge bases with a notion of justified exceptions on defeasible axioms: reasoning in such framework is realized by a translation into ASP programs. The resulting reasoning process for OWL RL, however, introduces a complex encoding in order to capture reasoning on the negative information needed for reasoning on exceptions. In this paper, we apply the justified exception approach to knowledge bases in $textit{DL-Lite}_{cal R}$, i.e., the language underlying OWL QL. We provide a definition for $textit{DL-Lite}_{cal R}$ knowledge bases with defeasible axioms and study their semantic and computational properties. In particular, we study the effects of exceptions over unnamed individuals. The limited form of $textit{DL-Lite}_{cal R}$ axioms allows us to formulate a simpler ASP encoding, where reasoning on negative information is managed by direct rules. The resulting materialization method gives rise to a complete reasoning procedure for instance checking in $textit{DL-Lite}_{cal R}$ with defeasible axioms. Under consideration in Theory and Practice of Logic Programming (TPLP).