  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).
