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In the last 20 years many proposals have been made to incorporatenon-monotonic reasoning into description logics, ranging from approaches basedon default logic and circumscription to those based on preferential semantics.In particular, the non-monotonic description logic$\mathcal{ALC}$+T$_{\mathsf{min}}$ uses a combination of the preferentialsemantics with minimization of a certain kind of concepts, which representatypical instances of a class of elements. One of its drawbacks is that itsuffers from the problem known as the \emph{property blocking inheritance},which can be seen as a weakness from an inferential point of view. In thispaper we propose an extension of $\mathcal{ALC}$+T$_{\mathsf{min}}$, namely$\mathcal{ALC}$+T$^+_{\mathsf{min}}$, with the purpose to solve the mentionedproblem. In addition, we show the close connection that exists between$\mathcal{ALC}$+T$^+_{\mathsf{min}}$ and concept-circumscribed knowledge bases.Finally, we study the complexity of deciding the classical reasoning tasks in$\mathcal{ALC}$+T$^+_{\mathsf{min}}$.

On the Non-Monotonic Description Logic $\mathcal{ALC}$+T$_{\mathsf{min}}$