On the Non-Monotonic Description Logic
  $\mathcal{ALC}$+T$_{\mathsf{min}}$
  In the last 20 years many proposals have been made to incorporate
non-monotonic reasoning into description logics, ranging from approaches based
on 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 preferential
semantics with minimization of a certain kind of concepts, which represent
atypical instances of a class of elements. One of its drawbacks is that it
suffers from the problem known as the \emph{property blocking inheritance},
which can be seen as a weakness from an inferential point of view. In this
paper we propose an extension of $\mathcal{ALC}$+T$_{\mathsf{min}}$, namely
$\mathcal{ALC}$+T$^+_{\mathsf{min}}$, with the purpose to solve the mentioned
problem. 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$^+_{\mathsf{min}}$.
