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 ALC+Tmin 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 property blocking inheritance, which can be seen as a weakness from an inferential point of view. In this paper we propose an extension of ALC+Tmin, namely ALC+T+min, with the purpose to solve the mentioned problem. In addition, we show the close connection that exists between ALC+T+min and concept-circumscribed knowledge bases. Finally, we study the complexity of deciding the classical reasoning tasks in ALC+T+min.