On the Non-Monotonic Description Logic $\mathcal{ALC}$+T$_{\mathsf{min}}$
This addresses a specific inferential weakness in description logics for knowledge representation, but it is incremental as it builds on an existing logic.
The paper tackles the problem of property blocking inheritance in the non-monotonic description logic ALC+T_min by proposing an extension called ALC+T^+_min to solve it, and shows its connection to concept-circumscribed knowledge bases while studying the complexity of reasoning tasks.
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$^+_{\mathsf{min}}$.