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

Abstract

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 $\mathcal{A}\mathcal{LC}$+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 $\mathcal{A}\mathcal{LC}$+T${}_{\mathsf{min}}$, namely $\mathcal{A}\mathcal{LC}$+T${}_{\mathsf{min}}^{+}$, with the purpose to solve the mentioned problem. In addition, we show the close connection that exists between $\mathcal{A}\mathcal{LC}$+T${}_{\mathsf{min}}^{+}$ and concept-circumscribed knowledge bases. Finally, we study the complexity of deciding the classical reasoning tasks in $\mathcal{A}\mathcal{LC}$+T${}_{\mathsf{min}}^{+}$.

arXiv commentProceedings of the 15th International Workshop on Non-Monotonic Reasoning (NMR 2014)