Fusions of Description Logics and Abstract Description Systems

TL;DR

This paper extends decidability transfer results from normal modal logics to a broad class of description logics by introducing abstract description systems, enabling a uniform approach to combining and analyzing these logics.

Contribution

It introduces abstract description systems as a unified framework and generalizes decidability transfer results to a wider class of description logics.

Findings

Decidability transfer results are extended to many description logics.

Abstract description systems unify description and modal logics.

The approach covers various combinations of description logics.

Abstract

Fusions are a simple way of combining logics. For normal modal logics, fusions have been investigated in detail. In particular, it is known that, under certain conditions, decidability transfers from the component logics to their fusion. Though description logics are closely related to modal logics, they are not necessarily normal. In addition, ABox reasoning in description logics is not covered by the results from modal logics. In this paper, we extend the decidability transfer results from normal modal logics to a large class of description logics. To cover different description logics in a uniform way, we introduce abstract description systems, which can be seen as a common generalization of description and modal logics, and show the transfer results in this general setting.