Obstacles on the Way to Spatial Reasoning with Description Logics: Undecidability of ALCRA⊖

This paper presents the new description logicALCRA⊖ . ALCRA⊖ combines the well-known standard description logic ALC with compositionbased role axioms of the form S ◦T ⊑ R1⊔· · · ⊔Rn. We argue that these axioms are nearly indispensable components in a description logic framework suitable for qualitative spatial reasoning tasks. An ALCRA⊖ spatial reasoning example is presented, and the relationships to other descriptions logics are discussed (namely ALCRA, ALCR+, ALC⊕, ALCHR+). Unfortunately, the satisfiability problem of this new logic is undecidable. Due to the high relevance of role axioms of the proposed form for all kinds of qualitative reasoning tasks, the undecidability of ALCRA⊖ is an important result.