Optimised Absorption for Expressive Description Logics

The Web Ontology Language (OWL 2) [19] is based on the very expressive Description Logic (DL) SROIQ [3] for which sophisticated algorithms are required to handle (standard) reasoning tasks. In practice, variants of tableau algorithms are often used since they are easily extensible and adaptable. Since such algorithms have a very high worst-case complexity, developing optimisations to nevertheless allow for highly efficient implementations is a long-standing research area in DLs (see, e.g., [4,18]). A very effective and widely implemented optimisation is absorption, which is a preprocessing step that aims at rewriting general concept inclusion (GCI) axioms such that non-determinism in the tableau algorithm is avoided as much as possible. In this paper, we present an improved variant of a recursive binary absorption algorithm that generalises the well-known techniques of binary absorption [7] and role absorption [17]. The algorithm also allows for absorbing parts of concepts and, as a result, more expressive concept constructors can be handled and non-determinism can often be delayed further. The algorithm has already been introduced in our previous work [12] as an essential pre-requisite for handling nominal schemas [8]. Here we simplify its presentation, prove the correctness, present several extensions for the algorithm, and provide a comparison with other absorption techniques. The algorithm is implemented in the tableau-based reasoner Konclude [15] and is essential for Konclude’s efficiency. In fact, many other optimisation techniques in Konclude are based on the presented absorption and they significantly benefit from the reduced or eliminated non-determinism [13,14]. We next introduce the basics of tableau algorithms and absorption. In Section 3, we introduce our recursive absorption algorithm for which we present several extension in Section 4. We discuss related work in Section 5 before we conclude in Section 6.