Abstract

Due to the wide range of modelling constructs supported by the expressive DL SROIQ, the typically used tableau algorithms in competitive reasoning systems such as FaCT++ [16], HermiT, 3 or Pellet [14] have a very high worst-case complexity. The development of tableau optimisations that help to achieve practical efficiency is, therefore, a longstanding challenge in DL research (see, e.g., [11, 17]). A very effective and widely implemented optimisation technique is “caching”, where one caches, for a set of concepts, whether they are known to be, or can safely be assumed to be, satisfiable or unsatisfiable [4]. If the set of concepts appears again in a model abstraction, then a cache-lookup allows for skipping further applications of tableau rules. Unfortunately, with increasing expressivity naively caching become unsound, for instance, due to the possible interaction of inverse roles with universal restrictions [1, Chapter 9]. With this contribution we push the boundary of the caching optimisation to the expressive DL SROIQ. The developed unsatisfiability caching method is based on a sophisticated dependency management, which further enables better informed tableau backtracking and more efficient pruning (Section 3). Our techniques are grounded in the widely implemented tableau calculus for SROIQ [9], which makes it easy to transfer our results into existing implementations. The optimisations are integrated within a novel reasoning system, called Konclude [13]. Our empirical evaluation shows that the proposed optimisations result in significant performance improvements (Section 4). 2