Extended Caching and Backjumping for Expressive Description Logics

Due to the wide range of modelling constructs supported by the expressive DLSROIQ, 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).