No abstract

This system description paper introduces the OWL 2 reasoner HermiT. The reasoner is fully compliant with the OWL 2 Direct Semantics as standardised by the World Wide Web Consortium (W3C). HermiT is based on the hypertableau calculus, and it supports a wide range of standard and novel optimisations to improve the performance of reasoning on real-world ontologies. Apart from the standard OWL 2 reasoning task of entailment checking, HermiT supports several specialised reasoning services such as class and property classification, as well as a range of features outside the OWL 2 standard such as DL-safe rules, SPARQL queries, and description graphs. We discuss the system's architecture, and we present an overview of the techniques used to support the mentioned reasoning tasks. We further compare the performance of reasoning in HermiT with that of FaCT++ and Pellet-two other popular and widely used OWL 2 reasoners.

We present a novel reasoning calculus for the description logic SHOIQ^+---a knowledge representation formalism with applications in areas such as the Semantic Web. Unnecessary nondeterminism and the construction of large models are two primary sources of inefficiency in the tableau-based reasoning calculi used in state-of-the-art reasoners. In order to reduce nondeterminism, we base our calculus on hypertableau and hyperresolution calculi, which we extend with a blocking condition to ensure termination. In order to reduce the size of the constructed models, we introduce anywhere pairwise blocking. We also present an improved nominal introduction rule that ensures termination in the presence of nominals, inverse roles, and number restrictions---a combination of DL constructs that has proven notoriously difficult to handle. Our implementation shows significant performance improvements over state-of-the-art reasoners on several well-known ontologies

Description logics (DLs) and rules are formalisms that emphasize different aspects of knowledge representation: whereas DLs are focused on specifying and reasoning about conceptual knowledge, rules are focused on nonmonotonic inference. Many applications, however, require features of both DLs and rules. Developing a formalism that integrates DLs and rules would be a natural outcome of a large body of research in knowledge representation and reasoning of the last two decades; however, achieving this goal is very challenging and the approaches proposed thus far have not fully reached it. In this paper, we present a hybrid formalism of MKNF + knowledge bases, which integrates DLs and rules in a coherent semantic framework. Achieving seamless integration is nontrivial, since DLs use an open-world assumption, while the rules are based on a closed-world assumption. We overcome this discrepancy by basing the semantics of our formalism on the logic of minimal knowledge and negation as failure (MKNF) by Lifschitz. We present several algorithms for reasoning with MKNF + knowledge bases, each suitable to different kinds of rules, and establish tight complexity bounds.

As applications of description logics proliferate, efficient reasoning with knowledge bases containing many assertions becomes ever more important. For such cases, we developed a novel reasoning algorithm that reduces a SHIQ knowledge base to a disjunctive datalog program while preserving the set of ground consequences. Queries can then be answered in the resulting program while reusing existing and practically proven optimization techniques of deductive databases, such as join-order optimizations or magic sets. Moreover, we use our algorithm to derive precise data complexity bounds: we show that SHIQ is data complete for NP, and we identify an expressive fragment of SHIQ with polynomial data complexity.