Worst-Case Optimal Reasoning for the Horn-DL Fragments of OWL 1 and 2

Horn fragments of Description Logics (DLs) have gained popularity because they provide a beneficial trade-off between expressive power and computational complexity and, more specifically, are usually tractable w.r.t. data complexity. Despite their potential, and partly due to the intricate interaction of nominals (O), inverses (I) and counting (Q), such fragments had not been studied so far for the DLs SHOIQ and SROIQ that underly OWL 1 and 2. In this paper, we present a polynomial and modular translation from HornSHOIQ knowledge bases into DATALOG, which shows that standard reasoning tasks are feasible in deterministic single exponential time. This improves over the previously known upper bounds, and contrasts the known NEXPTIME completeness of full SHOIQ. Thereby, Horn-SHOIQ stands out as the first EXPTIME complete DL that allows simultaneously for O, I, and Q. In addition, we show that standard reasoning in Horn-SROIQ is 2-EXPTIME complete. Despite their high expressiveness, bot...

• Type: Conference
• Year: 2010
• Where: KR
• Authors: Magdalena Ortiz, Sebastian Rudolph, Mantas Simkus
• Keywords: Automated Reasoning, Data Complexity, KR 2010, Standard Reasoning, Standard Reasoning Tasks