Tableau-based Reasoning for Description Logics with Inverse Roles and Number Restrictions

Tableau-based Reasoning for Description Logics with Inverse Roles and Number Restrictions Yu Ding, Ph.D. Concordia University, 2008 The tableaux algorithm is a general technique for deciding concept satisfiability problems in description logics (DLs). It is useful not only for practical implementations, but also for studying the correctness and complexity of concrete decision procedures. There is a family of DLs currently lack appropriate optimization techniques. The research focuses on these DLs which typically have inverse roles and number restrictions (corresponding to ontology languages OWL-lite and OWL-DL respectively). We provide solutions to known problems such as the unsoundness of global tableaux caching, and present new tableau-based algorithms for concept satisfiability problems in these DLs. The research presented in this thesis is significant in several aspects. Firstly, based on an equivalence discovered during the course of the research, we are able to show an elimination of inverse roles for a sub-family of DLs. Our experiments have confirmed the practicality of this technique. Secondly, we provide three sub-tableaux caching techniques that is sound and global (but with different power in caching functionality). Finally, we present two ExpTime tableau-based decision procedures, with the one for SHIQ achieving an improved worst-case upper bound in the strong sense of binary coding of numbers (based on the integer linear programming technique).