An ExpTime Tableau Method for Dealing with Nominals and Quantified Number Restrictions in Deciding the Description Logic SHOQ

Abstract

We present the first tableau method with an EXPTIME (optimal) complexity for checking satisfiability of a knowledge base in the description logic ${\cal{SHOQ}}$, which extends ${\cal{ALC}}$ with transitive roles, hierarchies of roles, nominals and qualified number restrictions. The complexity is measured using unary representation for numbers (in number restrictions). Our procedure is based on global caching and integer linear feasibility checking.