Using Tableau to Decide Expressive Description Logics with Role Negation

This paper presents a tableau approach for deciding description logics outside the scope of OWL DL/1.1 and current state-of-the-art tableau-based description logic systems. In particular, we de ne a sound and complete tableau calculus for the description logic ALBO and show that it provides a basis for decision procedures for this logic and numerous other description logics with full role negation. ALBO is the extension of ALC with the Boolean role operators, inverse of roles, domain and range restriction operators and it includes full support for nominals (individuals). ALBO is a very expressive description logic which subsumes Boolean modal logic and the two-variable fragment of rst-order logic and reasoning in it is NExpTime-complete. An important novelty is the use of a generic, unrestricted blocking rule as a replacement for standard loop checking mechanisms implemented in description logic systems. An implementation of our approach exists in the MetTeL system.