Using Tableau to Decide Expressive Description Logics with Role Negation

  • Renate A. Schmidt
  • Dmitry Tishkovsky
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4825)


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 define a sound and complete tableau calculus for the description logic \(\mathcal{ALBO}\) and show that it provides a basis for decision procedures for this logic and numerous other description logics with full role negation. \(\mathcal{ALBO}\) is the extension of \(\mathcal{ALC}\) with the Boolean role operators, inverse of roles, domain and range restriction operators and it includes full support for nominals (individuals). \(\mathcal{ALBO}\) is a very expressive description logic which subsumes Boolean modal logic and the two-variable fragment of first-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 \({\textsc{MetTeL}}\) system.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Renate A. Schmidt
    • 1
  • Dmitry Tishkovsky
    • 1
  1. 1.School of Computer Science, The University of Manchester 

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