Decidability of \(\mathcal{SHI}\) with Transitive Closure of Roles

  • Chan Le Duc
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5554)


This paper investigates a Description Logic, namely \(\mathcal{SHI}_+\), which extends \(\mathcal{SHI}\) by adding transitive closure of roles. The resulting logic \(\mathcal{SHI}_+\) allows transitive closure of roles to occur not only in concept inclusion axioms but also in role inclusion axioms. We show that \(\mathcal{SHI}_+\) is decidable by devising a terminating, sound and complete algorithm for deciding satisfiability of concepts in \(\mathcal{SHI}_+\) with respect to a set of concept and role inclusion axioms.


OWL Description Logics Tableaux Decidability 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Chan Le Duc
    • 1
  1. 1.INRIA Grenoble Rhône-Alpes - LIGFrance

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