A Decomposition Rule for Decision Procedures by Resolution-Based Calculi

  • Ullrich Hustadt
  • Boris Motik
  • Ulrike Sattler
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3452)

Abstract

Resolution-based calculi are among the most widely used calculi for theorem proving in first-order logic. Numerous refinements of resolution are nowadays available, such as e.g. basic superposition, a calculus highly optimized for theorem proving with equality. However, even such an advanced calculus does not restrict inferences enough to obtain decision procedures for complex logics, such as \(\mathcal{SHIQ}\). In this paper, we present a new decomposition inference rule, which can be combined with any resolution-based calculus compatible with the standard notion of redundancy. We combine decomposition with basic superposition to obtain three new decision procedures: (i) for the description logic \(\mathcal{SHIQ}\), (ii) for the description logic \(\mathcal{ALCHIQ}b\), and (iii) for answering conjunctive queries over \(\mathcal{SHIQ}\) knowledge bases. The first two procedures are worst-case optimal and, based on the vast experience in building efficient theorem provers, we expect them to be suitable for practical usage.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Ullrich Hustadt
    • 1
  • Boris Motik
    • 2
  • Ulrike Sattler
    • 3
  1. 1.Department of Computer ScienceUniversity of LiverpoolLiverpoolUK
  2. 2.FZI Research Center for Information Technologies at the University of KarlsruheKarlsruheGermany
  3. 3.Department of Computer ScienceUniversity of ManchesterManchesterUK

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