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)


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.


Inference Rule Decision Procedure Theorem Prove Description Logic Disjunctive Normal Form 
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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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