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Abstract

We show that finding finite Herbrand models for a restricted class of first-order clauses is ExpTime-complete. A Herbrand model is called finite if it interprets all predicates by finite subsets of the Herbrand universe. The restricted class of clauses consists of anti-Horn clauses with monadic predicates and terms constructed over unary function symbols and constants. The decision procedure can be used as a new goal-oriented algorithm to solve linear language equations and unification problems in the description logic \(\mathcal{FL}_0\). The new algorithm has only worst-case exponential runtime, in contrast to the previous one which was even best-case exponential.

Keywords

Decision Procedure Description Logic Replacement Sequence Tree Automaton Unary Predicate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Stefan Borgwardt
    • 1
  • Barbara Morawska
    • 1
  1. 1.Theoretical Computer ScienceTU DresdenGermany

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