SAT Encoding of Unification in \(\mathcal{ELH}_{{R}^+}\) w.r.t. Cycle-Restricted Ontologies

  • Franz Baader
  • Stefan Borgwardt
  • Barbara Morawska
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7364)


Unification in Description Logics has been proposed as an inference service that can, for example, be used to detect redundancies in ontologies. For the Description Logic \(\mathcal{EL}\), which is used to define several large biomedical ontologies, unification is NP-complete. An NP unification algorithm for \(\mathcal{EL}\) based on a translation into propositional satisfiability (SAT) has recently been presented. In this paper, we extend this SAT encoding in two directions: on the one hand, we add general concept inclusion axioms, and on the other hand, we add role hierarchies (\(\mathcal{H}\)) and transitive roles (R  + ). For the translation to be complete, however, the ontology needs to satisfy a certain cycle restriction. The SAT translation depends on a new rewriting-based characterization of subsumption w.r.t. \(\mathcal{ELH}_{{R}^+}\)-ontologies.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

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

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