Second-Order Quantifier Elimination on Relational Monadic Formulas – A Basic Method and Some Less Expected Applications

  • Christoph Wernhard
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9323)


For relational monadic formulas (the Löwenheim class) second-order quantifier elimination, which is closely related to computation of uniform interpolants, forgetting and projection, always succeeds. The decidability proof for this class by Behmann from 1922 explicitly proceeds by elimination with equivalence preserving formula rewriting. We reconstruct Behmann’s method, relate it to the modern DLS elimination algorithm and show some applications where the essential monadicity becomes apparent only at second sight. In particular, deciding \(\mathcal{ALCOQH}\) knowledge bases, elimination in DL-Lite knowledge bases, and the justification of the success of elimination methods for Sahlqvist formulas.


Modal Logic Description Logic Conjunctive Normal Form Elimination Method Boolean Combination 
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 International Publishing Switzerland 2015

Authors and Affiliations

  • Christoph Wernhard
    • 1
  1. 1.Technische Universität DresdenDresdenGermany

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