International Conference on Automated Reasoning with Analytic Tableaux and Related Methods

Automated Reasoning with Analytic Tableaux and Related Methods pp 253-269

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)

Abstract

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.

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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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