Quantifiers and the System KE: Some Surprising Results

  • Uwe Egly
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1584)


In this paper, we consider the free-variable variant of the calculus KE and investigate the effect of different preprocessing activities to the proof length of variants of KE. In this context, skolemization is identified to be harmful as compared to the δ-rule. This does not only have consequences for proof length in KE, but also for the “efficiency” of some structural translations. Additionally, we investigate the effect of quantifier-shifting and quantifier-distributing rules, respectively. In all these comparisons, we identify classes of formulae for which a non-elementary difference in proof length occur.


Automate Deduction Input Formula Proof Complexity Negation Normal Form Signed Formula 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Uwe Egly
    • 1
  1. 1.Institut für Informationssysteme E184.3Technische Universität WienWienAustria

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