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Quantifiers and the System KE: Some Surprising Results

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Computer Science Logic (CSL 1998)

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

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Abstract

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.

The author would like to thank Hans Tompits for his useful comments on an earlier version of this paper.

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Author information

Authors and Affiliations

  1. Institut für Informationssysteme E184.3, Technische Universität Wien, Treitlstraße 3, A-1040, Wien, Austria

    Uwe Egly

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  1. Uwe Egly
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Editor information

Editors and Affiliations

  1. Computing Laboratory, Oxford University, Wolfson Building Parks Road Oxford,, OX1 3QD, United Kingdom

    Georg Gottlob

  2. GREYC, Université de Caen, CNRS, Campus 2, F-14032, Caen cedex, France

    Etienne Grandjean

  3.  ,  

    Katrin Seyr

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© 1999 Springer-Verlag Berlin Heidelberg

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Egly, U. (1999). Quantifiers and the System KE: Some Surprising Results. In: Gottlob, G., Grandjean, E., Seyr, K. (eds) Computer Science Logic. CSL 1998. Lecture Notes in Computer Science, vol 1584. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10703163_7

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  • DOI: https://doi.org/10.1007/10703163_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65922-8

  • Online ISBN: 978-3-540-48855-2

  • eBook Packages: Springer Book Archive

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