Cut-Simulation in Impredicative Logics

  • Christoph E. Benzmüller
  • Chad E. Brown
  • Michael Kohlhase
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4130)


We investigate cut-elimination and cut-simulation in impredicative (higher-order) logics. We illustrate that adding simple axioms such as Leibniz equations to a calculus for an impredicative logic — in our case a sequent calculus for classical type theory — is like adding cut. The phenomenon equally applies to prominent axioms like Boolean- and functional extensionality, induction, choice, and description. This calls for the development of calculi where these principles are built-in instead of being treated axiomatically.


Sequent Calculus Proof Step Extensionality Axiom Functional Extensionality Comprehension Principle 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Christoph E. Benzmüller
    • 1
  • Chad E. Brown
    • 1
  • Michael Kohlhase
    • 2
  1. 1.Saarland UniversitySaarbrückenGermany
  2. 2.International University BremenBremenGermany

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