Semantic A-translations and Super-Consistency Entail Classical Cut Elimination

  • Lisa Allali
  • Olivier Hermant
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8312)


We show that if a theory R defined by a rewrite system is super-consistent, the classical sequent calculus modulo R enjoys the cut elimination property, which was an open question. For such theories it was already known that proofs strongly normalize in natural deduction modulo R, and that cut elimination holds in the intuitionistic sequent calculus modulo R.

We first define a syntactic and a semantic version of Friedman’s A-translation, showing that it preserves the structure of pseudo-Heyting algebra, our semantic framework. Then we relate the interpretation of a theory in the A-translated algebra and its A-translation in the original algebra. This allows to show the stability of the super-consistency criterion and the cut elimination theorem.


Deduction modulo cut elimination A-translation pseudo-Heyting algebra super-consistency 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Lisa Allali
    • 1
  • Olivier Hermant
    • 2
  1. 1.École Polytechnique, INRIA & Région Ile de FranceFrance
  2. 2.CRIMINES ParisTechFrance

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