Studia Logica

, Volume 82, Issue 1, pp 51–71 | Cite as

Cut Elimination inside a Deep Inference System for Classical Predicate Logic

  • Kai BrünnlerEmail author


Deep inference is a natural generalisation of the one-sided sequent calculus where rules are allowed to apply deeply inside formulas, much like rewrite rules in term rewriting. This freedom in applying inference rules allows to express logical systems that are difficult or impossible to express in the cut-free sequent calculus and it also allows for a more fine-grained analysis of derivations than the sequent calculus. However, the same freedom also makes it harder to carry out this analysis, in particular it is harder to design cut elimination procedures. In this paper we see a cut elimination procedure for a deep inference system for classical predicate logic. As a consequence we derive Herbrand's Theorem, which we express as a factorisation of derivations.


cut elimination deep inference first-order predicate logic 


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© Springer Science + Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Institut für angewandte Mathematik und InformatikBernSwitzerland

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