Atomic Cut Elimination for classical Logic

@inproceedings{Brnnler2003AtomicCE,
  title={Atomic Cut Elimination for classical Logic},
  author={Kai Br{\"u}nnler},
  booktitle={CSL},
  year={2003}
}
System SKS is a set of rules for classical propositional logic presented in the calculus of structures. Like sequent systems and unlike natural deduction systems, it has an explicit cut rule, which is admissible. In contrast to sequent systems, the cut rule can easily be reduced to atomic form. This allows for a very simple cut elimination procedure based on plugging in parts of a proof, like normalisation in natural deduction and unlike cut elimination in the sequent calculus. It should thus… Expand
Locality for Classical Logic
  • Kai Brünnler
  • Mathematics, Computer Science
  • Notre Dame J. Formal Log.
  • 2006
TLDR
D deductive systems for classical propositional and predicate logic in the calculus of structures are seen, which have a cut rule which is admissible and which leads to inference rules that are local : they do not require the inspection of expressions of arbitrary size. Expand
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