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Tree Grammars for the Elimination of Non-prenex Cuts

Authors Stefan Hetzl, Sebastian Zivota



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Stefan Hetzl
Sebastian Zivota

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Stefan Hetzl and Sebastian Zivota. Tree Grammars for the Elimination of Non-prenex Cuts. In 24th EACSL Annual Conference on Computer Science Logic (CSL 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 41, pp. 110-127, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
https://doi.org/10.4230/LIPIcs.CSL.2015.110

Abstract

Recently a new connection between proof theory and formal language theory was introduced. It was shown that the operation of cut elimination for proofs with prenex Pi_1-cuts in classical first-order logic corresponds to computing the language of a particular type of tree grammars. The present paper extends this connection to arbitrary (i.e. non-prenex) cuts without quantifier alternations. The key to treating non-prenex cuts lies in using a new class of tree grammars, constraint grammars, which describe the relationship of the applicability of its productions by a propositional formula.
Keywords
  • proof theory
  • cut-elimination
  • Herbrand's theorem
  • tree grammars

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References

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