Herbrand-Confluence for Cut Elimination in Classical First Order Logic

Hetzl, Stefan; Straßburger, Lutz

doi:10.4230/LIPIcs.CSL.2012.320

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Herbrand-Confluence for Cut Elimination in Classical First Order Logic

Authors Stefan Hetzl, Lutz Straßburger

Part of: Volume: Computer Science Logic (CSL'12) - 26th International Workshop/21st Annual Conference of the EACSL (CSL 2012)
Part of: Series: Leibniz International Proceedings in Informatics (LIPIcs)
Part of: Conference: Computer Science Logic (CSL)
License: Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license
Publication Date: 2012-09-03

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LIPIcs.CSL.2012.320.pdf

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Document Identifiers

DOI: 10.4230/LIPIcs.CSL.2012.320
URN: urn:nbn:de:0030-drops-36815

Subject Classification

Keywords

proof theory
first-order logic
tree languages
term rewriting
semantics of proofs

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Abstract

We consider cut-elimination in the sequent calculus for classical
first-order logic. It is well known that this system, in its most
general form, is neither confluent nor strongly normalizing. In this
work we take a coarser (and mathematically more realistic) look at
cut-free proofs. We analyze which witnesses they choose for which
quantifiers, or in other words: we only consider the
Herbrand-disjunction of a cut-free proof. Our main theorem is a
confluence result for a natural class of proofs: all (possibly
infinitely many) normal forms of the non-erasing reduction lead to the
same Herbrand-disjunction.

Cite As Get BibTex

Stefan Hetzl and Lutz Straßburger. Herbrand-Confluence for Cut Elimination in Classical First Order Logic. In Computer Science Logic (CSL'12) - 26th International Workshop/21st Annual Conference of the EACSL. Leibniz International Proceedings in Informatics (LIPIcs), Volume 16, pp. 320-334, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012) https://doi.org/10.4230/LIPIcs.CSL.2012.320

Author Details

Stefan Hetzl

Lutz Straßburger

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