LIPIcs.CSL.2012.320.pdf
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Herbrand-Confluence for Cut Elimination in Classical First Order Logic
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Computer Science Logic (CSL'12) - 26th International Workshop/21st Annual Conference of the EACSL (CSL 2012)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Computer Science Logic (CSL) - License:
Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license
- Publication Date: 2012-09-03
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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
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.
Subject Classification
Keywords
- proof theory
- first-order logic
- tree languages
- term rewriting
- semantics of proofs
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