Stefan Hetzl ; Lutz Straßburger - Herbrand-Confluence

lmcs:727 - Logical Methods in Computer Science, December 18, 2013, Volume 9, Issue 4 -

Authors: Stefan Hetzl ; Lutz Straßburger

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.

Volume: Volume 9, Issue 4
Published on: December 18, 2013
Accepted on: June 25, 2015
Submitted on: January 29, 2013
Keywords: Computer Science - Logic in Computer Science


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