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arXiv · 1310.8156

Herbrand-Confluence

Stefan Hetzl·Lutz Straßburger
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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.

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Stefan Hetzl, Lutz Straßburger. 2013-10-30. Herbrand-Confluence. https://doi.org/10.2168/lmcs-9(4:24)2013

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