Proof nets for Herbrand's Theorem

Details Proof nets for Herbrand's Theorem Proof nets for Herbrand's Theorem

2010-05-21

arxiv.org/abs/1005.3986v1

Mathematics

Logic

40 pages

Scientific paper

This paper explores the connection between two central results in the proof theory of classical logic: Gentzen's cut-elimination for the sequent calculus and Herbrands "fundamental theorem". Starting from Miller's expansion-tree-proofs, a highly structured way presentation of Herbrand's theorem, we define a calculus of weakening-free proof nets for (prenex) first-order classical logic, and give a weakly-normalizing cut-elimination procedure. It is not possible to formulate the usual counterexamples to confluence of cut-elimination in this calculus, but it is nonetheless nonconfluent, lending credence to the view that classical logic is inherently nonconfluent.

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