Herbrand's Theorem in Inductive Proofs

16 pages•Published: May 26, 2024

Abstract

An inductive proof can be represented as a proof schema, i.e. as a parameterized sequence of proofs defined in a primitive recursive way. A corresponding cut-elimination method, called schematic CERES, can be used to analyze these proofs, and to extract their (schematic) Herbrand sequents, even though Herbrand’s theorem in general does not hold for proofs with induction inferences. This work focuses on the most crucial part of the schematic cut-elimination method, which is to construct a refutation of a schematic formula that represents the cut-structure of the original proof schema. Moreover, we show that this new formalism allows the extraction of a structure from the refutation schema, called a Herbrand schema, which represents its Herbrand sequent.

Keyphrases: herbrand sequents, inductive proofs, proof schema, resolution calculus

In: Nikolaj Bjørner, Marijn Heule and Andrei Voronkov (editors). Proceedings of 25th Conference on Logic for Programming, Artificial Intelligence and Reasoning, vol 100, pages 295-310.

Links:	https://easychair.org/publications/paper/nt9G
	https://doi.org/10.29007/dwdf

BibTeX entry

@inproceedings{LPAR2024:Herbrands_Theorem_Inductive_Proofs,
  author    = {Alexander Leitsch and Anela Lolic},
  title     = {Herbrand's Theorem in Inductive Proofs},
  booktitle = {Proceedings of 25th Conference on Logic for Programming, Artificial Intelligence and Reasoning},
  editor    = {Nikolaj Bjørner and Marijn Heule and Andrei Voronkov},
  series    = {EPiC Series in Computing},
  volume    = {100},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {/publications/paper/nt9G},
  doi       = {10.29007/dwdf},
  pages     = {295-310},
  year      = {2024}}

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