On Proof Schemata and Primitive Recursive Arithmetic

14 pages•Published: May 26, 2024

Alexander Leitsch, Anela Lolic and Stella Mahler

Abstract

Inductive proofs can be represented as a proof schemata, i.e. as a parameterized se- quence of proofs defined in a primitive recursive way. Applications of proof schemata can be found in the area of automated proof analysis where the schemata admit (schematic) cut-elimination and the construction of Herbrand systems. This work focuses on the ex- pressivity of proof schemata as defined in [10]. We show that proof schemata can simulate primitive recursive arithmetic as defined in [12]. Future research will focus on an extension of the simulation to primitive recursive arithmetic using quantification as defined in [7]. The translation of proofs in arithmetic to proof schemata can be considered as a crucial step in the analysis of inductive proofs.

Keyphrases: inductive proofs, primitive recursive arithmetic, proof schema

In: Nikolaj Bjørner, Marijn Heule and Andrei Voronkov (editors). LPAR 2024 Complementary Volume, vol 18, pages 117-130.

Links:	https://easychair.org/publications/paper/W8XS
	https://doi.org/10.29007/4g2q

BibTeX entry

@inproceedings{LPAR2024C:Proof_Schemata_Primitive_Recursive,
  author    = {Alexander Leitsch and Anela Lolic and Stella Mahler},
  title     = {On Proof Schemata and Primitive Recursive Arithmetic},
  booktitle = {LPAR 2024 Complementary Volume},
  editor    = {Nikolaj Bjørner and Marijn Heule and Andrei Voronkov},
  series    = {Kalpa Publications in Computing},
  volume    = {18},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2515-1762},
  url       = {/publications/paper/W8XS},
  doi       = {10.29007/4g2q},
  pages     = {117-130},
  year      = {2024}}

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