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On Proof Schemata and Primitive Recursive Arithmetic

14 pagesPublished: May 26, 2024


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

BibTeX entry
  author    = {Alexander Leitsch and Anela Lolic and Stella Mahler},
  title     = {On Proof Schemata and Primitive Recursive Arithmetic},
  booktitle = {LPAR 2024 Complementary Volume},
  editor    = {Nikolaj Bj\{\textbackslash{}o\}rner and Marijn Heule and Andrei Voronkov},
  series    = {Kalpa Publications in Computing},
  volume    = {18},
  pages     = {117--130},
  year      = {2024},
  publisher = {EasyChair},
  bibsource = {EasyChair,},
  issn      = {2515-1762},
  url       = {},
  doi       = {10.29007/4g2q}}
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