Leitsch, A., Lolić, A., & Mahler, S. (2024). Towards an Analysis of Proofs in Arithmetic. In C. Kop (Ed.), 19th International Workshop on Logical and Semantic Frameworks, with Applications. LSFA 2024 Proceedings (pp. 122–135).
Inductive proofs can be represented as proof schemata, i.e. as parameterized sequences 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 expressivity of proof schemata. We show that proof schemata can simulate primitive recursive arithmetic. The translation of proofs in arithmetic to proof schemata can be considered as a crucial step in the analysis of inductive proofs.
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Project title:
Beweisanalyse und autom. Deduktion für rekursive Strukturen: I 5848-N (FWF - Österr. Wissenschaftsfonds)
