English

Following all the rules: Intuitionistic completeness for generalised proof-theoretic validity

Logic 2022-11-24 v1

Abstract

Prawitz conjectured that the proof-theoretically valid logic is intuitionistic logic. Recent work on proof-theoretic validity has disproven this. In fact, it has been shown that proof-theoretic validity is not even closed under substitution. In this paper, we make a minor modification to the definition of proof-theoretic validity found in Prawitz (1973) and refined by Schroeder-Heister (2006). We will call the new notion generalised proof-theoretic validity and show that the logic of generalised proof-theoretic validity is intuitionistic logic.

Keywords

Cite

@article{arxiv.2211.12563,
  title  = {Following all the rules: Intuitionistic completeness for generalised proof-theoretic validity},
  author = {Will Stafford and Victor Nascimento},
  journal= {arXiv preprint arXiv:2211.12563},
  year   = {2022}
}
R2 v1 2026-06-28T06:37:39.480Z