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

Will Stafford; Victor Nascimento

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arXiv · 2211.12563

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

Will Stafford·Victor Nascimento

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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.

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BibTeX RIS

Will Stafford, Victor Nascimento. 2022-11-22. Following all the rules: Intuitionistic completeness for generalised proof-theoretic validity. https://arxiv.org/abs/2211.12563

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