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

Year: 2022

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2211.12563

Authors: Stafford, Will, Nascimento, Victor

Language: English

Topic: Advanced Algebra and Logic

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, Akademie Věd České Republiky

Awards: G2849476320, G29316538

OpenAlex ID: W4309953022

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