Game of grounds

Davide Catta; Antonio Piccolomini d'Aragona

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arXiv · 2502.17511

Game of grounds

Davide Catta·Antonio Piccolomini d'Aragona

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Abstract

In this paper, we propose to connect Prawitz's theory of grounds with Girard's Ludics. This connection is carried out on two levels. On a more philosophical one, we highlight some differences between Prawitz's and Girard's approaches, but we also argue that they share some basic ideas about proofs and deduction. On a more formal one, we sketch an indicative translation of Prawitz's theory grounds into Girard's Ludics relative to the implicational fragment of propositional intuitionistic logic. This may allow for a dialogical reading of Prawitz's ground-theoretic approach. Moreover, it becomes possible to provide a formal definition of a notion of ground-candidate introduced by Cozzo.

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Davide Catta, Antonio Piccolomini d'Aragona. 2025-02-22. Game of grounds. https://arxiv.org/abs/2502.17511

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