Harmony in the Light of Computational Ludics

Alberto Naibo
(IHPST, Université Paris 1 Panthéon-Sorbonne)
Yuta Takahashi
(Ochanomizu University)

Prawitz formulated the so-called inversion principle as one of the characteristic features of Gentzen's intuitionistic natural deduction. In the literature on proof-theoretic semantics, this principle is often coupled with another that is called the recovery principle. By adopting the Computational Ludics framework, we reformulate these principles into one and the same condition, which we call the harmony condition. We show that this reformulation allows us to reveal two intuitive ideas standing behind these principles: the idea of "containment" present in the inversion principle, and the idea that the recovery principle is the "converse" of the inversion principle. We also formulate two other conditions in the Computational Ludics framework, and we show that each of them is equivalent to the harmony condition.

In Ugo Dal Lago and Valeria de Paiva: Proceedings Second Joint International Workshop on Linearity & Trends in Linear Logic and Applications (Linearity&TLLA 2020), Online, 29-30 June 2020, Electronic Proceedings in Theoretical Computer Science 353, pp. 132–156.
Published: 30th December 2021.

ArXived at: https://dx.doi.org/10.4204/EPTCS.353.7 bibtex PDF
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