Harmony in the Light of Computational Ludics

Abstract

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.