Prawitz’s semantics, an instance of proof-theoretic semantics [1, 13], has come in basically two forms: semantics of valid arguments – SVA, see e.g. [9] – and theory of grounds – ToG, see e.g. [10]. Here, I shall focus mostly on SVA, and I will only occasionally refer to ToG. SVA is based on the notion of valid argument. The latter is inspired by Prawitz’s normalisation results for Gentzen’s Natural Deduction [8], stating that derivations for Γ ⊢ A can be transformed, through suitable reductions, to derivations for Γ∗ ⊆ Γ ⊢ A without detours. A detour is given by a formula which occurs both as conclusion of an introduction, and as a major premise of an elimination. In intuitionistic logic, Prawitz’s theorems imply what Schroeder-Heister called the fundamental corollary [12]: A is a theorem iff there is a closed derivation of A ending by an introduction. This may confirm Gentzen’s claim that introductions fix meaning, while eliminations are unique functions of the introductions [2].