In this Appendix, we would like to add some specifications about our paper and ourbibliographical references.The use of games in logic is manifold. In proof theory, the idea of employingwinning strategies for games associated with sentences in order to interpret the con-tent of proofs goes back at least to Lorenzen (1959). From a more semantical point ofview, Hintikka developed at about the same time game theoretical semantics (GTS)for logic.In recent years, Coquand and Krivine have done some very insightful work on thecomputational content of classical proofs. In Coquand (1995), Coquand introducedgames with backward moves and reformulated Gentzen’s and Novikoff’s “finitistsense”ofanarithmeticpropositionasawinningstrategyforthegameassociatedwithit.Moreover,heprovedthatclassicalmeansofproofwereconstructivelyadmissibleinthesensethat,startingfromwinningstrategiesforpremisses,aproofwouldeffectivelyyieldawinningstrategyfortheconclusion.Asimilarlinkbetweenclassicalproofsand