 Different versions and generalizations of these dialogue games have been studied recently. Various aspects of these developments are discuss, e.g., in Fermüller (2008) and Fermüller/Roschger (2014). Such approaches are not only able to provide game semantics for e.g. Gödel logics and product logic. There are also bridges which connect such games with the design of sequent calculi for many-valued logics, cf. Fermüller/Metcalfe (2009). 