 Christian Fermüller and George Metcalfe (2009) have pointed out a correspondence between optimal strategies in Giles’s game and cut-free proofs in a hypersequent system for Łukasiewicz logic. The game has also been extended in Fermüller &amp; Roschger 2014 to characterize various types of (semi-)fuzzy quantifiers, intended to model natural language expressions like “about half” or “almost all”.