 In game-theoretic semantics, a sentence \(\phi\) and a model \(M\) are made to correspond to a (usually two-player) game \(G_M(\phi)\). Then truth is defined in terms of the existence of winning strategies for one of the players (who, in this work, will be called simply “Player \(0\)”): in other words, if \(\sigma_0\) is a (possibly non-deterministic) strategy for Player \(0\) and \(\Pi(G_M(\phi), \sigma_0)\) is the set of all plays which are compatible with \(\sigma_0\) then \(\phi\) is true if and only if every play in \(\Pi(G_M(\phi), \sigma_0)\) is winning for Player \(0\). It is possible to think of the game \(G_M(\phi)\) as a debate between two players, one of whom (Player \(0\)) wishes to demonstrate that it is the case that \(\phi\) while the other (Player \(1\)) wishes to demonstrate that it is not the case that \(\phi\).