 In dialogical logic (game semantics), tree calculations (generally, of Gentzen type calculus) are written upside down, so that the initial assertion of a proponent stays above and is defended against an opponent as in a game.This is a linguistically more congenial approach to logic which is more suitable as a model for argumentation than the formal derivation in a calculus or truth tables.Lorenz presented for the first time a simple demonstration of Gentzen's consistency proof on this game-theoretic basis.