 Lorenz developed (along with Paul Lorenzen) an approach to arithmetic and logic as dialogue games.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.