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What does it mean to talk of a grammar of game design? And does specifying such a grammar give us an insight into the underlying structure of games, or a new method for approaching game design - or both? Because games vary from pure mathematical formalisms (at the ludic extreme) to behavioural descriptions (at the opposite extreme), any formal reductionistic system will either be focused primarily on the former, or require sufficient latitude to express practically infinite diversity. One such approach is to define a categorial grammar of game design.