 Having established the connection to logical languages, further model-theoretic themes can be applied fruitfully to games. Language based reasoning allows, for instance, to examine the preservation of properties between different games, based on the exact syntactic shape of their definition. Besides, logical syntax also supports logical proof theory. Hence, the latter’s rich pool of proof calculi may help to analyze basic results in game theory. This entry illustrates major recurring patterns of reasoning about interaction that come to light in this way.