  The application of games to logic has a long history. One influential application with important implications for linguistics is Game Theoretic Semantics (GTS) (Hintikka et. al. 1983), where validity is defined by the outcome of a game between two players one trying to verify and the other trying to falsify a given formula. GTS has significantly stronger resources that standard Tarski-style semantics, as it can be used (for example) to explain how meaning evolves in a discourse (a sequence of sentences).