Abstract
First we show that the classical two-player semantic game actually corresponds to a three-valued logic. Then we generalize this result and give an n-player semantic game for an n + 1-valued logic with n binary connectives, each associated with a player. We prove that player i has a winning strategy in game \({G(\varphi, M)}\) if and only if the truth value of \({\varphi}\) is t i in the model M, for 1 ≤ i ≤ n; and none of the players has a winning strategy in \({G(\varphi, M)}\) if and only if the truth value of \({\varphi}\) is t 0 in M.
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