 which has a straightforward Tarski truth condition in second order logic. Hintikka then observed that one can read the Skolem functions as winning strategies in a game, as in the entry on  logic and games.  In this way one can build up a compositional semantics, by assigning to each formula a game. A sentence is true if and only if the player Myself (in Hintikka’s nomenclature) has a winning strategy for the game assigned to the sentence. This game semantics agrees with Tarski’s on conventional first-order sentences. But it is far from fully abstract; probably one should think of it as an operational semantics, describing how a sentence is verified rather than whether it is true.