informally, a sequence of moves in a game formula_52 is a history. at the end of each history formula_75, some subgame formula_76 is played; we call formula_77 the "assignment associated to" formula_75, and formula_79 the "subformula occurrence associated to" formula_75. the "player associated to" formula_75 is eloise in case the most external logical operator in formula_79 is formula_83 or formula_84, and abelard in case it is formula_85 or formula_86.