Semi-Open is a type of game where the moderator has revealed all of the roles that can possibly be in the game. The exact distribution of these roles is unknown, but roles that are not on the list cannot appear in the game.
As an example, the moderator may promise that only Cop, Doctor, Vigilante, and Roleblocker can be in the game. No other roles can be in the game. It is perfectly valid for no Doctors or two Vigilantes to be a part of the actual setup, though.
It is possible for some roles to be restricted to one alignment.
Semi-Open games usually mask a game with an unusual setup, often featuring uncommon role interactions or multiple copies of the same role. In practice, many of the promised roles do not actually exist in the game.
Contrast Modular Open.