 To provide some hint at this variety, here is a limited description of some of the modal operators that turn up in the analysis of games and some of the things that can be expressed with them. The basic idea in the semantics is that a game consists of a set of players 1, 2, 3, …, and a set of W of game states. For each player i, there is an accessibility relation \(R_i\) understood so that \(sR_i t\) holds for states \(s\) and \(t\) iff when the game has come to state \(s\) player \(i\) has the option of making a move that results in \(t\). This collection of relations defines a tree whose branches define every possible sequence of moves in the game. The semantics also assigns truth-values to atoms that keep track of the payoffs. So, for example in a game like Chess, there could be an atom \(\win_i\) such that \(v(\win_i, s)=T\) iff state s is a win for player \(i\). Model operators \(\Box_i\) and \(\Diamond_i\) for each player i may then be defined as follows.