  A model consists of a collection of states, some determination of which states are relevant to which, and also some specification of which propositional letters hold at which of these states. States could be states of the real world at different times, or states of knowledge, or of belief, or of the real world as it might have been had circumstances been different. We have a mathematical abstraction here. We are not trying to define what all these states might ‘mean,’ we simply assume we have them. Then more complex formulas are evaluated as true or false, relative to a state. At each state the propositional connectives have their customary classical behavior. For the modal operators. \(\Box X\), that is, necessarily \(X\), is true at a state if \(X\) itself is true at every state that is relevant to that state (at all accessible states). Likewise \(\Diamond X\), possibly \(X\), is true at a state if \(X\) is true at some accessible state. If we think of things epistemically, accessibility represents compatibility, and so \(X\) is known in a state if \(X\) is the case in all states that are compatible with that state. If we think of things alethically, an accessible state can be considered an alternate reality, and so \(X\) is necessary in a state if \(X\) is the case in all possible alternative states. These are, by now, very familiar ideas.