 Modelling intentional states, such as knowledge and belief, is a prominent motivation for introducing impossible worlds. The intuitive idea is that one gains knowledge or belief by ruling out would-be possibilities (the epistemic/doxastic possibilities for that agent). An agent’s knowledge is whatever is true according to all epistemically possible worlds accessible to that agent, i.e., the worlds which represent ways things could be, for all the agent knows (and similarly for belief).