ABSTRACT: The information principle of epistemic logic says that an agent believes that P when that agent has eliminated all of the P alternatives. I will call a set of epistemic possibilities an information space. This principle depicts belief as an interplay between a background, absolute space of possibilities and a space of those that remain possible from a given agent’s perspective. When coupled with a specific assumption about the structure of information space, this leads to the problem of logical omniscience. The framework of ‘impossible worlds semantics’ was advanced by Cresswell and Hintikka to solve this problem. The challenge is to avoid taking it too far. If we allow just any impossible worlds into our epistemic framework, we end up modeling irrational belief, which is not what we set out to do in the first place. Mark Jago has recently offered a principled reply to this worry: rank impossible worlds by their proximity to the most obvious logical impossibilities and allow that rationality is compatible with failing to eliminate some of the less-obvious impossibilities. JC Bjerring however, argues that this method fails to distinguish between impossibilities as advertised. In this paper, I will generalize Jago’s approach to settings where the background logic is non-classical — to show that the essential ingredient of this approach is its treatment of epistemic contexts themselves — then I will show where Bjerring’s criticism goes wrong.