A less discussed aspect of the problem of logical omniscience is that standard epistemic logic also leads to conceptual omniscience: you know all the conceptual consequences of what you know. A conceptual consequence of what you know is anything that follows from it by a necessary, a priori, non-logical link between concepts. For example, if you know that a knot is a trefoil, the logic has you knowing that it is chiral (i.e. it cannot be deformed into its mirror image). In general, since a necessary truth holds at every possible world, knowledge is closed under conceptual consequence, not just logical consequence. No real agent knows all of these. This is the problem of conceptual omniscience.

This problem matters because much of what separates an expert from a novice is conceptual, not logical. Standard epistemic logic erases this difference. Most responses to omniscience target its logical side: how logical competence limits closure. My aim is to model how conceptual competence limits closure. I do so by extending standard epistemic logic with impossible worlds. Since Hintikka (1975), impossible worlds have been used to block closure. But the move is cheap if the modeller adds them just to fit the verdicts the model should explain. To do better, I show that facts about an agent’s conceptual competence fix which impossible worlds she can rule out, and that these facts can be established independently of what she knows. I call the resulting model KRC, for knowledge relative to competence.