Non-Normal Worlds and Representation

World semantics for relevant logics include so-called non-normal or impossible worlds providing model-theoretic coun-terexamples to such irrelevant entailments as (A ∧ ¬A) → B, A → (B ∨ ¬B), or A → (B → B). Some well-known views interpret non-normal worlds as information states. If so, they can plausibly model our ability of conceiving or representing logical impossibilities. The phenomenon is explored by com-bining a formal setting with philosophical discussion. I take Priest’s basic relevant logic N4 and extend it, on the syntactic side, with a representation operator, r, and on the semantic side, with particularly anarchic non-normal worlds. This com-bination easily invalidates unwelcome “logical omniscience ” in-ferences of standard epistemic logic, such as belief-consistency and closure under entailment. Some open questions are then raised on the best strategies to regiment r in order to express more vertebrate kinds of conceivability.