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 combining 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 combination easily invalidates unwelcome “logical omniscience” inferences 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.