 One may instead adopt impossible worlds that retain some logical structure, e.g., worlds closed under some weaker-than-classical logical consequence. One approach of this kind is found in Levesque 1984 (see also Cresswell 1973). This employs impossible worlds of the kind used in paraconsistent relevant logics, which can be locally inconsistent and incomplete but are well-behaved with respect to conjunction and disjunction, that is, they are adjunctive and prime. Laws of classical logic fail at them, and by accessing them a cognitive agent can have inconsistent beliefs. However, we still have a weakened form of logical omniscience: the beliefs of an agent are closed under the weaker paraconsistent-relevant logic at issue. This seems incorrect as an attempt to model finite agents.