The standard model of knowledge and belief attributes to agents the ability to reason perfectly in classical logic. This is known as the problem of logical omniscience and, in accordance with the requirements of their contexts of use, has led to the development of a number of alternative epistemic logics. Some of these alternatives can, like the standard model, be regarded as presenting for discussion and analysis in a base language a system of reasoning, or consequence relation: the relation under which beliefs are closed. Adopting this perspective with regard to a useful four-valued logic, the resulting extension of the standard model is described and many technical points of comparison with the original model are given.