 The beliefs held by an agent are represented by a set of such belief-representing sentences. It is usually assumed that this set is closed under logical consequence, i.e., every sentence that follows logically from this set is already in the set. This is clearly an unrealistic idealization, since it means that the agent is taken to be “logically omniscient”, i.e. a perfect logical reasoner. However, it is a useful idealization since it simplifies the logical treatment; indeed, it seems difficult to obtain an interesting formal treatment without it. In logic, logically closed sets are called “theories”. In formal epistemology they are also called “corpora”, “knowledge sets”, or (more commonly) “belief sets”.