The way beliefs are "procedural" includes the requirement that you must be able to instantiate them, but permitting this bounded step vastly increases the number of possible beliefs. Beliefs are answers to questions, and epistemic mind is a question-answering engine. Without logical omniscience, the process of computation increases information about statements over time (even without learning new facts from environment). When first confronted with a question of what 385+23 is, the one-second reply is "about 400", and only then "408".