Seems to me that a belief can follow directly from logic. That is, you observe and experience phenomena, you use logic to interpret those phenomena, and from that you develop a very firm belief based on the conclusions to which your logic led you.

Everybody does that. A cop, for example, does it when observing evidence and solving a murder case. He reaches a point where he firmly believes that a certain person committed that murder, and he does so by observing the evidence and using his powers of logic.