Most of the false assumptions that Othello makes are based in reason and logic. What is most surprising in the play is that he never sits down and talks to his wife, Desdemona. He never asks her if she has been unfaithful. Instead, he allows Iago to manipulate him again and again. The trouble is, most of what Iago says is convincing because it has some strains of truth. The lies that he tells sound reasonable. They sound logical. He uses logic and reason to come to the conclusion that his wife is cheating. He uses logic and reason to believe that Iago is his true friend. Iago uses his own sense of warped logic to validate his diabolical behavior.
Reason and logic are two characteristics which Othello lacks after act 3. Initially Othello character is very logically, particularly in act 1 where he refutes Brabantios' accusations of witchcraft. He logically explains and reasons desdemona's love for him. After act three he ceases to be logical. This is because the skewed logic of Iago's has awakened his jelousy, that is emotions rule his actions after this point. His illogical inclination is shown by the fact that he losses physical control and falls into epilepsy in act 4. His speech also deteriorates, losing syntax and becoming fractured.
Haha. I don't think that Othello uses much reason or logic. Instead, he decides based on his emotions. He tries to use reason, but ends up letting his jealousy and anger take over.
Without knowing it, Othello already believes Iago by the end of Act 3. He's demanded proof, but already the rumors and nagging at him. Soon, no amount of proof from Desdemona is going to fully convince him.
I guess that you could say he uses reason and logic in the beginning of the play when he comes across Brabantio and decides that fighting isn't the best solution.