Simplified & short; If P, then Q. Q. Therefore, P.
While propositional logic may be a special case of Bayesian reasoning, the Bayes's theorem formalization of the scientific method cannot be usefully reduced to propositional logic.
Also, welcome to Less Wrong!. It sounds like you may want to check out Bayes' Theorem and/or Technical Explanation.
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"It is startling to realize how much unbelief is necessary to make belief possible. What we know as blind faith is sustained by innumerable unbeliefs."