Logic is a system whereby one can determine if a conclusion can validly be drawn from a set of premises. It has nothing to say about the factual truth of those premises or conclusions.
Science is a method for establishing facts about the natural world and formulating theories to explain them.
Reason in this context is a more nebulous concept, and I doubt it really belongs in a set with the other two. That being said, valid logical arguments may be made for theism, but I have yet to see one where the premises are good and can stand a challenge. Also, unless a deity allows itself to be studied in a controlled environment, science has nothing to say on the subject.
So, logic and science have no real bearing on belief in a deity, and reason is so nebulous a term (in this context) that I think it must be disregarded.
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