Logic is the science of correct thinking. A classic definition is new and necessary reasoning. It's new because you didn't know the item before, and necessary because a correctly formulated syllogism...
Classical Logic allows two truth values, True and False. Multivalued or "many-valued logic" allows other kinds of truth values and it allows there to be more than two truth values.
Things can be logical but not scientific. If it makes logical sense, it is logical. But if it's a claim that can never be proven right or proven wrong, then it's not scientific.