Logic (used correctly) is the process of deriving true statements from other true statements. We can create imaginary worlds, purely analytic abstract systems were we establish a set of foundational axioms, create properties and rules of interaction to be used within our purely abstract system, and in doing so, with the right axioms, properties, and rules, anything can be made to be logically true (or possible) within that abstract system. The possibilities open to the realm of abstraction are limitless, or at least only limited by our imagination.
If you base your logic on faulty premises, or premises that have not been established, and your intent is to conform and remain consistent within the possibilities of the real world, then your logic is flawed. Garbage In to the algorithm of logic will only produces Garbage Out.
From what true statements have you established "the supernatural" or what can be contained within "the supernatural"?