Deductive logic manages definitions where inductive logic manages observations. We can use deductive logic to explore the rest of our
Concept-space for a given inductively attained belief. We can use the probability that our inductively attained belief is true to inform the deductively attained consequences of that belief. In turn, we can use those deductively attained consequences to provide an extension with which to further test our inductively attained belief. In a way, I guess this is science.
Science is the systematic use of Full Logic.