I believe bayes’ theorem is the tool to use for inductive logic, because a belief is a degree of certainty.

I suspect that we can actually explain deductive logic with the same framework. All deductive logic requires a base assumption, which is like having a prior of 100% for a given state in inductive logic. This cannot be a true inductively achieved state for our map, since 100% certainty is infinite certainty. However, we can use deductive logic as a tool to append to our inductive logic.

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.