In the original first draft of this drawing above with Boogie pushing the lever, I had incorrectly written "Behavior 2 has been Punished" and "Kale is a punisher for Behavior 2". This was because I used to assume that Punishment was the opposite of Reinforcement. This is how the information is usually presented to us in dog training books.
Reinforcement and Punishment appear to be opposite processes because R increases the likelihood of a behavior happening in the future, and P decreases the likelihood of a behavior happening in the future. Which makes sense if this were simply about the math component, which it isn't.
What I understand now:
Reinforcement strengthens a behavior because there is a functional relationship between the behavior and what happens afterwards that brings pleasure or relief. Reinforcement shapes and predicts behavior.
Punishment does not shape or predict behavior. It doesn't even eradicate a behavior completely if the thing that is reinforcing the behavior in the first place has not been addressed. The punished behavior may stop temporarily if the threat of an aversive is present and come back when the coast is clear. There is no function in a Punishment contingency.
My notes from Lauren Novack's course below (2021). Another way to understand the "Quadrants". They are CONTINGENCIES where the before and after conditions are opposites.