Let’s look at the quadrants from a different perspective.
Our behaviors change our environment, how we feel about these changes will determine if we choose those behaviors again in the future. If our behavior makes an aversive go away or earns us something that feels good, we will likely do it again. If our behavior makes us feel bad or takes away something we like, we might not want to do it again.
Working to make an aversive go away happens all the time in life, sometimes we are bothered by the hot sun, so we go in the shade or bugs are irritating us so we swat them away. This is mildly annoying, but if we succeed in making the thing go away, we feel relief. Its very different when someone else controls the situation though. The aversive isn’t a natural part of the environment, it was intentionally added by someone, classically conditioning the person with the aversive they added. So when we train with R- we must first apply an aversive so that we can remove it when they do the behavior we want.
Is it the same for P-? The removal of an appetitive – only if you gave the horse some food then grab it out of their mouth! If you feed them a finite amount of food, they got the food and there is no removal.