"But isn't adding pressure to the dog a form of positive punishment? Those two are always confusing, because I think when you take away something unpleasant, don't you first have to give it or apply it?"
This is, for some reason, one of the most confusing concepts in dog training, yet we use it all the time! I'm still on the prep list for the CPDT-KA exam, and this is by far the most common question that comes up.
Positive punishment and negative reinforcement go hand in hand, and it really just depends on the way you phrase it. For example, the use of a gentle leader is an example of both positive punishment AND negative reinforcement depending on what behavior you re focusing on. If you are focused on the pulling behavior, and the pressure from the gentle leader STOPS the pulling, then it is positive punishment (Uncomfortable pressure = positive, pulling stops = punishment).
However, if you phrase it in such a way that the pressure is released when the dog is walking by your side, and therefore the behavior of walking next to you is increased, then it is negative reinforcement (Pressure released = negative, more walking by your side = reinforcement).
So they go hand in hand, and it really is all just about the way you are looking at and phrasing it. The easiest way to decipher between the two is to break it down like this:
What is the behavior?
Is the behavior increasing or decreasing? Increasing = Reinforcement, Decrease = Punishment
Is something being added or taken away? If something is added then its Positive, if something is taken away then it is Negative.
And for your initial question of looking for example -
Negative Punishment - Turning your back to your dog when he jumps on you, resulting in him no longer jumping (Removal of attention for a decrease in behavior)
Negative Reinforcement - The gentle leader releasing its pressure when your dog walks nicely at your side, resulting in your dog walking by your side more (Removal of pressure for increase in walking by your side).
It's important to point out whether the behavior increased or decreased, because THAT is what determines if something is punishment or reinforcement. For instance, if you squirt your dog with a hose every time he barks, and he starts barking MORE, you have actually reinforced the behavior, even though your intention was to punish.
(Basically I just summed up what everyone else has said, and just put it all into one post

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