When a dog learns not to bark in its crate after 20-30 minutes of silence, what principle does this exemplify?

The correct choice is extinction, which refers to the process of reducing or eliminating a behavior, in this case barking, through the removal of reinforcement. When a dog is consistently quiet in its crate for a period of 20-30 minutes and is not reinforced for barking, the barking behavior diminishes over time.

In this scenario, the absence of a reward for barking (which might have been attention from the owner or escape from the crate) leads to a gradual reduction in the barking behavior. The dog learns that barking does not lead to the desired outcome, thus leading to the extinction of that behavior.

The other principles given in the options involve different mechanisms of behavior modification. Negative punishment would involve taking away something the dog enjoys when it barks, while positive punishment would involve adding an unpleasant consequence when the dog barks. Positive reinforcement, on the other hand, would mean providing a reward for quiet behavior. Since none of these mechanisms are what's occurring in the described situation, extinction is the most accurate principle illustrated by the dog's learning process.