what is negative reinforcement
Negative reinforcement is applying an unpleasant consequence for undesired behavior.
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http://allpsych.com/psychology101/reinforcement.html
Positive reinforcement is reinforcing behavior by providing a pleasant/desired consequence. For example, giving you an ice cream cone.
Negative reinforcement is reinforcing behavior by taking away an unpleasant/undesired consequence. For example, a jail sentence is reduced for good behavior or taking medication to reduce pain or other unpleasant symptoms.
So, rather than applying/increasing the unpleasant consequence (punishment), it is reducing the negative consequence. See the sources cited by Ms. Sue.
I hope this helps a little more. Thanks for asking.