An abatement is a deduction, or lessening. If you start bluntly telling people what you think of them, you might see an abatement in their friendliness toward you.
Abatement comes from the French word for batter, but abatement doesn’t usually have a negative sense––abatement reduces something, but doesn’t beat it to a pulp. Many cities offer tax abatements to reward businesses starting up in areas they want to develop. If your heat doesn't work, you could sue your landlord for a rent abatement, since you shouldn't have to pay rent for days you don't have heat.