Question

on what principal is the fire extinguisher based?

Answer 1

It works due to presence of carbon dioxide in it which applied to the fire and covers the fire like a blanked and extinguish it.

Answer 2

Fire extinguisher contains dry carbon dioxide which cover the fire and prevent oxygen from reaching it and we know without oxygen, fire can't be carried out.
This is the basic principle on which fire extinguishers are built that help to extinguish a fire.