Question:why does the resistance of a semiconductor decrease with temperature

According to band theory , the semiconductor is having three region, the conduction, valence and the forbidden gap., in a semiconductor the forbidden gap, is narrow therefore little thermal excitation( increase in temperature) can cause electrons to move from the valence band to the conduction band. an increase in temperature can bridge the gap and allow the current  through in order word will lower the resistance of the conductor.  this is common with intrinsic semiconductor where the its conductivity depend on thermal agitations.