Abstract: Using function P-sets model,  its dynamic characters and law feature, the law disturbance concept, recovery of disturbances and disturbance scale are presented. Using these concepts, the outer-disturbances and attributes conjunctive shink theorem, attributes conjunctive shrink and outer-disturbances law mining-separating theorem, outer-disturbances and law mining-identification theorem and outer-disturbances and law mining attributes constancy theorem are proposed.

Key words: law mining and separating theorem, law mining and identification theorem, recovery of disturbances, outer-disturbances, function P-sets, attributes conjunctive shrink