Abstract: The constructio n and inference of field expert system play an important role on expert system, paper introduces the architecture of knowledge representation based on description logic and its elementary components, and the no-cycle TBox、cyclic TBox、having inclusion TBox and empty TBox respectively in description logic ALC, defines cyclic TBox by fixed-point semantic and eliminating the TBox by equivalent extension to simplify the inference; it gives the inference algorithm of empty TBox and brief explain on correctness of the algorithm.