Abstract: The great fixed point in logic programming is discussed. If the mapping of Herbrand interpretations T_p preserves filtered infs, or there are no function symbols in a definite program, or each variable in the body of the clause also appears in the head for each clause in the definite program, the set　T_p↓ω is the great fixed point of the mapping T_p. By Defined another mapping of Herbrand interpretations F_p, some Lloyd J W’s results on the fixed points are generalized.

Key words: logic programming； fixed points； Herbrand interpretation； Herbrand model；