Approximate reasoning with the incomplete information is one of the difficulties that the knowledge engineering has faced. A precedent logic program theory with the property of nonmonotonicity is proposed in this paper. The synthesis evaluation for the interpretation of knowledge can be taken with the theory, such that the optimal selection of interpretation is made possible which becomes the best approach to the current knowledge. The theory completion in the significance of optimal selection is achieved and the requirement of completion and consistency of knowledge are avoided. To acquire the precedent logic programs in the applications, based on an inductive logic programming, learning algorithm is presented which incorporates the multiple inductive methods and has greater ability of induction. The presented theory and the algorithm have been applied in an expert system and gained satisfactory results.