Although there is a spectrum of different logical definitions of model-based diagnosis, fortunately, there exists a unified abstract definition which generalizes the definitions proposed in the past. Based on this definition, the concept of kernel model-based diagnosis is proposed. Then by characterizing the process of kernel model-based diagnosis, the direct relationship between it and the prime implicants/implicates is also demonstrated. Therefore, the theoretical results in this paper can be linked with algorithms such as the ATMS (assumption-based truth maintenance system). Furthermore, it is pointed out that the characterization of kernel consistency-based diagnosis is only a special case of the characterization in this paper.