The methods for computing the kernel consistency-based diagnoses and the kernel abductive diagnoses are only suited for the situation when part of the fault behavioral modes of the components are known. The characterization of the kernel model-based diagnosis based on the general causal theory is proposed, which can breakthrough the limitation of the above methods when all behavioral modes of each component are known. Using this method, when observation subsets deduced logically are respectively assigned to be empty or the whole observation set, the kernel consistency-based diagnoses and the kernel abductive diagnoses can deal with all situations. The direct relationship between this diagnostic procedure and the prime implicants/implicates is proved, which links theoretical result with implementation.