The concept of Homicide has two dimensions. One dimension is the domain of homicide; “the killing of a human being by a human being.” The other dimension is the range of homicide such as “social harmfulness, blameworthiness of that wrongful results, conduct, attendant circumstances, etc.”The domain of concepts and the range of concepts have functional correspondence. In Frege's analysis on the function y = f(x), elements of x constitute domain, and values of y constitute range. The illegality and culpability of homicide are in the range of homicide, which corresponds functionally to each element in the domain of homicide. The frame of domain and range is valid to the elements of “justification” and “excuse”. The domain and range of criminal concepts are useful instruments in the analysis of mistakes on elements of justification. That mistake is called as the mistake over the factual premises of exclusion clause of illegality. According to a theory in current criminal Jurisprudence, we should apply the rule for the mistake of fact to this case since there are neither illegal-intention nor behavior-illegality. According to the other theory, we should apply the rule for the mistakes of law to this case since there are no culpability-intention. The actor shall not be punished for his intentional offenses by any theory, even though he has intention in Tatbestand. All theories in current criminal Jurisprudence about this case are in the fallacy of category mistake. They confuse the domain of intention and the range of it to put them into the same row. Then, in the case of the mistake over the factual premises of exclusion clause of illegality, the problem is whether it is confirming to the justification or not. If the actor had probable causes(or reasonable grounds) at the mistake of facts to be true, his act is confirmed to the “justification”A crime is defined as an illegal and culpable act conforming to 'Tatbestand (elements of an offence)' in current criminal Jurisprudence. But if we look at the real situation of affairs, we can find four exclusive and exhaustive kinds of behaviors in the world: ‘Tatbestand’, “justification”, “excuse” and residuals. The residuals have no meaning in criminal Jurisprudence. The relation of the remaining three is an exclusive confrontational system, not a serial staged system. Then what are illegality and culpability? The illegality(or rightfulness) and culpability(or immunity) are the range of Tatbestand, justification and excuse. These are new paradigm of system theory of crime.