The Japanese “theory of presupposed ultimate facts” (called “Yoken-jijitsu-ron” in Japanese) for interpreting the Japanese civil code has been underway for over forty years mainly by judges in the Japanese Legal Training Institute, but not yet formalized in a mathematical way. This paper attempts to mathematically formalize this theory and presents the correspondence between the theory and logic programming with “negation as failure”. It is quite surprising that Japanese judges independently developed such a theory without knowing about logic programming.