Legal logic as an extremely important legal methodology in legal practice, China's theory and practice circles on its positioning and research methods have a certain amount of debate. This paper reviews the discussion on the relationship between law and logic in the western legal philosophy circles. These discussions, especially the legal argumentation theories that have emerged in the western legal philosophy circles since the 1970s, provide a new perspective and dimension for the positioning of Chinese legal logic, which should be the logic of legal argumentation. In the middle and late 20th century, the non-formal logic thought emerged in the western logic field, which provides a new method and theoretical basis for the theoretical study and practice of Chinese legal logic.