Logic is the science of studying the forms and laws of thinking. Mastering the logic of knowledge and applying them to the cognitive activities and practices is essential. Article focuses on the formation and development of formal logic as an explicit object, content and its research method. Since then, highlight the magnitude and significance of formal logic as an effective tool of all cognitive science. At the same time, the post will analyze and clarify the application of logic value in the form of social life, especially in the field of law and education.