the study of formal systems, such as those under the branches of logic and mathematics, which use an a priori, as opposed to empirical, methodology.
The formal sciences are the branches of science that are concerned with formal systems, such as logic, mathematics, theoretical computer science, information theory, systems theory, decision theory, statistics.
Unlike other branches, the formal sciences are not concerned with the validity of theories based on observations in the real world (empirical knowledge), but rather with the properties of formal systems based on definitions and rules. Hence there is disagreement on whether the formal sciences actually constitute a science. Methods of the formal sciences are, however, essential to the construction and testing of scientific models dealing with observable reality, and major advances in formal sciences have often enabled major advances in the empirical sciences.