Formal science is a branch of science studying formal language disciplines concerned with formal systems, such as logic, mathematics, statistics, theoretical computer science, artificial intelligence, information theory, game theory, systems theory, decision theory, and theoretical linguistics.

Whereas the natural sciences and social sciences seek to characterize physical systems and social systems, respectively, using empirical methods, the formal sciences are language tools concerned with characterizing abstract structures described by symbolic systems. The formal sciences aid the natural and social sciences by providing information about the structures the latter use to describe the world, and what inferences may be made about them.

Physics is the natural science that studies matter, its motion and behavior through space and time, and that studies the related entities of energy and force, so it's not a formal science.

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