As a formal science, logic investigates and classifies the structure of statements and arguments, both through the study of formal systems of inference and through the study of arguments in natural language. The scope of logic is therefore large, ranging from core topics such as the study of fallacies and paradoxes, to specialized analyses of reasoning using probability and to arguments involving causality. Logic is also commonly used today in argumentation theory.

Traditionally, logic is studied as a branch of philosophy, one part of the classical trivium, which consisted of grammar, logic, and rhetoric. Since the mid-nineteenth century formal logic has been studied as the foundation of mathematics. In 1903 Bertrand Russell and Alfred North Whitehead established logic as the cornerstone of mathematics with the publication of Principia Mathematica. The development of formal logic and its implementation in computing machinery is the foundation of computer science.