A categorical proposition is a statement that asserts a relationship between two categories or classes. It typically takes the form of "All A are B," "No A are B," "Some A are B," or "Some A are not B." These propositions help in understanding how different groups relate to one another in logic and reasoning. In logic, categorical propositions are essential for constructing syllogisms, which are arguments that draw conclusions from two premises. They are foundational in the study of Aristotelian logic and are used to analyze the validity of arguments in various fields, including philosophy and mathematics.