Categorical propositions are statements that assert a relationship between two categories or classes. They typically take 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, making them fundamental in logic and reasoning. In logic, categorical propositions are used to form syllogisms, which are arguments that draw conclusions based on two premises. For example, if "All mammals are warm-blooded" and "All dogs are mammals," one can conclude that "All dogs are warm-blooded." This structure is essential in fields like philosophy, mathematics, and computer science.