A categorical statement is a type of assertion that expresses a relationship between two categories or classes. It typically takes the form of a subject and a predicate, indicating whether all, some, or none of the members of one category belong to another. For example, the statement "All dogs are mammals" is a categorical statement that asserts a relationship between the categories of dogs and mammals. These statements are fundamental in logic and reasoning, as they help in forming valid arguments and conclusions. Categorical statements can be classified into four types: universal affirmative, universal negative, particular affirmative, and particular negative. Understanding these types is essential for analyzing logical structures in various fields, including philosophy and mathematics.