First-order logic is a formal system used in mathematics, philosophy, and computer science to express statements about objects and their relationships. It extends propositional logic by incorporating quantifiers, such as "for all" (∀) and "there exists" (∃), allowing for more complex expressions. This enables the representation of general statements and the ability to reason about properties of objects. In first-order logic, statements are made up of predicates, which describe properties or relations, and terms, which refer to objects. For example, a statement like "All humans are mortal" can be expressed using first-order logic, making it a powerful tool for formal reasoning and knowledge representation in fields like artificial intelligence and mathematical logic.