Quantificational logic is a branch of logic that extends propositional logic by incorporating quantifiers, which allow for the expression of statements about some or all members of a domain. The two primary quantifiers are the universal quantifier, often represented as ∀, which indicates that a statement applies to all elements, and the existential quantifier, represented as ∃, which indicates that there is at least one element for which the statement holds true. This type of logic is essential in various fields, including mathematics, computer science, and philosophy, as it provides a formal framework for reasoning about properties and relationships within a set. By using quantificational logic, one can construct more complex arguments and analyze the validity of statements involving variables and their relationships to one another.