What is "algebraic logic"

In mathematical logic, algebraic logic is the reasoning obtained by manipulating equations with free variables.

What is now usually called classical algebraic logic focuses on the identification and algebraic description of models appropriate for the study of various logics (in the form of classes of algebras that constitute the algebraic semantics for these deductive systems) and connected problems like representation and duality. Well known results like the representation theorem for Boolean algebras and Stone duality fall under the umbrella of classical algebraic logic.

Works in the more recent abstract algebraic logic (AAL) focus on the process of algebraization itself, like classifying various forms of algebraizability using the Leibniz operator.