在逻辑和数学中，二阶逻辑是一阶逻辑的扩展，一阶逻辑是命题逻辑的扩展。二阶逻辑接着被高阶逻辑和类型论所扩展。

一阶逻辑和二阶逻辑都使用了论域（有时叫做“域”或“全集”）的想法。论域是可以在其上量化的个体元素的集合。一阶逻辑只包括取值为论域的个体元素的变量和量词。例如在一阶句子∀x(x ≠ x + 1)中变量x被用来表示一个任意的个体。二阶逻辑扩展了一阶逻辑，通过增加取值在个体的集合上变量和量词。例如，二阶句子声称对于所有个体的集合S和所有的个体x，要幺x在S中要幺不在（这是二值原理）。最一般的二阶逻辑还包括量化在函数上的变量，和在下面语法章节解说的变量。

In logic and mathematics second-order logic is an extension of first-order logic, which itself is an extension of propositional logic. Second-order logic is in turn extended by higher-order logic and type theory.

First-order logic quantifies only variables that range over individuals (elements of the domain of discourse); second-order logic, in addition, also quantifies over relations. For example, the second-order sentence says that for every unary relation (or set) P of individuals, and every individual x, either x is in P or it is not (this is the principle of bivalence). Second-order logic also includes quantification over functions, and other variables as explained in the section Syntax and fragments below. Both first-order and second-order logic use the idea of a domain of discourse (often called simply the "domain" or the "universe"). The domain is a set over which individual elements may be quantified.