开放句子是「在用特定的数，替代其中的变量的时候，将使得结果的表达式被求值为真的一个句子」。

数学家没有接受这种术语，而是称之为带有自由变量的方程序或不等式等。

这种替代也叫做对句子的解。恒等式是所有数都是解的开放句子。

开放句子的例子包括：

所有开放句子都必须（通常暗含的）有描述那些数可被当作解的论域。例如，你可以考虑所有实数或只是整数。例如，在例子2中，1.6是一个解，如果论域是所有实数，如果论域只是整数则不是。在这种情况下，只有大于3/2的整数是解：2, 3, 4等等。在另一方面，如果论域由所有复数构成，则例子2甚至没有意义（尽管其他例子有）。恒等式只要求对在它的论域中的数成立。

In mathematics, an open sentence is described as "open" in the sense that its truth value is meaningless until its variables are replaced with specific numbers, at which point the truth value can usually be determined (and hence the sentences are no longer regarded as "open"). These possible replacement values are assumed to range over a subset of either the real or complex numbers, depending on the equation or inequality under consideration (in applications, real numbers are usually associated also with measurement units). The replacement values which produce a true equation or inequality are called solutions of the equation or inequality, and are said to "satisfy" it.