"God made first-order logic and all the rest is the handiwork of man."

There are a few other reasons to restrict study of first-order logic to normal models.

Some variables correspond to elements of the domain, as in first-order logic.

Given a closed formula of first-order logic, first do the following:

Let be a formula in the language of first-order logic.

Typically, however, a translation is given from these languages to answer set programming rather than first-order logic.

In the context of first-order logic, a signature is sometimes called a language.

There are several different conventions for using equality (or identity) in first-order logic.

Ordinary or first-order logic has two types of terms, respectively assertions and data.

Neither of these principles can be expressed in first-order logic.