Judgment assertion judgment form judgment form instances

A Judgment form is a relation, interpreted as a Predicate.

Typically written as $-J$ (for unary relation).

Take the judgment form above, the notation $aJ$, for some value $a$, is an instance of the judgment form.

Take the judgment form instance above, $a$ is the judgment form instance’s subject.

A judgment/assertion is a stance on whether an instance of the judgment holds or not.