Judgment assertion judgment form judgment form instance s

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

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

Take the judgment form above, the notation $a\ J$, 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.