Definition:Language of Predicate Logic/Formal Grammar

Definition
Part of specifying the language of propositional logic is to provide its formal grammar.  The following rules of formation constitute a bottom-up grammar for the language of predicate logic $\mathcal L_1$.

The definition proceeds in two steps.

First, we will define terms, and then well-formed formulas.

Well-Formed Formulas
The WFFs of $\mathcal L_1$ are defined by the following bottom-up grammar: