Definition:Language of Propositional Logic/Formal Grammar/Bottom-Up Specification

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 propositional logic $\mathcal L_0$.


 * Let $\mathcal P_0$ be the vocabulary of $\mathcal L_0$.
 * Let $Op = \left\{{\land, \lor, \implies, \iff}\right\}$.

The rules are:

Any string which can not be created by means of the above rules is not a WFF.