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 formation of well-formed formulas (WFFs) of the language of propositional logic $\LL_0$.


 * Let $\PP_0$ be the vocabulary of $\LL_0$.
 * Let $\mathrm {Op} = \set {\land, \lor, \implies, \iff}$.

The rules are:

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