Definition:Language of Propositional Logic/Formal Grammar/Backus-Naur Form

Definition
Part of specifying the language of propositional logic is to provide its formal grammar. In Backus-Naur form, the formal grammar of the language of propositional logic takes the following form:

Note that this is a top-down grammar: we start with a metasymbol   and progressively replace it with constructs containing other metasymbols and/or primitive symbols, until finally we are left with a well-formed formula of $\mathcal L_0$ consisting of nothing but primitive symbols.