 The vocabulary of quantified propositional logic contains propositional letters \(p\), \(q\), \(r\), \(p_1\), … and propositional connectives \(\neg, \rightarrow, \wedge, \vee, \leftrightarrow\). We may as usual treat \(\neg\) and \(\rightarrow\) as primitive and take the others as defined. The usual recursive definition of a formula for propositional logic is appropriately supplemented with a clause that states that \(\forall p A\) is a formula whenever \(A\) is a formula.