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Propositional formula is a well-formed expression of propositional logic. What counts as a propositional formula is defined by the syntax of propositional logic:
(i) a propositional letters in the vocabulary of L are formulas in L b if psi is a formula of L, Neg psi is too c if phi and psi are formulas in L, (phi & psi), (phi V psi), (phi -> psi) and (phi <-> psi) are too d only that which can be generated by the clauses (a)-(c) in a finite number of steps is a formula in L.
The clauses (a)-(c) define what counts as a formula; clause (d) states that nothing else can be a formula of L.
- Gamut, L.T.F. 1991. Logic, language, and meaning, Univ. of Chicago Press, Chicago.