Propositional formula

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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.