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Published online by Cambridge University Press: 21 January 2025
1 The result goes back to Meyer’s E and S4, Notre Dame Journal of Formal Logic, vol. 11 (1970), pp. 181–199.
2 For such a calculus, see Brady, Natural Deduction Systems for Some Quantified Relevant Logics, Logique et Analyse, vol. 27 (1984), pp. 355–277, in which a logic
$RF$
is outfitted with such a calculus.
$RF$
proves every logical theorem of classical logic as recognized in Brady, Rules in Relevant Logic—II: Formula Representation, Studia Logica, vol. 52 (1993), pp. 565–585.