Abstract
We show that if the structural rules are admissible over a set \(\mathcal{R}\) of atomic rules, then they are admissible in the sequent calculus obtained by adding the rules in \(\mathcal{R}\) to the multisuccedent minimal and intuitionistic \(\mathbf{G3}\) calculi as well as to the classical one. Two applications to pure logic and to the sequent calculus with equality are presented.
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The authors are very grateful to the referee for helpful comments and suggestions.
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Work partially supported by funds PRIN-MIUR of Italy, Grant “Logica, Modelli, Insiemi” and the department PRID funding HiWei and presented to LC2018 (Udine).
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Parlamento, F., Previale, F. Absorbing the structural rules in the sequent calculus with additional atomic rules. Arch. Math. Logic 59, 389–408 (2020). https://doi.org/10.1007/s00153-019-00696-5
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DOI: https://doi.org/10.1007/s00153-019-00696-5