Abstract
A normalizable natural deduction formulation, with subformula property, of the implicative fragment of classical logic is presented. A traditional notion of normal deduction is adapted and the corresponding weak normalization theorem is proved. An embedding of the classical logic into the intuitionistic logic, restricted on propositional implicational language, is described as well. We believe that this multiple-conclusion approach places the classical logic in the same plane with the intuitionistic logic, from the proof-theoretical viewpoint.
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Boričić, B., Ilić, M. An Alternative Normalization of the Implicative Fragment of Classical Logic. Stud Logica 103, 413–446 (2015). https://doi.org/10.1007/s11225-014-9573-0
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DOI: https://doi.org/10.1007/s11225-014-9573-0