Abstract
We provide a finite axiomatization of the consequence ⊢∧∪⊢∨, i.e. of the set of common sequential rules for ∧ and ∨. Moreover, we show that ⊢∧∪⊢∨ has no proper non-trivial strengthenings other than ⊢∧ and ⊢∨. A similar result is true for ⊢↔∪⊢→, but not, e.g., for ⊢↔∪⊢+.
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To the memory of Jerzy Słupecki
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Rautenberg, W. A calculus for the common rules of ∧ and ∨. Studia Logica 48, 531–537 (1989). https://doi.org/10.1007/BF00370205
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DOI: https://doi.org/10.1007/BF00370205