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  1. Replacement in Logic.Lloyd Humberstone - 2013 - Journal of Philosophical Logic 42 (1):49-89.
    We study a range of issues connected with the idea of replacing one formula by another in a fixed context. The replacement core of a consequence relation ⊢ is the relation holding between a set of formulas {A1,..., Am,...} and a formula B when for every context C, we have C,..., C,... ⊢ C. Section 1 looks at some differences between which inferences are lost on passing to the replacement cores of the classical and intuitionistic consequence relations. For example, we (...)
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  • An Abelian Rule for BCI—and Variations.Tomasz Kowalski & Lloyd Humberstone - 2016 - Notre Dame Journal of Formal Logic 57 (4):551-568.
    We show the admissibility for BCI of a rule form of the characteristic implicational axiom of abelian logic, this rule taking us from →β to α. This is done in Section 8, with surrounding sections exploring the admissibility and derivability of various related rules in several extensions of BCI.
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  • BCK is not Structurally Complete.Tomasz Kowalski - 2014 - Notre Dame Journal of Formal Logic 55 (2):197-204.
    We exhibit a simple inference rule, which is admissible but not derivable in BCK, proving that BCK is not structurally complete. The argument is proof-theoretical.
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