Substructural implicational logics including the relevant logic E

Studia Logica 63 (2):181-212 (1999)
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Abstract

We introduce several restricted versions of the structural rules in the implicational fragment of Gentzen's sequent calculus LJ. For example, we permit the applications of a structural rule only if its principal formula is an implication. We investigate cut-eliminability and theorem-equivalence among various combinations of them. The results include new cut-elimination theorems for the implicational fragments of the following logics: relevant logic E, strict implication S4, and their neighbors (e.g., E-W and S4-W); BCI-logic, BCK-logic, relevant logic R, and the intuitionistic logic.

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Citations of this work

Trees for E.Shawn Standefer - 2018 - Logic Journal of the IGPL 26 (3):300-315.
Substructural logics with Mingle.Norihiro Kamide - 2002 - Journal of Logic, Language and Information 11 (2):227-249.

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