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.
Similar content being viewed by others
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kashima, R., Kamide, N. Substructural Implicational Logics Including the Relevant Logic E. Studia Logica 63, 181–212 (1999). https://doi.org/10.1023/A:1005210613711
Issue Date:
DOI: https://doi.org/10.1023/A:1005210613711