Substructural Implicational Logics Including the Relevant Logic E

Authors: Kashima, Ryo¹; Kamide, Norihiro²

Source: Studia Logica, Volume 63, Number 2, September 1999 , pp. 181-212(32)

Publisher: Springer

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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.

Keywords: substructural logic; relevant logic; cut-elimination

Document Type: Research article

DOI: http://dx.doi.org/10.1023/A:1005210613711

Affiliations: 1: Email: kashima@is.titech.ac.jp 2: Email: kamide@jaist.ac.jp

Publication date: 1999-09-01