BCI-Algebras and Related Logics

Kabzinski in [6] first introduced an extension of BCI-logic that is isomorphic to BCI-algebras. Kashima and Komori in [7] gave a Gentzen-style sequent calculus version of this logic as well as another sequent calculus which they proved to be equivalent. They used the second to prove decidability of the word problem for BCI-algebras. The decidability proof relies on cut elimination for the second system, this paper provides a fuller and simpler proof of this. Also supplied is a new decidability proof and proof finding algorithm for their second extension of BCI-logic and so for BCI-algebras

A note on monothetic BCI

In "Variations on a theme of Curry," Humberstone conjectured that a certain logic, intermediate between BCI and BCK, is none other than monothetic BCI-the smallest extension of BCI in which all theorems are provably equivalent. In this note, we present