New generalizations of BCI, BCK and Hilbert algebras

TL;DR

This paper introduces numerous new generalizations of BCI, BCK, and Hilbert algebras, establishing hierarchies and providing examples to expand the algebraic framework in logic.

Contribution

It presents 31 new generalizations of BCI and BCK algebras and 20 of Hilbert algebras, along with the hierarchy relations among all these algebraic structures.

Findings

Established hierarchies among old and new algebraic structures

Provided proper examples for each new generalization

Significantly expanded the algebraic landscape in logic

Abstract

We introduce more generalizations of BCI, BCK and of Hilbert algebras, with proper examples, and show the hierarchies existing between all these algebras, old and new ones. Namely, we found thirty one new generalizations of BCI and BCK algebras and twenty generalizations of Hilbert algebras.