Kites and Pseudo BL-algebras

TL;DR

This paper introduces a new construction called a kite for pseudo BL-algebras derived from $ ext{l}$-groups, unifies various fuzzy logic algebras, and explores their structural properties and variety classifications.

Contribution

It presents the kite construction for pseudo BL-algebras, connects it to known fuzzy logic algebras, and identifies new varieties including a countably infinite family.

Findings

Many fuzzy logic related algebras can be constructed as kites.

Subdirectly irreducible kites are characterized.

A new infinite family of pseudo BL-algebra varieties is described.

Abstract

We investigate a construction of a pseudo BL-algebra out of an $\ell$-group called a kite. We show that many well-known examples of algebras related to fuzzy logics can be obtained in that way. We describe subdirectly irreducible kites. As another application, we exhibit a new countably infinite family of varieties of pseudo BL-algebras covering the variety of Boolean algebras.