Centers of quantum-Wajsberg algebras
Logic
2024-08-06 v2
Abstract
We define the Wajsberg-center and the OML-center of a quantum-Wajsberg algebra, and study their structures. We prove that the Wajsberg-center is a Wajsberg subalgebra of a quantum-Wajsberg algebra, and that it is a distributive sublattice of its corresponding poset. If the quantum-Wajsberg algebra is quasi-linear, we show that the Wajsberg-center is a linearly ordered Wajsberg algebra. We also show that the lattice subreduct of the Wajsberg-center is a Kleene algebra. Furthermore, we prove that the OML-center is an orthomodular lattice, and the orthomodular lattices form a subvariety of the variety of quantum-Wajsberg algebras.
Keywords
Cite
@article{arxiv.2311.02483,
title = {Centers of quantum-Wajsberg algebras},
author = {Lavinia Corina Ciungu},
journal= {arXiv preprint arXiv:2311.02483},
year = {2024}
}
Comments
arXiv admin note: text overlap with arXiv:2303.16481