English

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