Implicative-orthomodular lattices
Abstract
Based on implicative involutive BE algebras, we redefine the orthomodular lattices, by introducing the notion of implicative-orthomodular lattices, and we study their properties. We characterize these algebras, proving that the implicative-orthomodular lattices are quantum-Wajsberg algebras. We also define and characterize the implicative-modular algebras as a subclass of implicative-orthomodular lattices. The orthomodular softlattices and orthomodular widelattices are also redefined, by introducing the notions of implicative-orthomodular softlattices and implicative-orthomodular widelattices. Finally, we prove that the implicative-orthomodular softlattices are equivalent to implicative-orthomodular lattices and that the implicative-orthomodular widelattices are special cases of quantum-Wajsberg algebras.
Cite
@article{arxiv.2401.12845,
title = {Implicative-orthomodular lattices},
author = {Lavinia Corina Ciungu},
journal= {arXiv preprint arXiv:2401.12845},
year = {2024}
}
Comments
arXiv admin note: text overlap with arXiv:2401.04140