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arXiv · 2303.16481

Quantum-Wajsberg algebras

Lavinia Corina Ciungu
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Abstract

Starting from involutive BE algebras, we redefine the quantum-MV algebras, by introducing and studying the notion of quantum-Wajsberg algebras. We define the $\vee$-commutative quantum-Wajsberg algebras and we investigate their properties. We also prove that any Wajsberg algebra is a quantum-Wajsberg algebra, and give conditions for quantum-Wajsberg algebras to be Wajsberg algebras. Furthermore, we prove that Wajsberg algebras are both quantum-Wajsberg algebras and commutative quantum-B algebras. Finally, we provide certain conditions for quantum-MV algebras to be MV algebras.

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Lavinia Corina Ciungu. 2023-03-29. Quantum-Wajsberg algebras. https://arxiv.org/abs/2303.16481

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