Generalizations of quantum-Wajsberg algebras
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929426760990720 |
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| author | Ciungu, Lavinia Corina |
| author_facet | Ciungu, Lavinia Corina |
| contents | Starting from involutive BE algebras, we redefine the pre-MV and meta-MV algebras, by introducing the notion of pre-Wajsberg and meta-Wajsberg algebras, as generalizations of quantum-Wajsberg algebras. We characterize these algebras, we show that any pre-Wajsberg algebra is a meta-Wajsberg algebra, and we prove that an implicative-orthomodular algebra is a quantum-Wajsberg algebra if and only if it is a meta-Wajsberg algebra. It is shown that the commutative quantum-Wajsberg (implicative-orthomodular, pre-Wajsberg, meta-Wajsberg) algebras coincide with the Wajsberg algebras. We give conditions for the implicative-orthomodular, pre-Wajsberg and meta-Wajsberg algebras to be Wajsberg algebras. The commutative center of an implicative-orthomodular algebra is defined and studied, and it is proved that it is a Wajsberg subalgebra of the implicative-orthomodular algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_04140 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalizations of quantum-Wajsberg algebras Ciungu, Lavinia Corina Logic Starting from involutive BE algebras, we redefine the pre-MV and meta-MV algebras, by introducing the notion of pre-Wajsberg and meta-Wajsberg algebras, as generalizations of quantum-Wajsberg algebras. We characterize these algebras, we show that any pre-Wajsberg algebra is a meta-Wajsberg algebra, and we prove that an implicative-orthomodular algebra is a quantum-Wajsberg algebra if and only if it is a meta-Wajsberg algebra. It is shown that the commutative quantum-Wajsberg (implicative-orthomodular, pre-Wajsberg, meta-Wajsberg) algebras coincide with the Wajsberg algebras. We give conditions for the implicative-orthomodular, pre-Wajsberg and meta-Wajsberg algebras to be Wajsberg algebras. The commutative center of an implicative-orthomodular algebra is defined and studied, and it is proved that it is a Wajsberg subalgebra of the implicative-orthomodular algebra. |
| title | Generalizations of quantum-Wajsberg algebras |
| topic | Logic |
| url | https://arxiv.org/abs/2401.04140 |